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Donald Hoffman Λ Joscha Bach on Consciousness, Free Will, Gödel, and Computational Reality
February 7, 2022
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
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This is an episode that's been almost one year in the making, the theolocution of Donald Hoffman and Yoshabok, both of whom should be extremely familiar to you if you've surveyed this channel before, as we've done an unduly technical dive into Donald Hoffman's research papers, and we've spoken to Yoshabok several times before as well.
If you're unfamiliar, Donald Hoffman is a professor at the University of Irvine, California, studying consciousness and evolutionary psychology using mathematical models, and Yoshua Bach is a cognitive scientist recognized in the field of AI as being exceptionally ingenious. Both have unexampled views of consciousness and free will, which harmonize and contradict
in prepossessing and informative ways. Click on the timestamp in the description if you'd like to skip this intro. My name is Kirchheim Angle. I'm a Torontonian filmmaker with a background in mathematical physics dedicated to the explication of the variegated terrain of theories of everything from a theoretical physics perspective, but as well as analyzing consciousness and seeing its potential connection to fundamental reality, whatever that is.
Essentially, this channel is dedicated to exploring the underived nature of reality, the constitutional laws that govern it, provided those laws exist at all and are even knowable to us. If you enjoy witnessing and engaging with others on the topics of psychology, consciousness, physics, etc., the channel's themes,
then do consider going to the discord and the subreddit which are linked in the description there's also a link to the patreon that is patreon.com slash kirchheimungl if you'd like to support this podcast as the patrons and the sponsors are the only reasons that i'm able to have podcasts of this quality and this depth
Given that I can do this now full-time, thanks to both the patrons and the sponsors' support. Speaking of sponsors, there are two. The first sponsor is Brilliant. During the winter break, I decided to brush up on some of the fundamentals of physics, particularly with regard to information theory, as I'd like to interview Chiara Marletto on constructor theory, which is heavily based in information theory.
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okay this should be live if you can see this type in animaniacs into the chat animaniacs great there are already 275 people watching firstly it's a distinct honor to be here thank you both don and yosha i appreciate it tremendously and the audience does as well this theories of everything
Don, why don't we start with your definition of free will as well as how you view consciousness, and you mentioned that you would like to give an overview of your point of view on science and theories of everything in general.
And then Yocha, you'll join afterward and commend Donald or amend him. And then I'll pretty much shut my mouth and allow you both to speak to one another, interjecting only seldom. Okay, thank you, Kurt. And good to see you, Yocha. My attitude about science is sort of like what Newton famously said, right? He said toward the end of his career that he thought of himself as like,
a little boy playing on the seashore looking at some nice pebbles and shells while all before him lay the vast ocean of truth that was undiscovered. And I think that that's a good attitude for us as scientists to have is that as much as we've done
We've really not even begun to explore the possibilities of truth. And what's interesting is that Newton's followers famously didn't follow him on that. In the late 19th century, a lot of Newtonians thought that it was pretty much over. They had a theory of everything. There were a few little wrinkles. You know, there was the problem of Michelson-Morley experiment and
And black body radiation wasn't quite working out according to Newton, but they thought that that was pretty minor stuff and they would figure that all out. And physics was pretty much done. And we've discovered that no physics was hardly beginning. There was so much more to discover. And so my attitude is that science cannot have a theory of everything in principle.
that we will always be on Newton's seashore. We'll always be like Newton, the little boy playing with pebbles and shells while the vast truth lays undiscovered before us, the ocean of truth. And it's for a principled reason that scientific theories, if you look at how they're structured, we start with a good scientific theory tells you exactly what its assumptions are. This is what I'm assuming.
These are the derivation rules that I allow, and then everything about the theory follows from that. But that theory doesn't explain its assumptions. The assumptions are what's assumed. So Einstein, in his special theory of relativity, assumes that light travels at the same speed for all observers in all inertial reference frames. But that theory doesn't tell you what light is.
In fact, Einstein spent his whole life wondering what light is and toward the end of his life said, I've spent my whole life studying it and I still have no idea what light really is. And so we're in that situation as scientists where what we're doing is valuable. It's absolutely essential because we're being precise about our assumptions. We're being precise about what they entail. But there is going to be a fundamental limit. And my guess is that science
As valuable as it is, it's one of the most important advances that humanity has made. We'll always and only scratch the surface beyond the seashore with Newton while the vast ocean lays undiscovered. So when we talk about theories of consciousness and free will and so forth going forward, I do it with sort of a very modest look at my own ideas. The ideas are going to be very much
In the framework of these are the best ideas we've come up with so far, of course, there's going to be much, much deeper work ahead and much more to discover ahead. So we just have to, as scientists, be precise about the current assumptions we're making and why we're making them and what follows from them, but be completely open to radical transformations in knowledge and radical new understandings. Your view on consciousness and free will.
So in a nutshell, my views on consciousness are not physicalist. So physicalist approaches will say that we will start with space time and some of its contents, particles, neurons, neural systems, neural networks.
Those will be, so that's a scientific theory in which those are our assumptions. Space-time and its contents are fundamental. And particular contents may be very, very important. For example, dynamical systems on neural networks, for example. And from that, we're going to try to boot up subjective experience. And that's perfectly a fine project to try to do. What I would want from that physicalist approach would be
not a hand wave but but a specific accomplishment so how do we start with dynamical systems of neural networks and come up with the taste of chocolate or the smell of garlic or something specific some specific conscious experience where we say my my scientific theory says why this
Dynamical system of activity in neurons or in computer system or something like that must be the taste of chocolate. It could not be the smell of garlic. And these are the principled reasons why. If something like that were on the table, I would be impressed. Until then, I'm not impressed. And there's nothing on the table yet that can do that. So that's one reason why I've been casting around and looking for a different direction. It's not starting with the physical
But starting somewhere else, and partly because, and we can talk about this in greater detail, because our best scientific theories right now, namely quantum field theory and general relativity on the one hand, and evolution of a natural selection on the other, both entail that space-time is not fundamental.
Our two or three premier scientific theories really tell us their limits. They tell us that space-time cannot be fundamental and that therefore the contents of space-time are not fundamental. And so if we're going to look for a theory of consciousness and we start with something inside space-time, we're already starting where our best scientific theories tell us it's not fundamental.
So as a result, I've been trying to then say, well, if space-time isn't fundamental and we don't yet know what's more fundamental, why don't we first start with trying to get a mathematical theory of consciousness on its own terms? What is consciousness? What kinds of assumptions can we make about it? And then we can ask the question, is consciousness more fundamental than space-time? What is the relationship between consciousness and space-time?
So I can go into some of the details if we want to on that model, but the big picture is that I'm taking very seriously that evolution of a natural selection entails that none of our sensory systems tell us the truths about objective reality, and that therefore space-time is not an objective truth, it's just a representation of fitness chaos, and that
Physicists are finding the same thing that Nima or Connie Hamed for example at Institute for Advanced Study at Princeton basically has lectures where he says space-time is doomed and here's why and The best physicists are now trying to figure out what's next space-time has had a good run for several centuries and it's over space-time is not fundamental and the contents of space-time are not fundamental and so we need to figure out and he's got things with you've working with Juan Maldacena on things like cosmological polytopes and
They're finding structures beyond space-time from which space-time can emerge as a projection, as a special case. But in these deeper theories, there is no time and there is no space. But there are symmetries that are true of, for example, scattering amplitude's data that are true that you can't see in space-time. They can predict the data, but they don't use space and time as the fundamental concepts. And I think that
As we start to go into scientific theories of consciousness, we cannot ignore what our physicist colleagues are telling us. They're telling us, if you're looking for something fundamental, it's not space-time, and in particular, it's not time. And that is a real show-stopper. It's for the physicists, too. I mean, trying to think outside of the time box is not easy for the physicists. And so what do we do if we don't have space-time, if we don't have
So I think that that's one of the interesting questions that we have to face. If we're going to come up with a theory of consciousness, what do we take as fundamental in our theory? If we take anything inside space-time, we're already sort of cutting ourselves off because we know that as physics progresses, things inside space-time will just be shown to be secondary. So we can go into my details on
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It's interesting that you start outing yourself as a Mysterionist in a way, right? Mysterionism being the position that human minds are basically not equipped to understand how they work or how the universe works that they are embedded in at a very deep level. And I sometimes joke that Mysterionism is the position that something cannot be understood if it cannot be understood by Noam Chomsky. Noam Chomsky is a Mysterionist with respect to the mind. At the Science of Consciousness conference, he once
gave a presentation where he talks about Descartes and then mentions that Descartes was actually a very smart fellow because he could already anticipate stuff that would only be discovered much, much later on. And I was perking up and wondering, my God, Chomsky is giving this guy credit. And it turned out what he anticipated was that we would later like Chomsky discover that the mind is unintelligible. Right, so this
It's fascinating, of course, if you are one of the smartest minds of your own generation and you see that other people don't understand things and that you understand. And there is a boundary where nobody seems to have an understanding and you crash against it. You might think, okay, maybe there is no way that humans can do it. Not convinced that this is the case. I'm not a mysterious at this point in my intellectual career. And that's part because I come from the other side.
So many of the things that people took as a given for a long time, like space and time, appeared to me in the beginning quite mysterious. So basically the dissolution of space and time was not that mysterious to me. Basically, I'm a computer scientist. I started very, very early on in my life to program before I properly understood mathematics and before I understood physics. And I understood how to make things in a computer.
and Einstein's watch that is taking away and you can observe its movements and so on, but you cannot open it and you can come up with theories what's happening inside. To me, this watch was the screen of a computer.
And I understood that there is no limit to what can be put into the computer if it has enough resources, right? So if the computer is fast enough and has enough memory, there is no pattern that cannot be shown on the screen. There is no limit to the sequence of patterns that is to be shown on the screen. So any observation that I am making, if I understand it as a pattern on some kind of screen that is visible to me, I will always be able to construct something, a mechanism that is on the other side and produces the sequence.
And now the question is, can I produce an elegant sequence? Can I produce a minimal pattern? Can I produce something from which I think it's plausible that it emerged by itself? And that is, to me, this big important question of physics. The idea of physicalism to me is the notion that we live in a reality that is fully emergent over a causally closed mechanical layer. And we are in that base reality that emerges from it.
And the alternatives to physicalism is that the space layer is somewhere else. Because even if we live in a simulation that is created by some kind of supernatural being, something must have created the supernatural being and its parent universe. Right. So ultimately every supernatural event is going to have some kind of natural course, some kind of prime mover that is taking away in the void and producing the patterns that you observe. And the patterns that you observe are so damn regular.
There is all this conservation going on of information that doesn't seem like a conspiracy to me. It seems that we're not in a simulation. It seems that the idea that consciousness could be primary to our reality is not true, because consciousness being primary means that you would have to live in somebody else's mind, that we live in some kind of conspirational simulation that somebody has set up for us.
Well, that is possible and I can principle not exclude it because there can be no evidence that can ever be fully conclusive if somebody sets it up to deceive me. There is no reason for me to believe it because they're not enough things happening in my reality that counteract the notion that I live in a mechanical universe. The few things that pop up, I can still explain this by faulty memories and psychosis.
So the only thing that needs to be explained, that was puzzling people like Turing and other thinkers, is there's a possibility that telepathy is true. If that would be true, it would not be compatible with the way in which we understand physics right now. And there's this question, is there a point at which we have to discard physics fully and accept that you live in some kind of simulation, in some kind of dream universe that somebody has set up, like a computer game where you can arbitrarily break causality when it's convenient?
Or is this something that we need to extend physics? Or is it just something where our minds are playing tricks with us? And we know our minds are playing lots of tricks with us. So Turing considered the possibility that telepathy exists as very real to the point where he included this in his 1950 paper, Computing Machinery and Intelligence, where he sketches out the Turing test and seriously asked what a Turing test would have to involve with such a system, the ability to be telepathic.
And if it's not, what difference would it make? Doesn't get to the point where you assess out loud that if telepathy is possible, you cannot be sure which of your thoughts and feelings originate in your own brain. They could come from somewhere else, right? So this opens up the door to lots and lots of things. But for the time being,
I think that the evidence for telepathy is weak. And if telepathy would exist, I would be seriously willing to consider this together. This is not clear by whether we cannot find a mechanical explanation for it. There's always going to be some kind of computer program that explains the patterns on the screen. Now, if we think about space, to me as a kid that was programming, the notion of a continuous space never made sense.
Because it's not computable. I cannot write something that is continuous space. And when I tried to wrap my mind around the mathematics, the language broke. I was not able to understand how to make a point that is infinitely small, yet fits together. If you add infinitely many of these points into a continuum, this doesn't work, right?
It's not a problem to make something that exactly looks like this. It's not a problem to make a computer game that looks continuous. It's not a computer game that produces physics that looks similar to what we can observe, at least in the simplification. Of course, our computers are extremely inefficient when it comes
to simulating the substrate layer, the quantum mechanics that we can observe or a layer below the quantum mechanics, because quantum mechanics is probably not the lowest layer in which physics plays out. It's just the lowest layer in which we can currently make observations that we can conceptualize. And this leads us to what you also mentioned, what is a photon? I don't think that Einstein started out with the assumption that the speed of light is fixed. I think it was a derivation that he made.
He concluded that the speed of light is fixed. And he basically, once he had this conclusion, he had implications for the possible descriptions of space-time that emerged. Because when the speed of light is fixed, you end up with some very interesting paradoxes if you stay in a Newtonian universe, right? You have this issue, imagine you fly in a very fast spaceship and you are lighting, putting light out of your flashlight inside of your spaceship.
wouldn't the speed of light necessarily add up to the speed of the spaceship to an external observer, right? So wouldn't this external observer not need to observe a different speed of light than the person traveling in a spaceship? And if the speed of light is constant always, it means that the thing that now has to change is time or space or both, right? You can still fix this if you make sure that the speed of time runs in a different way. And this leads us to the insight that
The time and space that we observe from our own perspective as emergent observer and whatever universe produces us are interdependent. They're not independent of each other. The speed of light depends on the trajectory that the speed of time depends on the trajectory that you are taking through the universe. And if you want to think about something that could be more fundamental, we would say that the photon is a carrier of the electromagnetic force. It's a type of boson, which means that
can be described as a certain pattern that has an integer spin, and it has the property that it is describing the potential value for measuring some electromagnetic interaction. So if we take space time from the perspective of the observer, it's the set of locations that can contain information and the set of trajectories that the information can take. And the photon is a model of information traveling through space time.
And what we have discovered and what Einstein also sometimes suspected is that space itself cannot be fundamental. And there were concrete reasons to see this, because what was discovered during Einstein's career even, and he was aware of this discovery, was that there were singularities in space-time.
which means points at where the mathematics of continuous space breaks down. So your mathematics doesn't work anymore. You have some kind of a division by zero, something unpleasant happens where your mathematics is no longer valid. And what Einstein saw is that he can fix this by shifting the singularities around in our spacetime model. And we can basically put them below the carpet. You can put them in centers of mass,
So in the center of mass, there is basically something like a little black hole where mathematics doesn't work anymore. The mathematics of space-time where your mathematical description of that world doesn't work anymore. And what could be more fundamental than space-time? I think it could be transitions. So you describe the universe as some kind of state vector, a set of information, and this information is dynamic. You have the way in which information moves between the locations. And in this paradigm, the speed of light,
could be the rate at which information propagates between locations. And this would be an upper limit of all interactions that you observe within this lattice, where stuff is densely connected. What would be necessary if you have a set of locations, some kind of graph, a causal graph and information flowing between them to understand that there is causal structure? Well, you need to understand where the information comes from to understand what it signifies so you can model it.
How can a single bit mean anything to you if it's just a single bit, if it's not attached with the source, with the type, with the context? So what could be a way to figure out where information comes from? Well, it needs to have some kind of momentum, some kind of direction to carry information about direction. And you send this to a graph that by itself just has just locations, connections. The only way that you can do this is if this thing is
extended if it's not just a single location to which the information propagates, but if it's neighboring connections and you get information that verifies it. So you need to be in some kind of densely strung lattice for information that you can pinpoint. Basically, you need to have something that looks like a continuous space. So you can identify controllable structure that you can identify where stuff comes from, like a photon.
And if there is information that is traveling across distance, so to speak, that is not local, that is not going through densely connected local connections, but that is going over individual long-range links, this information will look like a random fluctuation or a distant entanglement that you can no longer track if you don't know where it originated. And this will look like something like indeterminism from your local observer perspective.
Still, it would not be in contradiction to the preservation of information. It would still be a universe in which information is not invented, but in which the amount of discernible information is constant. And if the universe was not in such a way that information would be preserved, of course, it would not be learnable, because it would mean that the present state of the universe is forgetting what happened before in the universe. It gets disconnected. The world line of the universe just gets disconnected.
And so from an epistemological perspective, we can only learn the aspects of the universe that look like they are conserved. If there are things in the universe that are not conserved, then they will not be intelligible to us. And of course, it's conceivable that the universe is some kind of automaton that forgets information. Another thing that shows us that space-time cannot be fundamental besides
about theorem which destroys the notion of locality is the notion of the collapse of the wave function basically this collapse of the wave function is the point in the history of an observer beyond which we cannot obtain a model of locations of events in time and space right beyond that point it's no longer not just
that we don't have enough information to construct it, but it makes no sense anymore to assume that the photon was at a particular point when it went through the double slit. At this point, the space-time model breaks down. The space-time model is a mathematical abstraction that works relatively well to look at things happening in the limit, but it's not a model that can be fundamental, I think.
And but I'm not a physicist, so I'm not actually qualified to have these opinions. This is just what it looks like to me as a computer scientist who tries to understand the mind and things like Donald that we have to understand a certain degree of physics to make sure that our theories of consciousness are tight and that that makes sense. And we have to understand in which way they could possibly relate to physics.
I'm less convinced that a deep understanding of physics is necessary or that physics is going to teach us about consciousness, in part because I don't think that consciousness is that mysterious anymore. I spent a lot of time in my life thinking that it was mysterious, but it seems to be a riddle that can be solved. And basically, I think that there's some aspects to consciousness, for instance, that you're observing yourself to be observing, but consciousness is
Something that is entirely virtual. It's not a physical thing. Electrons, photons, physical entities, neurons, brains cannot be conscious. They're just mechanisms. And what we can see is that the elements of our consciousness are not mechanical. They're magical somehow. There is magic happening. And if there is magic happening, it means that it's an a causal structure. It's something that has been made on some kind of causal loom.
but that is not necessarily built in the same mechanical way as physics is built. It's a story. It's a, it's a tale being told by a physical system to itself. And if you think about organisms, you often think of them as physical systems and then neither, right? The organism doesn't exist. It's not the same if you think about it.
What exists are cells that interact with each other. And even the cells don't really exist. What exists are molecules. And even the molecules don't really exist, right? They're all layers of descriptions. They're models that we can make because they are coherent. They hold to some degree. It might be freshening out at the boundaries, but there are ways of thinking about the flow of information in the universe. And the organism is a coherent pattern that you observe in the interaction between cells.
And the cells have been set up by evolution to interact in this coherent pattern, because when they interact as if they were driven by a single spirit, by a single target, by a single telos, and if their behavior is coherent and consistent, that a state building, then they have an advantage over cells which don't do that and just fight for themselves, because together they can play longer games. By playing longer games, they can occupy a niche in nature that cannot be occupied by control systems that play shorter games.
This is the benefit that organisms have, these coordinations between cells. And an organism is a function that describes this pattern in the cells. And the organism is facilitated by information processing across cells, among other things. To coordinate its interactions, the organism needs to have something like a telegraph network by which it's able to make models of reality and coordinate them between the cells and coordinate the behavior of the cells.
And in animals, this telegraph system is facilitated in large part by the nervous system. It would not be necessary that the nervous system, basically every cell type can do this. But if you want to make it fast, you need to have specialized cells that have a very quick, expensive metabolism and can send information over very long distances very quickly, which other cell types cannot. So humans are a specific type of cells that allow particular kinds of information processing.
And this information processing has the property that it can put stuff on the screen. So it's some kind of computer. It's the thing that can produce arbitrary sequences of patterns if it discovers a suitable function to produce them and implement them in the distributed networks of cells. And part of what they're doing is that they create a story about a being that lives in the outside world.
And in our culture, we have difficulty understanding how that is because we, in our culture, as a default, teach our kids that what they see is the physical world, that the physical world has sounds and colors and so on. Only much later we tell them, well, it's slightly more complicated and sounds and color are not actually in physics. Everything that you consider to be sounds and colors is photons. Photons make electromagnetic interaction, which let air molecules push against each other so they can form regular waves.
And colors are local dimensions that you get by measuring sampling the frequency of the electromagnetic spectrum using different receptor types and making a model of them using polar coordinates. Right. So this is something that we don't tell the story fully to our children, which makes it even more confusing. And then we tell them photons are actually not little billiard balls, but there are regions in the space time that have a potential for an electromagnetic interaction.
And this space that you're talking about is the photonic space. It's the space where you can possibly have photon interactions. For some reason, it's three-dimensional. And maybe there are other spaces that are not three-dimensional. And maybe in these spaces, you cannot have interacting matter in the same way. Because maybe in order to get stable objects, you need to make little knots in the electromagnetic structure or in the spatial structure. And you cannot make knots in 2D and in 4D, they fall apart.
So maybe that's the reason, or maybe there's another one and we haven't completely figured it out yet. And there are some candidates that explained by the space that you're in is three-dimensional. So why is it that we are interacting with the photonic space and not with the others? Why are the others not seeming to form a connected space? And this is connected letters. But we don't know the answer yet. At least I'm not aware of the work that is sketching out the answer. And if I stumbled on it, I pray that I understand it.
But I think that there are other cultures that have a better intuitive understanding of what consciousness is. And if you look around, you find that some cultures don't find consciousness mysterious. I even suspect that in the core of our own culture, before the Tower of Babel that destroyed the shared understanding, it's still in there. So a little bit obsessed these days with thinking about
Genesis in the Bible and read this epistemologically correct, not as a myth that is a stand in for an origin theory until real science comes along, but as something that is literally true. So what would that mean? You know, I'm talking about the first book, I'm talking about the book that starts out with the creation of sky and darkness and heaven and earth and so on. And the thing with this story, if you take it literally the way in which Christianity interprets it,
It's a story about a supernatural being creating a physical universe. And what's wrong with the story is that whoever tells it to you had no evidence that it was true. So there is no claim. If somebody makes a claim without evidence, you don't have to listen. It could be interesting as a story for cultural reference, or it could be interesting as an idea for something that you could test. But if it's in principle not testable, this person cannot have that evidence.
There is no secret source of knowledge that this person had. There is, in principle, nothing that some other person can have with some kind of backchannel by talking to a burning bush that would constitute a valid experiment. So this reading makes no sense. It would never make any sense, but it could make sense, especially if you understand that sky and ground and light and sound and plants and animals and their names don't actually exist in physics.
They only exist in our mind as a division of the universe into separate objects, so they become intelligible to us. And the way in which we construct these objects is inside of the mind. So the creation of the universe that is being described in Genesis is not the physicalist universe with quantum mechanics. It's the creation of the experiential universe in which we are actually in, in which we find ourselves to be in. And the first thing that the mind is discovering when it creates this universe is how to make light.
How to create neural oscillators that are creating a contrast between light and darkness. So separate the light from the darkness and then organize this into multiple dimensions until you get a space. And then you align the space with the information from your vestibular organs and what you get is the two-dimensional plane of the ground and the three-dimensional space of the sky above it. So after you create light and darkness, you create
Literally every mind does this in their cognitive development, the sky and the ground. And then you discover the objects in it. So you basically learn how to model materials in your mind. So you have solids, and you have liquids, and you have organic shapes, and you have animated agents. And then you discover features that you cannot interact with, like celestial bodies, and anchor them in the world, and you learn how to navigate this world.
And then you discover all the plants and the animals and you construct them in your mind and you associate them all with their names. Again, of course, not a feature of the physical world. They are socially exchanged, these names and so on. We create this world together. And then last but not least, we create a person. So the thing that creates it is not a person yet. It's a mind that exists before a person is around. We don't remember how we made light. We don't remember
how we discovered the sky and the ground in the first space. This was another observing agent in our own brain. And this observing agent in our own brain at some point discovers the needs of a person, of the needs of an organism, the organism that its brain is embedded in. And it creates a model of that too. So it creates an agent that is observing this universe, that is embedded in this universe, because this first observer in our own mind,
is discovering that such an entity exists. It's a useful model to describe reality, that there is a person that has needs and desires and social embedding and dreams and hopes and memories and expectations. And it will create a story of that. And that story is just as real as the trees that exist in our mind as imaginations or the trees or that in the forest and beyond the horizon.
and as real as the sky and the clouds and the colors and so on. But they're all virtual. They're all simulacra. They all exist to tell a story to the organism that is useful for the organism to model the world. And this part where we become a person seems to be happening, I think, around the age of one and a half to two and a half, roughly, in most children that I observed. And at this point, a person that is different from before emerges in their mind. It's not that there is nobody there before. It's just that the thing before is different.
You notice that there's a gap in their memories. They have memories when they're in the first year when you talk to them, where they remember what happened and have expectations already. But later on, there's this point where they don't remember these things anymore. It's very weird. And most people, when they think back, don't have memories that they can consciously access before they're like two and a half years old.
And so I wonder if this transition is the result of just a re-indexing of memories due to our newfound linguistic ability, so we can later on no longer access these memories, or if it's really just basically a new agent that is created by the first agent in its own image as an observer that is aware of the fact that it's observing. But in a different way, as men and women, as something that thinks it's a person, that thinks it's a human being.
And I'm not a human being. I realized it at some level. I don't have an identity as a human being. This is a story that my mind tells itself as an additional thing. My consciousness doesn't have an identity. My consciousness is also not of the nature that it's the same as everybody else's consciousness, right?
The question, do we all have the same consciousness looking through different eyes or we separate consciousnesses is in some sense as meaningless as the question of asking is the text editor that you're running onto your computer, the same text editor that everybody else runs on the computer, or is it a different one.
The program vert is in some sense a natural law. If you put the circuits of your computer in the same functional configuration, then those things are going to happen with the circuits of your computer and they will afford the following interactions. But the program vert doesn't have an identity and it's also not that it has no identity in the sense, it's just not a meaningful category to apply to it. In the same sense, my consciousness is not in this category that would have an identity or none.
So it's not something that is shared with others, and it's not something that is separate from others. It's a principle that applies to the observation. And when the consciousness gets tied to a self model, then it becomes perspectival and I have an identity and so on. But this identity is a particular kind of model that my organism tells itself by changing certain factors in my own brain.
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the physical world and computation and the finiteness versus continuity of space-time and so forth. I think that the work, you know, the Gödel's incompleteness theorem is very relevant here, that the notion of truth is far deeper than the notion of proof. There are any system
Any computational system will have things that it can prove, but there will be truths that that computational system cannot access. And if you add those new truths, add a new truth of, you know, a girdle statement to your set of axioms, then there will be yet more truths that cannot be accessed from that. And so what you can compute is always going to be trivial to what is true.
There will always be, as far as I can tell, again, it's sort of like Newton's notion of we're at the seashore and the vast ocean of reality, of the truths. He actually used the word truth. The vast ocean of truths is out there beyond what we can compute. And every truth that you add to your base for computation doesn't solve the problem.
And you might say, well, that's true of abstract mathematics, but that's not true of physics. I mean, physics itself is computable. But there's some recent work suggesting that that's not the case. So Tony Kubit, a physicist, and his colleagues have recently proved that a very important problem to condensed matter physicists
called the spectral gap problem is not computable. And that's a stunning result. And they also suspect, and they're working on this, they haven't proven this yet, but that something that's a big open problem, I think the Millennium Prize committee has is this is one of their problems is to understand the Yang-Mills gas gap problem, which is, you know, why do
Photons and gravitons have no mass, but the carriers of the strong-weak force do have mass. And Kubit and his collaborators think, again, that we're going to find that something non-computational is going on here. It's not decidable. And my guess is that this is just the beginning, that we're going to find that as powerful as computation is, and I
I was in the artificial intelligence lab at MIT for my PhD and I'm all for AI and for computation and I, you know, I think it's fabulous what computation can do and the naysayers who think that the computation can't do amazing things and artificial intelligence can have, you know, important limits that I think that I disagree with the naysayers. On the other hand, I do believe Gödel's incompleteness theorem is correct and I do think that
The notion of truth is just vastly, the notion, the set of truths, I'll put it this way, the set of things that we can prove from any system is essentially probability zero in the set of all truths. In other words, we're always going to be, as Newton said, on the seashore with computation and is for principled reasons. So it's not a mysteriousism that's not founded, it's saying our best theories tell us
The truth and proof are not the same thing, and that proofs will always only leave you on the seashore. And so that's why, I mean, I didn't like that conclusion, but, you know, Gödel proved it, and now physicists are finding it in the spectral gap.
As much as I like computation, I'm a computer scientist myself, as much as I like computation, I have to defer to the mathematical proofs that say computation goes thus far and no further. Then ask myself, okay, how can, so my conceptual system then is itself just a symbolic system with derivation rules. So what I can compute by my thought,
is also going to be limited, which is why I was saying upfront what I think about scientific theories, right? Scientific theories are going to have these limitations. We will put down a set of axioms. Each theory, a good scientific theory, will tell you exactly what it assumes. And it will also give you a hint about the kind of derivations that you can give from those assumptions. And then you use, you find what that theory will entail. But our best theories, like
quantum theory and relativity and evolution with natural selection. The best theories will also tell you where they stop. They will say we go this far and no further. And for example, physics tells us that space time itself cannot be fundamental, that the very notion of space time cannot be fundamental, which is stunning because physics for several centuries has essentially been the study of what happens in space and time.
And so to say that space-time is not fundamental means that the physicists have to redefine what physics is about. And that's what, for example, Juan Maldacena and Neymar Condejamed are trying to do with things like the cosmological polytope and amplituhedron and so forth. They're finding structures where there are no Hilbert spaces. So there's no quantum theory. There is no time. There is no space. There are these positive geometries. And what you find is you can predict
events in space time like scattering processes that you see at the Large Hadron Collider, you can predict them and in fact you can actually compute them in some sense better than if you assume space time. So they're finding that if you use Feynman diagrams and try to compute
Scattering amplitudes for two gluons coming in and four gluons scattering out using the standard quantum field theoretic approaches where space and time is assumed. You get hundreds of pages of algebra and it's a mess. Whereas if you let go of space-time and look at these structures with symmetries that cannot be expressed in space-time, dual conformal symmetry
Then you find that the same scattering amplitudes can be processed in just two or three terms that you can write down pen and paper on a sheet of paper. So all of a sudden, so what they're seeing is space-time has had a good run, but
If you force yourself to stick with space-time, then the math is ugly. You get hundreds of pages of algebra to compute scattering amplitudes. You can't see the symmetries that are there, like dual conformal symmetry. If you let go of space-time, you're finding these amazing structures that they don't know what they're about, but all of a sudden you see the right symmetries and the computations become trivial. So there's some big hint that I think on a couple fronts, from Gödel
And from the work by Tony Kubit and his team that the computation is as powerful as it is, and as much as I love it as an AI person and a cognitive scientist, it's always going to be on the seashore with Newton. And when we let go of space time, we're still, of course, as theorists, always going to have
A finite set of axioms and derivations about the cosmological polytope and so forth that Neema and Juan are finding. We're still going to have a finite set of concepts and derivations, so we're not going to get around Gödel's incompleteness theorem, but at least we're going beyond the notion of time, which is really critical.
And that also cuts at the computational issues pretty interesting computational complexity is is about a lot of it about time complexity and what physicists are telling us is that ultimately we're gonna have to let go of the notion of time and so as computer scientists we're gonna have to rethink complexity issues when the very notion of time itself isn't fundamental.
So that's going to be a real kicker for us in computer science. How do we think about complexity issues when time itself is not the right way to think about things? And therefore, the sequence of computations in time is not the right way to think about things. We have some really deep thinking to do ahead. But where I think we share some common ground, Yosh, is I think a lot of
Our experiences and so forth are models that we build. I think that we are building internal models. But the question is, what is the apparatus that's building those models? And I'm saying it's nothing inside space and time. So in particular, I'll be very, very explicit. I don't think that neurons exist when they're not perceived. I don't think space time exists when it's not perceived.
I think neurons and space-time and even particles are simply data structures that we use. And there is a formulation of quantum theory that's very similar to this. It's called cubism, quantum Bayesianism, Chris Fuchs and David Merman, where they take this point of view that it's the every act of observation
In physics, every experiment that you do is an act of fact creation, right? That it's not that there are pre-existing particles with pre-existing states and you're measuring those states. Rather, they're subjective basions. So all the probabilities in quantum theory are subjective probabilities. They're not objective probabilities. And every outcome is a
a fact creation. And they do have, I mean, Chris Pukes has a very interesting 2010 paper called Cubism that I highly recommend. And in that paper, he actually points to a very interesting quantum discovery that there's a sequence of, what's proven is that even if you know what the outcome of your experiment is going to be with probability one,
That does not entail that the outcome is there and exists independent of your observation. That's a stunning thing to say. You know with probability one what you're going to measure, and yet you can prove with quantum mechanics that it's impossible that the outcome was there, the value existed before you made the measurement. So it's really the case that the acts of observation are fact creations, not fact discoveries.
So most of the work that's done in consciousness assumes, and I would say this is 99% of the theories that I've seen in consciousness, assume that space-time is fundamental, assume that physical particles are fundamental, and that somehow neural activity in humans and perhaps other kinds of more complex activity in AIs creates consciousness.
But the very founding assumptions that space-time is fundamental, that neurons exist when they're not perceived, contradicts our best physics. It also contradicts evolution of natural selection, which is very, very clear. Natural selection makes it very clear that the probability is zero, that the sensory systems of any organism tell them any truths about objective reality.
They tell what they tell organisms, sensory systems evolved to tell organisms how to behave in order to stay alive, period. That's it. And so that gives you a user interface for staying alive, but gives you no access to the truth. And that fits with what physics is telling us that space time is a user interface, but it's not the final truth. And so what I want from a theory of consciousness as a scientist
I want a clear statement of what am I assuming? What are the exact things that my theory takes as primitive? What are the exact rules that allow me to derive things from those primitives? And how exactly do I get the taste of chocolate from that? That's what I'm looking for from the theory of consciousness.
precise statement of exactly what i'm assuming upfront with mathematical precision and then precise derivation if i'm not taking the taste of chocolate as fundamental if i'm saying that somehow some dynamical system is going to give it to me that i want to know exactly which dynamical system is giving me the taste of chocolate and why that dynamical system could not be the smell of garlic i want to know exactly otherwise there's no there's no real science on the table
at all. So that's what I'm looking for is theories that say exactly what the assumptions are and tell me exactly for at least one specific conscious experience, how that conscious experience must be derived in that way. And so that's where I'm coming from on those. Now, in the case of cells in the brain, I would just mention something that's very interesting that you probably know about Mike Levin's work. Right. And he's finding that
that cells, not just neurons, but any cell in animals that in fact outside of the brain, they can learn and they can compute
and they can do morphogenesis of the cell's body. They use gap junction, communication, electric. So they're effectively doing what neurons do, but in a very, very different way. And this is all cells can communicate in this way with gap junctions and so forth. So I suspect that we're going to find that
Neurons aren't special in the sense of being information processors, that information processing, and this seems to be where Mike is heading, is that information processing is happening in what he calls these bioelectric fields, even if there are no neurons. And they can learn, they can retain memories, and they can be very intelligent. And so even as neuroscientists, we may find that we'll have to expand our horizons beyond neuroscience,
Understand if I were reductionist and trying to do biological reduction, I would at this point with Mike Levin stuff be interested to say, well, maybe I wouldn't necessarily reduce consciousness to neural activity. Maybe these gap junctions and the computations that cells can do would also be a suitable format. But again, I'm not a reductionist in that sense, but I'll stop unless you respond. Yes, sir.
Thank you. You went very far and wide and try to be a little bit more concise. Let's start out with Gödel. Gödel's proof had a very profound and not necessarily very positive influence on philosophy. And basically, Lukas and others in philosophy opened up a tradition where the underlying current is that what Gödel has shown is that mathematics is impotent to describe reality.
And therefore, reality can only be described by people who don't really know mathematics, that is philosophers. So philosophers like that intuition, but it implies that there is something beyond mathematics that allows you to make sense of things that assign truth. And slightly deeper, when you say that you like computation and you value it and so on, and you see its limits, it implies that you see what comes beyond these limits and you're using that thing beyond the limits to think.
And I don't think that you are. Everything in my own mind that I can observe, when I observe myself perceiving, when I perceive myself reflecting, when I perceive myself reasoning, is computational. It means that I go from state to state in a somewhat deterministic way. The random parts are just deleting bits that I computed before, so I have to do it again. The randomness and determinism doesn't help me. So the part of my mind that is relevant to my thinking
is fundamentally computational. What Gödel discovered and is often misunderstood and also by Gödel himself is a very important thing. What Gödel has discovered is not that truth is deeper than proof. That was, in some sense, the suspicion which he started with. He knew that, in his view, that truth is platonic, that things can be true or not, regardless of whether we find out or whether it can be found out. And he hoped
to find a notion of truth, of proof that could reach truth. And he found that it couldn't, and he found this in a devastating way. And he drew the conclusion that there is truth that cannot be found with mathematics. And the opposite is true. There is no deeper notion of truth than proof. You see, perception cannot be true or false. Perception just is. Physics, physical events out there in the universe
cannot be true or false, they just are. A pattern that you observe is not true or false, it just is.
You could be erroneously thinking that you're perceiving a pattern when you don't because you're suffering from false memory or a delusion or whatever that makes your thinking or perception inconsistent. But the pattern itself is not true or false. It's an interpretation that can be true or false. And the interpretation has to be in a symbolic language to have the property that can be true or false. A perceptual interpretation by itself is not true or false. It just is. So in order to be true or false, you need to have a language.
The language needs to be defined in such a way that truth can be established and the process of establishing truth is a computation. There are two types of languages in which truth can be defined. The language of classical mathematics is a stateless language. It's one where time doesn't exist, where everything happens all at once or in some kind of eternal moment.
So if you want to go from state to state in this language of eternal mathematics, in the stateless language, you just assign an index and then you iterate over the index and you do this in a single instant in one moment. And the stateless mathematics has a very beautiful property. It allows you to deal with infinities because you can now construct functions that take infinitely many arguments in a single step, perform an operation over them in a single step and give the result back in a single step. It's a language in which you can assign a value to pi.
In the computational system, you cannot really assign a value to pi. You can have a function that gives you digit by digit, but you never get to the latest last digit. It also means that pi can never be written down in such a way that you can have a process that relies on knowing all the digits of pi and consumes them to tune the outcome of some physical process. If you make the switch to a stateful language, in which you can only go from step to step,
You're losing certain things. You're losing the ability to treat pi as a value. Pi is now suddenly a function that you can only approximate to a certain degree. And many other things stop being values. You get a fundamental difference between a value and a function. A value is something that you have already computed, that you know how to compute by extension. And this means that also the truth changes. Truth is no longer this platonic thing that precedes mathematics and where we can use mathematics as a tool to figure it out.
It has to be contingent on the language in which you use it. If your language has internal contradictions, then truth becomes impossible to determine. You get into areas in this language where it falls apart. You can no longer use it to express coherent thoughts about reality and coherent models about reality.
You can never make statements in the language that you can prove outside of the language. So you cannot use your language to prove things that cannot be described in the language. Your only hope to prove statements about the universe that you exist in in the language is that you are able to recreate the observations that you make inside of the language, which means you recreate a model of the universe that is so good that it gives you what you observe currently.
And then you can hope that the statements that you make in your language capture something about the reality outside of you that gives rise to your observations. Of course you cannot know because it could also be different. But if your language is not able to produce what's on your screen, then your language is wrong. And Hilbert basically gave out this task to mathematicians to find a machine
any kind of structural sound language that is able to run the semantics of mathematics without breaking. And what Gödel discovered is that the semantics of stateless mathematics cannot be recovered. If you assume that there is a solution to get stateless mathematics to work, you will run into contradictions of the way that Gödel discovered. But there is a way out. You just
drop the notion of truth that is independent of the sequence of operations, the number of the set of steps that you took, the algorithm that you took to get to your result. It means that when you have a self-referential statement, like this sentence is false, right? This is a sentence that of the type that Gödel has shown leads into contradictions. If you assume that there is a stable notion of truth that is stateless,
If you accept that truth is not necessarily a stable value and you look at the sentence, then as long as you look at it, the truth value will fluctuate because the assumption that the sentence is true will lead to the sentence being false and vice versa. So suddenly you have no longer a stable truth predicate. And it just means that the property of the languages in which you can actually deal with truth and assign it is that under some circumstances, the truth predicate will not be stable.
And it's fine. There's nothing wrong with that. And the same thing applies to the Entscheidungsproblem that Turing was dealing with when he came to the Harting problem. He defined originally the Turing machine in such a way that we could translate stateless mathematics into algorithms. And this might require that you have to go through an infinite sequence of steps. And if you make this assumption that you sometimes, in order to get to a truth, you have to go through an infinite sequence of steps, you run into contradictions.
So you might use an unbounded sequence of steps that gives you continuously results. That's fine. But you cannot accept that anything exists in any kind of universe that has causal structure that is going to produce you a solution to the heartache problem, which would give you back stateless mathematics. So basically what Gödel and Turing have shown is that stateless mathematics doesn't work. And when we look back at the history of mathematics, mathematicians have never used stateless mathematics. They only pretended to.
Whenever they actually wanted to compute something with mathematics, they under the hood use stateful descriptions. They never took in infinitely many arguments and performed infinitely many operations on them. And the intuition that stateless mathematics makes sense is because we had this intuition that continuity, that space and time in a continuous fashion exist.
Why do we have this intuition? Well, that's pretty easy to answer, right? The number of things that we interact with, if we zoom in, we find that they are discrete. All our observations have a discrete resolution in time and in space. All our knowledge that we store about these observables has a discrete number of bits that we can assign to them. There is only a finite number of information that we can access and that we can deal with as an observer that is embedded in this universe. So everything was discrete to begin with.
But it's too many parts to count. If you deal with too many parts to count, the insight that the number of atoms that you are in an ocean is a finite bounded number doesn't help you at all because it's still almost infinite from the perspective of an observer. So when you want to describe what the ocean is doing, it doesn't help to count the molecules in it and to assign locations to them and model the interactions. It doesn't work. There is too much
So when you look at the dynamics of too many parts to count, you're looking for operations that converge in the limit, which means they behave quite similar, whether you're using a trillion or 10 trillion or a gazillion particles. Once you have these operators that give you the same dynamics under all circumstances, when you take more and more elements to them, this part of mathematics that describes the convergent operators, that's geometry.
And some of geometry is uncomputable, so you can only approximate it. But our brain has discovered geometry to deal with a world of too many parts to count. And this plays into what you're pointing out when you say that our perception doesn't give us reality, it gives us something that we can work with. Of course, the reality that we are embedded in has too many parts to count. We need a different reality. We need one that you can actually handle, even if it's not computable and can only be approximated.
And this experiential reality is a very coarse simplification. It's about as coarse as a gaming engine is when you play a computer game as compared to real physics. It's not much better than that. In many ways, it's even worse, which you can verify if you put yourself into a lucid dream and look at the fidelity of what your brain is able to generate. Light switches will usually not work. You will not be able to read the same stuff twice on the same page and you imagine it and so on.
There's only so many bits in your working memory. The fidelity of what your perceptual system can track and imagine is limited. It's relatively easy to overcome that. Don't really know what the number of bits in my working memory is, and I would be very curious to find out. But it's not as big as I thought when I was a child. It's not infinite. It's not unlimited. Perception of infinity is super easy to generate when your mind is very finite. Super easy to overwhelm my finite resolution mind.
So this deep thing that Gödel is misunderstood, that Gödel has not discovered that mathematics cannot reach truth, but that truth is no more than the result of a sequence of steps that is compressing a statement to axioms losslessly and doesn't go beyond that. That was the deep insight and it's one that basically has not percolated in most areas of philosophy and even physics yet because the physicists have checked out the code base for mathematics before that result was obtained and understood.
So basically that we need to switch from continuous stateless mathematics to constructive mathematics that was not understood back then. And it needs to be understood now. So basically my question to somebody like Donald would not be so much how to explain the spectral gap from because I think problems of this case of this type are with the result of using continuous notions of space time and infinities.
and assuming them as given. So that's a statement about certain theories that are expressed in a language that has inconsistencies. In this language, with these inconsistencies, you get to the point that you cannot get certain results. There's also an issue of computational irreducibility, which is difficult to understand in stateless mathematics. Computational irreducibility is a property of a system that means that you cannot obtain the state of the system without running the system to that point.
There is no way to predict the system except by taking the system with all its detail and fidelity and going through the sequence of steps. So you cannot predict what the universe is going to do when the universe is computationally irreducible. You're going to predict some things, but not all of things. Indeed, some things only with a certain degree of certainty because you can often not insulate them from the parts that you cannot predict because they are computationally irreducible.
In a universe that is played out and implemented in a stateless language, that is a confusing property, because the cost of computation doesn't play a role when you are in a stateless universe. In a stateful universe, the number of state transitions that your model needs to make plays a certain role, and this specter of computation irreducibly is large. It means that you cannot compute things for practical reasons.
because you don't have enough information yet and you cannot have information to make that prediction. But there is no deep miracle that is not caused by the language when you discover that the spectral gap problem is incomputable. So my question to Donald would be, if you think that there is a limit to computation that you can see, and you would still do something and make statements, what is it that you use to make statements beyond the limits of computation?
What parts of your mind are you drawing from when you make statements beyond what a computational system can derive? Right, so one way of trying to focus this would be to talk about the integers versus the real numbers and the rational numbers. So from your point of view, Josje, do you think that
For example, if we look at just the set of all functions from the integers to the integers, it's trivial to show that that's not countable. Turing showed that the set of computable functions is countable, the set of Turing machines is countable. In that simple example, just to make things very, very concrete,
The set of all functions from the integers to the integers isn't countable. The Turing computable functions are countable, and so there's a sense in which the Turing computable functions have measure zero. They're probability zero in the set of all functions. So do we want to conclude from this computationalist point of view that
that all those other functions don't exist? So you're saying those functions, so real numbers don't exist? Yes, for something to exist it has to be implemented. If something is not implemented anywhere it doesn't make sense to claim that it exists. I think it's a confusion of the notion of existence to say that something that is not implemented and is not implementable could exist.
the things that produce patterns that we observe in order to exist and need to be implemented. So you could say, does the financial system exist? Well, it exists to the degree that it's implemented. There are some boundaries where we project it, and it's not actually implemented, where it doesn't actually exist, only at some course of approximation. But by and large, something exists. Some causal structure is implemented here. The set of all the functions between the integers is not implementable. Therefore, it doesn't exist.
It's something that you can specify and this difference between specification and existence is something that is very obvious to a computer scientist and sometimes not obvious to a traditional mathematician. There is stuff that you can specify that makes no sense. It is only specifiable in your language, but that's because your language is much more permissible
Then the set of things that can exist and computation is less permissible. Computation only permits you to build things that can actually exist. If you can build things that cannot exist, it's a problem of your language in which you're building things. It's not a problem of reality, just confused.
I have a comment. This one's from Professor Edward Lee of Berkeley, and it may provide some insight and you both can tell us your thoughts on this. So this is from Professor Edward Lee of Berkeley. This question is a major theme in the second half of my book, Plato and the Nerd. UTMs, so universal Turing machines, have the following properties. Number one, their operation is a sequence of discrete steps. Number two, the data comes from a countable set. Number three, that sequence terminates.
It is a huge leap of faith to assume that physical processes have any of these constraints. I show in Plato and the Nerd that the hypothesis that physical processes all have these properties is actually untestable. I remember earlier, Josha, you mentioned that if it's untestable and you can't provide evidence for it, then perhaps it shouldn't be talked about. So this reminded me of this. And he says in brackets, this follows from an information theorem due to Claude Shannon, known as the channel capacity theorem.
The converse hypothesis that the physical world is not so constrained is also untestable by experiment. But I argue, in Plato and the Nerd, that the converse hypothesis leads to simpler models of the universe and therefore is a better choice by Occam's razor. My claim is that universal Turing machines as realized on today's computers are simulations, quote unquote, of a process that is fundamentally non-algorithmic. So I just want to place that out there and perhaps you can use that as a jumping off board, Donald and then Yoshi.
I'll be interviewing Edward at some point in the next few weeks as well. Oh, very good. That's really quick because these are very, very deep issues. It seems to me that this also interacts with what the physicists are telling us that there is no time fundamentally.
So if time is not fundamental, then these computational issues where there are fundamental limits to what can be computed because we're assuming time. So in computer simulations, computer algorithms, we're assuming a sequence in time of computations that can be, and the kinds of limits that Yoshi was talking about,
It seems to me are a consequence of assuming time to be fundamental. And if we have to go to a physics in which time is not fundamental, then that places this whole conversation in a completely different context. And so what we may be pointing to is time has
been a very useful and helpful thing for physics for several centuries. And now the hard work that we have to do is to understand how to go beyond the notion of time. And when we go beyond the notion of time, will the kind of discussion we're having right now be fundamentally revised? The computational versus non-computational notions, we may have to really revise how our whole conversation here is going. I'd be very interested in what Yoshi has to say on that.
Thank you. Also thanks, Edward Lee, for your argument. I concur with you that it's in principle not testable what physics is really like. What we can only say is which theory that we can come up with is more elegant. For a small thing, I think that this notion that the Turing machine has to get to result after a finite sequence of steps might be a mistake.
in the sense in which two machines were originally defined. So basically, a computer that can be built is not a Turing machine in this sense, but it's always a finite state machine. And in a finite state machine, you can have a sequence of steps that is unbounded, that doesn't stop.
And that gives you more and more digits of pi while you're looking at. In a sense, it doesn't come to a conclusion if you want to compute physics, but it's not the problem to build a computer that as long as it runs gives you more digits of pi. And so I think from a formal perspective or from a, it doesn't make much of a difference because you can easily fix it, but it's important if you think about hear that sound.
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Your intuitions about how things work or the proofs that you make in other contexts that the value of computation doesn't hinge on there being a finite number of steps until a computation that is going to give you a result that was formulated in classical mathematics terminates.
But it means that everything that you get is the result of finite interactions. And if you assume that infinite interactions are possible, you run into the difficulties that Gödel and Turing have discovered, which means that your theories no longer work, they no longer make sense. And different from Edward, maybe doing him injustice here, I have not read this book. So I would say that
It's much more elegant from the perspective of Occam's razor to describe reality in a language that doesn't break. Because if your language breaks and you still try to make a model of reality, it's going to be arbitrarily expensive. It doesn't work. You have to find a language that works. So if we find that the languages in which we can describe reality have to be computational languages, because the others lead into contradictions.
Then we have to use the computational languages. That's the situation that I find myself to be in. This doesn't mean that I can know what physics is like. It just means that all the physics that I can talk about without my language breaking has to play out in this way. The notion of what is time, so coming back to Donald, is very important. There are two notions of time. One is this intuitive notion that we have as human beings, which is basically this Newtonian time.
This time which clocks run the same speed everywhere and so on, and it describes the transition of the universe from the past into the future via the present. And this notion of time is somewhat similar to the notion of the state transition in your computer, except that the state transition in the computer has some kind of global clock where everything in the computer goes from state to state all at once and
goes or progresses to the next step. But what we see in our universe that it only makes sense if we assume that it's dynamic. If the universe would just be a decoupled sequence of states without a transition function, there would not be any law that we can discover. There is nothing that we can control. Organisms would not exist in the way in which they do. So from the observations that we make, we have to assume that the transitions in the universe are somehow fundamental, that the universe is moving.
And state transitions seem to be crucial in order to be able to understand the universe. There is some notion of transition and this notion of transition is much more basic than time. And the time that we are talking about when we see that time is not fundamental in the notion of space time is relativistic time. The relativistic time is what the universe looks like to a relativistic observer. And we can obtain relativistic time if we understand that
What we perceive as time is basically the speed of the clocks in our environment. And the speed of the clocks that we observe depend on our own speed. So if I move you through the universe and you are a supervenient pattern on the structure of the universe, imagine the universe is something like an ocean. And the present is the crest of a traveling wave through that ocean. And there are
waves maybe in front and behind us, but they're not our future, they're past, they're different universes that just happen to be a little more long or a bit less along. The future and past would require you to leave the crest of the wave and you can't because you're always traveling with the wave. So there is no way to leave that present because only the present exists from the perspective of that crest. And you and me, we are vortices inscribed on the crest of that traveling wave.
And the rotation that the vortex is doing when it updates itself to observe the universe, to form a memory and so on, and to register its perceptions and so on, will depend on the speed in which this vortex rotates. Right? And so if the vortex is moving along with the wave, then the updates in the vortex are a function of the movement in the wave itself, the basic parasitize on the movement of the main wave.
And you cannot, as this vortex traveling with the wave, ever leave the wave. You can move a little bit in the wave to the left or to the right. Moving to the left or to the right would be movement in space. You cannot move in time. You just move with the time. And the faster you move to the left or to the right, the less there will be updates available for interning your internal state.
So the fluctuations of the vortex becomes slower and slower, the more the vortex moves in space. And this leads to relativistic time. It means that from the perspective of the vortex, when it looks at its environment, the environment gets distorted in time and space. So in this notion, we realize why something would look like to a vortex that moves like this, like relativistic time. And we understand that the relativistic time from the fundamental perspective, how to make all this happening, how to build a system that functions like this,
cannot be fundamental. It's a result to the observer. It will be what the universe looks like to the observer of the observer screens as we always do, right? But it is not fundamental, but fundamental are the state transitions. So what we need to do is basically replace the physicalist time that is relativistic for good reason in the frame of certain models by something that is more fundamental and allows us to derive the relativistic time. And this would be state transitions.
Very interesting. In that spirit, or at least in that kind of direction, there's work by Marcus Mueller and Philip Hohn, and then also some more recent work by Fabio Mercati and Giovanni Emilino Camiglia, where they're showing how relativistic spacetimes can be constructed.
from exchange of quantum information so you don't assume it upfront but you try to get a dictionary to that allows different quantum agents to send information back and forth and it turns out if you send enough information back and forth and try to set up a dictionary to make everything consistent you will get
Einstein's special relativistic space time coming out of us. So that's an interesting direction to go. Another interesting direction to think about, just a simple notion, time and entropy are, at least physical time and entropy are deeply connected. And so we would like to have some way of getting entropic time coming out of
a deeper system in which there is no entropic time, right? And there is a, I'm not saying this is the deepest way of doing it, but an interesting, simple way, just in the case of Markovian dynamics. So if I have a Markovian system, homogeneous, and it's in a stationary, then the entropy of that system doesn't change. So if for state X sub n and Xn minus one and so forth,
the entropy h of x of n equals h of x sub n minus one for all n. So there is no entropic time. But it's trivial to prove that if you just do a simple conditioning, if I look at xn given x1, or xn given, then it turns out that h of xn given x1 is greater than or equal to h of xn given
In other words, the very fact of doing conditioning, which is projection. So you can think about, I take this dynamical system, which has a notion of state transition, this Markov chain, but it doesn't have any entropic time. But as soon as you start projecting that non-entropic system onto different perspectives by conditioning H of Xn given X1, all of a sudden, now you have entropy.
And so now you have that kind of notion of time. So is that a direction that we could go where we could still have, in some sense, a dynamical system, but it's not an entropic time system, and show how we get space-time arising from that in the way that some of these physicists are trying to do. I think that will be interesting. I think that it's a separate question whether the real numbers exist versus...
It's a pretty strong statement to say that real numbers don't exist. That's really quite interesting to say that they don't exist. But I guess that's where you want to go anyway. Yeah, well, I agree with Patagoras that real numbers don't exist. And the time was not right back then. So real numbers are actually functions. And you can give you this function instead of a real number. And it can give you as many digits as you want, or as you can afford to compute. But this is it.
It's fine. So basically real numbers can be derived in a deterministic fashion. They are predetermined in this sense, but you will not know the billions digit of the square root of two unless you find a procedure to compute it and the energy or the neck entropy to actually get there.
And this derivation of a result via using apnic entropy, I think, relates to our perception of time, this causal error of time, which is aligned with the entropic arrow. Eric Drescher finds a very good metaphor in his book Good and Real, I think, to give an intuition how a symmetric system
where the transitions are symmetric in both directions, is still not going to be symmetric at scale when you look at it. So he takes as an example, a ball that is made of large and small billiard balls. And you put one of these billiard balls in motion and the transaction between the billiard balls are all symmetrical, which means if you take a movie and you play it forward and backward,
will see for the every interaction between two billiard balls that it's the same if you go the movie backwards or forwards. It's a simplified model where you have no friction and so we have no thermodynamic stuff going on. We look at the universe at the level where thermodynamics doesn't exist yet because this maybe the stuff is too small to have these losses. So we just look at the billiard ball universe where everything is deterministic and without noise and in this model what we see is
that when we zoom out, there is something that is happening at scale, and that is some balls move after they have been hit and keep moving, hitting other balls. And if you play the movie backwards, it looks as if some balls are anticipating that they are going to be soon hit and start moving as a result, as if they would be hit, right? So there is this asymmetry that your balls leave a vague behind them.
And this vague is describing, in some sense, the entropy that we are looking at in our universe. That's the direction in which you can, as an embedded observer, form memories. Because in order to form memories, you rely on the dissipation of information between locations. And so whenever there is a way to form memories, it means that you are aligned with some kind of entropic arrow.
If you zoom out, it means that you can now sort the states of the universe in such a way that you discover the concentric waves that you are part of, and our ocean-like universe has a point of origin. And this point of origin is a construction that you make. You discover this by the wave expanding, and you discover it by information moving, diffusing across the locations in the wave. So there is a hypothetical point in the middle
where the information is not diffused yet. And this hypothetical point is what we imagine to be the Big Bang. Right, and it's a mathematical singularity in a way, because if you are in the Big Bang, you don't know which direction to go unless the Big Bang is not completely perfect and symmetrical. And the interesting thing about this before the Big Bang means it's the wrong question to ask, because
Sorry to interrupt, is this related to the Janus point? Have you heard of Julian Barber's theory of time?
No, but it's an artifact of a certain description. Basically, we create a certain mental model in which we describe the entropic arrow of time as the diffusion of information across locations in the universe. And then we imagine that there is a single point where this ends up and we go through this point. On the other side, we go back into another future. So the further we go away from this point in any direction, the further we go into a future in which systems could form memories of the past.
And to form memories of the past, you need to have some kind of reservoir of neck entropy that you can tap and some kind of puddle of neck entropy. And then you can reason about the conditions, how such puddles of neck entropy could form under which conditions and how long they might last. I would like to get to the topic of free will as well. And then also some audience questions. So why don't you, Donald, outline your views on free will? OK, yeah.
If in a physicalist framework, which so now I'll just talk about what most of my cognitive neuroscience peers think, right? Most of them assume that physical systems are fundamental. Neural activity causes all of our behavior. And in that case, there can be a fiction of
a useful fiction of free will, but it's really just going to be a useful fiction. If I do something, it's really my neurons with the neural activity that did it. And there is a sense in which you can say I chose to do it because actually neurons are part of me. So I think that's the point of view that Dan Dennett takes, for example, on this. And
And Sam Harris replies on that. He says, well, yeah, I also grow my fingernails. I'm not sure that I'm doing that by free will. So it's not real clear that just because my neurons are doing it, I have free will, just in the same sense that I'm not using free will to grow my fingernails. So Sam would say there's no such thing as free will if you're a physicalist. Dan Dennett would say I'm a physicalist. And there is this important notion of free will.
I think that, of course, space-time isn't fundamental, and so that we have to completely think outside of that box altogether. And as scientists, we have to say upfront what our hypotheses, what our axioms or fundamental assumptions are, and be very clear about them upfront. These conscious agents, in the mathematics, they get certain inputs. We call them experiences that they have.
And then there's something called the Markovian kernel that describes what actions they take, and those actions affect the experiences of other conscious agents. So that's just the mathematics that my team has written down. It's a very simple notion of Markovian dynamics of conscious agents interacting. And it's not in physical spring work. We're assuming that this is
you know, in its own world, right? These are conscious agents, and that's the foundation. Space and time are not the foundation, conscious agents. So conscious experiences and interactions of conscious agents are the foundational notion. And so then the question is, how shall we understand the probabilities? So if I get a particular experience that comes into a conscious agent, and it then probabilistically affects the experience of other agents, how shall I
understand that probability that it shall understand it as as a free will choice or or what and you know I could say you know I refuse to answer the question I just there's a probability there and that's that's as far as I go with with a theory there you know this agent so I leave that probability as just where my theory stops right I say
In some sense, wherever we see a probability in a theory, that's where explanation stops, right? That's basically saying, I don't know. So I always say this, whenever in a scientific theory, you see probabilities coming up, you're seeing the theory say, this is where I halt. This is where my explanation stops. And there are two major
approaches toward understanding those probabilities, the objectivist and subjectivist to probabilities, right? So objectivists say that these probabilities are pointing to some real thing in the world. There is some real random generator in the world. And subjectivists say, no, these are just degrees of beliefs. Whenever you see probabilities, you're only talking about
degrees of belief. But in either case, explanation stops, right? How do I come to that belief? Well, I can only tell you probabilities. What is that random objective process? I don't know, but I can just tell you probabilities. And so really, whenever you see probabilities in a scientific theory, and they're all over the place, I read that as saying, here's where explanation stops.
And our theories our theories halt and and if we want to go further we're gonna have to unpack that probability into some some deeper deeper theory, so If I say that it's free will in the case of the conscious agents Then I mean in some sense that's just words what theory has is the probabilities and
And it has no further explanation so if i say if i call the probability of free will that i can call it that but but i haven't really done much to. Give much insight into the notion of free will free will then becomes a primitive and maybe that's what i want to do i want to say this is where explanation stops.
And so free will is primitive. So these probabilities are free will and I agree to that that's where my theory stops that I can do no further. Now what's interesting in the conscious agent dynamics that we're working on is that any group of conscious agents
together also satisfy the definition of a conscious agent and so they are a conscious agent so any conscious agents interacting are also conscious agents so they're in the third there's one conscious agent because if you take all of them together they form one conscious agent but then there are as many if you're computational there's only countable number of them or in my case i don't know if it may be an uncountable number of conscious
agents but what's interesting is that the you unpack this probability in the Markovian kernel there could be one big probability for the one agent but you can unpack that into all these dynamical systems that are interacting conscious agents with their own probabilities in their own kernels and what's what's interesting is that you could then give in some sense an unpacking of the notion of free will in that way you could say well yeah the the one agent has free will in this this probability but i can actually
do some non-trivial unpacking of that notion in this sort of recursive unwinding of those probabilities throughout the network. So there is the possibility here of, I mean, ultimately there will be a primitive notion of free will that is just primitive and not explained. But given that one, I can explain all these other free wills sort of interacting, arising from this most primitive notion of free will in a non-trivial
non-trivial way. But once again, I would point out something that I see all the time in scientific theories. No theory in science will ever explain everything. And I would love to see if Joscha agrees or disagrees. I will just state, to make a strong claim, there cannot be a theory of everything because every theory has to make assumptions and those assumptions are not explained, they're assumed.
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Okay, am I correct in my summary of your views on free will that if in a physical theory you have probability, now some of that probability is just due to our ignorance, but if there's a fundamental probability, you can just say, well, that's indicating that the theories break down, we just don't know. Or you can say that there's something underneath producing those and that which is underneath the probabilities is what you're calling free will. Is that correct? Or is that off?
Right. So if I'm a physicalist, I'll say that that probability is due to some process that I can say no more about, but there's some process that generates this stuff. It's not free will. It's just a physical process that I don't know. But if I'm taking consciousness to be fundamental, then it's an interesting move to say that that probability can be interpreted as free will. Now, of course, I'm not explaining anything. I'm not, I mean,
I'm just putting the notion free will, the word free will on it, right? And free will becomes just a primitive notion as well. So that's where my explanation stops. And the most unpacking I can do is that recursive unpacking that I mentioned, which is an interesting unpacking. But ultimately, there's this primitive notion of free will that I have nothing further to say about. But I think that that's not
a problem specific to this theory. The last thing I was saying was that that's endemic to all scientific theories. Every scientific theory will have miracles at its foundation. By miracles, I mean assumptions that are taken for granted and not explained. If you explain them, then you have a deeper theory with new assumptions that explain those assumptions, but the new assumptions aren't explained. And so in this sense, science can never have a theory of everything because science theories always have
Assumptions and the assumptions are what you don't explain. Yoshi, I know Donald said quite a few, there are quite a few elements to pick from there. So we interlocking claims, but let's address them. First of all, I don't know whether there can be one theory of everything, because my reasoning is not tight enough to make that proof one way or the other.
So at this point I have to remain agnostic, because from various stand it seems to be possible that there can be a theory of everything and it seems to be possible that there cannot. From a computationalist perspective, whenever you have a set of observations that is finite, you will be able to construct a computational model that explains how to make such patterns. So in principle, there can always be a theory of everything that you observe.
This is something that I cannot, they don't see a way around this. So this seems to be sound to me, and I think that can be formally proven, but it seems to be almost trivial that it's proven. So it's more interesting. The question is, can you narrow this down to a single one, to one theory of everything?
You will be always stuck with infinitely many theories of everything, where most of these theories will be super inelegant and redundant and basically recordings of your observations. Or will there be one theory that is the most elegant and explains everything deeply and wraps it up? And of course, if you think about the space of all theories and think of them as things that you can do in a language and
in which you can define truth. And if you realize that the languages in which you can define truth consistent, these are the computational languages, it turns out that all your models are going to be automata.
And that you can sort the space of automata by the length of the definitions. So it also seems that in principle, it should be possible to find the shortest automaton between to every pair of automata that you can construct and can up this. And now the question is, what's your search procedure for all the possible automata? Do you have a search procedure that you can hope that terminates?
And this is not a question of whether it's mathematically possible, but whether it's efficient. So is there an efficient strategy to find the theory of everything that is the shortest one? And so far we haven't found one. And it relates to what AI is doing in machine learning when it tries to identify what's going on in the domain.
So in principle, we can always be sure that we could be a brain in a vat and everything is just a nefarious conspiracy that is playing out. And because we cannot exclude this, we can never be sure that our theory of everything is the best theory that could exist of things. So that's obviously the case. But if we take out this single thing and make the assumption that reality is not a conspiracy, I think then it starts to look a lot brighter.
Let's get to the notion of free will. I think that free will is tied into the notion of agency. And the best explanation of what an agent is that I found so far is that an agent is a control system that is intrinsically combined with its own set point generator. A control system is a notion from cybernetics. It means you have some system like a thermostat that is making a measurement using sensors, for instance, the temperature in the room.
And that has effectors by which it can change the dynamics of the system. So the effector would be a switch that turns the heating on and off. And the system that's being regulated is the temperature in the room. And the temperature in the room is disturbed by the environment.
And a simple thermostat will only act on its present measurement and then translate this present measurement using a single parameter into whether it should switch or not. And depending on choosing that parameter well, you have a more efficient regulation or not. But if you want to be more efficient, you need to model the environment and the dynamics of the system and maybe the dynamics of the sensory system and the actuator itself.
When you can do this, it means that you model the future of the regulation based on past observations. So if you endow the controller with the ability to make a model of the future and use this control model to fine tune the actions of the controller, it means that the controller now is more than a thermostat. It's not going to just optimize the temperature in the room in the next frame.
But it's going to optimize the integral of the temperature over a long time span. So it basically takes a long expectation horizon, the further it goes, the better probably. And then it tries to minimize all the temperature deviations from the ideal temperature from the set point over that time span. This means that depending on the fidelity and detail of the model of its environment and its interactions with the environment in itself,
It's going to be better and better if it assumes that there are trajectories in the world that are the result of its own decisions.
By turning the temperature on and off at this particular point in time, I'm going to get this and this result, depending on the weather outside, depending on how often people open and close the door to the room at different times of the day, depending on the aging of my sensor or the distance of my sensor to the heating, and depending on whether the window on top of the sensor is currently open or closed and so on.
I get lots and lots more ways to differentiate the event flow in the universe and the paths that the universe can take and the interactions that I can have with the universe that determine whether somebody will open the window and so on and so on. So you have all these points where the controller is a very differentiated model of reality where it's going to prefer some events of others and is going to assign its own decisions to these trajectories.
This decision-making necessarily happens under conditions of uncertainty, which means the controller will never be completely sure which one is going to be the right decision. The controller will have to make educated guesses, bets on the future. This even includes the models of itself. The better the control system understands itself and the limitations of its modeling ability,
the better its models are going to be. So at some point of complexity, this thing is going to understand its own modeling procedure to improve it and to find gaps in it and so on. And this also means that when it starts to do this, it is going to discover that there are agents in the world, other controllers that have set points generators and model the future and make decisions. For instance, people that might open the window when you make the room too hot and you lose energy because of that. So maybe not overheat the room and people are in the room.
This means you have to model agency at some point and you will also discover yourself as an agent in the world as a controller with a set point generator and the ability to model the future and you will discover this before you understand your own modeling of the future works. So you also have to make bets on how you work before you understand yourself. So you will discover a self-model. The self-model is the agent where the contents of your own model are driving the behavior of that agent.
It is a very particular agent. It's one where your reasoning and your modeling has an influence on what this agent is going to do, a direct coupling. It's a very specific model, a very specific agent that you discover there. And so in some sense, free will, I think, is a perspective on decision making under uncertainty, starting from the point where you discover your own self model, up to the point where you deconstruct it again. And of course, you will deconstruct it again at some point.
you will be able to fully understand how you're operating. And once you do this, making your decision becomes indistinguishable from predicting your decision. Because of computational irreducibility, often you will not be able to predict the decision before you make it, right? But as soon as you understand that it's just a computational process going on, and you understand the properties of that process, you will no longer experience yourself as having free will.
Free will is a particular kind of model that happens as a result of your own self model being a simulacrum, instead of being a high fidelity simulation of how you actually work. And we are young beings, we don't get very old, it's very difficult for us to get to the point where we fully understand how we work.
Except in certain circumstances, right, when we observe our children, very often we get to the point as parents that we fully understand what they will be doing in the given situation. We can fully understand their own actions and anticipate their decisions and the child might experience that it has free will. We experience that the child has free will up to the point where we suddenly understand, oh, this is what's going on. And at this point, I can completely control the child because it can outmodel it.
And it's only to the point where this system is going to introduce levels that are, again, reaching my own level, that decisions become unpredictable. But if I am a few levels of monitoring depth above the other agent that might think that it's free will, the free will starts to disappear from my own perspective and also happens in my own mind. There's many things that I do, but I thought as a child I'm acting out of my own free will and now I understand how mechanical it is and I can deal with myself.
By controlling myself, by outmodeling myself successively and becoming one more complex in this way. And all that, the computational process, the probabilities in the transition rules, you would view those as objective probabilities.
Yes, so there is also this issue that I don't actually exist in the way in which I model myself. I only exist to some degree of approximation. I'm not this big tree that is strictly implemented in physical reality. I'm more like a bunch of shrubbery. And some of the shrubbery is tasked with making a model of myself as a tree. And that model is going to be a coarse approximation. So the fact that I am unable to follow up on my plans means that I'm only approximately implemented.
The rubber hand illusion is a good example of how we're continually redefining who we are, right? Where you tap and drag on a hand at the same time you're tapping and dragging on a rubber hand. If you do it just right with a person, they'll take this rubber hand and incorporate it into their body image. So we're always learning who we are. But those probabilities in that learning process you would take as objective probabilities and not free will kinds of probabilities.
What does it mean that a probability is objective? It only means based on the models in which which I have currently made. And if I go far beyond that, I cannot assign an objective probability to the probabilities that I am observing because they are contingent on the assumption, for instance, I'm currently not in a dream or that my memories are correct or that my data are correct or that the theories that event into establishing the relationships between my measurements and my data and so on are correct.
So I do agree that at some point there are a lot of assumptions that go into this. And these assumptions, where I differ with you, are usually mild. Because I make so many observations that at some point the errors cancel each other out, or there's so many people that can verify my ideas and shut them down. And so my ideas don't exist in isolation. They are being shot against every philosophy and physics book that I can get my hands on and that I understand, right, in every conversation that I have.
So that doesn't mean that I will discover the truth in this way, but it means that I discover many, many of the possible errors that I can make. And at some point, I realized that there is a finite space of theories that exists and that we are discovering the same things again and again. So when we ask ourselves, what are integers, for instance, or what are rational numbers? There are many ways of making theories about what integers are. For instance, we can say that there are the cardinalities of sets.
So basically you count members of a set, and this is an integer, and all the numbers of members of sets that you can have are integers. Or you can say that there are a subsequent Lieberling scheme. That's the definition that I currently prefer. Or you can use Peano's axioms to formalize them. And it turns out that they all describe exactly the same thing.
There are all different perspectives on the same thing, and once you understand the larger space that surrounds the integers, you also understand why there are different perspectives, because you understand how these perspectives are being constructed, and you can show that it's all the same thing. So in some sense, the integers are fractal, and you can describe this fractal using a generator function, and you can also describe it in many other ways.
And it seems that mathematics or all the languages that we can use that work are usually small, relatively intelligible set of fractals. And there are the boundary of what is intelligible to the human mind, but not that far above it and probably still inside of it. So I'm more optimistic than you are. I have a question for the both of you.
It's about your models. How much of it would have to change, let's say, Yocha in your case, if classical logic was indeed correct, if continuities exist? And for Donald, if the opposite was true, so continuity doesn't exist, intuitionist logic is primary.
At some point in my life, I thought that continuity must exist because everybody was assuming that it did. Like most of the eminent physicists thought that the universe must be fundamentally continuous. Many of the foundational theories that we have in physics assume that there is continuity. And I thought that my inability to derive continuity to construct a continuous system is the result of my lack of understanding. And it took me quite some time to realize that
What Gödel has stumbled upon was actually the insight that continuity cannot exist because it's not constructive, cannot be implemented. So once you have the infinities, once you presuppose them, there are an amazing cornucopia, all sorts of stuff falls out.
Like you have Hilbert's hotel that is completely booked out, but there's infinitely many rooms and then there are infinitely many buses coming on and you just ask everybody to move in the room with twice the number and then you fit in the infinitely many new people, right? This is not a feature. This is a bug. This shouldn't happen. I know how hotels work. No hotels work like this.
This is not good if something like this happens. And it's not surprising that this blows up when you try to make proofs. And so I think that Hilbert's Hotel points not to a miracle in the universe that under certain circumstances, you get something for nothing, which is very nice if you want to derive the universe from nothing. But hear that sound.
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It shows that your language can break.
And so I don't see a way to get the languages in which continuity exists to work. And I cannot exclude that I'm wrong. And I might see a way in the future or somebody else does in a way that I don't. I just don't see a way how to make continuity work. But I get all the benefits from continuity for the description of practical systems using discrete logic. So in this sense, I would say that dynamical systems that are truly continuous don't exist.
They're not causally existing. They cannot be causal. There are a layer of description that are used to deal with too many parts to count. And there are sometimes a very useful abstraction, but they cannot be used for a foundational theory. Because the foundational stuff
has to work. It has to be described in a language where all the elements, parts have to interface in such a way that your language doesn't blow up because otherwise the terms in your language don't mean anything. So what this means is that the word continuity does not actually mean anything in my world. It does not have a useful reference. I cannot point at anything that is truly continuous without my language breaking.
So it doesn't exist. It's a word that only exists as a confusion, but it exists approximately. It exists as the dynamics of too many parts to count, which is fine.
So I'm a confused man. And when you say that the language is breaking, I just see it as you saying that they're extremely unintuitive results that, well, they don't seem to make sense. But it doesn't mean that they don't make sense because you defined work as what's implementable. What it doesn't work means that you can no longer derive truth. It means, for instance, in axiomatic system, if you have a contradiction in your axioms, it means that you can suddenly derive everything and nothing.
It just means that your fractal is no longer having a discernible structure. This is what it means that it's breaking. What is the exact contradiction in classical logic? Because it seems as though mathematicians are getting along fine, and it's difficult, extremely difficult to prove certain theorems. And it wouldn't be if there was a contradiction. Well, not necessarily, but you understand what I mean? Yes. So the issue is that the assumption of a stateless platonic notion of truth
that holds independent of the process by which you discover the truth leads into contradictions. And this was what Gödel had proven. It basically means that a sentence that is true under these assumptions is also false under these assumptions. So it cannot be true. And this is where undecidability comes in. It's not just about that some sentences are not reachable because you don't know whether they're true or false. It also means that there are some sentences that are true and false at the same time.
But if you have to find truth in such a way that it can, that it includes false falsity, right? Something is either true or false. If you have an excluded middle, then this cannot be the case. So this is a very bad result. It just means that your language is not working. It gets to illegal states. It just means that the application of steps that you have prescribed in your logic, if you apply them properly, leads to an undefined result.
It means that your language is sex faulting. It means your mind is breaking apart. It means that the thoughts that you are thinking no longer have meaning because they can no longer point to anything that could be implemented. Okay, so Don, the question that I asked before was, let's imagine the intuitionist logic is correct. How does your theory change? Well, yeah, so I mean, I could easily
Implement the theory of conscious agents in an intuitionist logic kind of approach and run it that way. So that wouldn't really change my theory of conscious agents fundamentally. But my own thinking on this, I guess, does differ from Yosh's in an interesting way here. And that is, I do take Gödel's result, not necessarily to show that the notion of continuity is
is nonsense or contradictory, but rather that if I have a finite system of axioms and derivation rules, then you can look at the set of statements that can be proven by that system, then you can find statements that are not provable within that system, so they're undecidable from within that system. But what Gertl did was to put a mapping
on to the language of the system so he could write down an analogy as Douglas Hofstad likes to talk about. He found an analogy that he could write down where there is this sentence I could write down that says I am true but not provable within the system.
And that doesn't seem to me to require me going all the way off to uncountable infinities and continuity and so forth. It's just saying, I mean, here's a deflationary reading of Gödel. It's just saying, you give me any computational system, I'll find a statement that's true but can't be derived from within that system. Therefore, any computation that you pick isn't the final word. I don't have to go all the way to, you know,
uncountable sets and so forth. I can just use that to say that the computation can't be the final truth. And so that would be sort of the minimal way out. And that's why I think a lot of researchers have interpreted Girdle, but I guess Yosha disagrees on that. Okay, what would be the thing that goes beyond that? So what is the other language that you can use after Girdle's language broke?
Well, what you do is you take the new statement that you showed was undecidable within that computational system and you add it to your computational system. Every computational system has axioms. You don't compute without some assumptions, so your computation has to have certain axioms to begin with, so you add it to your axioms. It's now still a finite set of axioms.
And now you say, OK, now I'm good. I took that undecidable sentence and I put it into my set of axioms. I'm good. Now I'm done. Well, no, you're not. Now because Gertl comes back and says, you know what, I just found another statement within your new system and that's not computable. So I'm not getting anywhere near to these uncountable infinities. No, wait, wait, wait. You are making a step too far here, I think. You have just found this procedure that discovers that something is true that is not true according to mathematics.
So Gödel is trying to find a foundation for all of mathematics and he does this by reducing the mathematics that he's interested in to piano arithmetic and then computes all of mathematics in piano arithmetic and discovers that he cannot recover the semantics that he wanted to discover, which was a platonic notion of truth, one that is independent of the state sequence that he runs it through. This is the thing that he cannot recover and you try to recover the original mathematics by extending
the axiomatic system, Peano's axioms, with an infinite set of arbitrary statements. This doesn't seem to be very elegant. Also, of course, Gödel shows that it doesn't terminate. It doesn't work. It's not fixing mathematics in any way. So you still have the intuition here that you have a procedure that allows you to discover truths in ways that Gödel's procedure could not. And if you have that procedure, you should be able to prove that it's true.
If you cannot prove that it's true, I'm not going to believe you. I don't think that the statements that you think are true, but my system cannot prove are true. Unless you can compute them. So you have to show a way that would force me as a rational observer and colleague of yours that is completely charitable and so on and reasonable and rational to follow you there. So if you can give me a rational procedure,
Then I expect that this procedure will be computational, that there will be a sequence of steps that I can follow to see why your claim that the sentence is true is actually valid. If you cannot make such a claim, I don't see how I can believe you. Well, so the way I understand Gödel doing it is that he comes up with this whole Gödel numbering approach.
And he takes you through and shows you this mapping from the numbers into these girdle numbers that are making statements about the numbers themselves. And you look at that and you go, yeah, okay, I understand that mapping, that's perfectly fine. And now I can write down within that mapping, I can write down this number. And when I look at the interpretation of that number under this mapping, the number says,
I am true, but not provable within piano. And so now, at this point, I sort of agree with Roger Penrose. Penrose looks at that and says, OK, that means that there is something true here. I can see that it's true. I don't disbelieve. I mean, I saw the whole girdle numbering construction. I saw how the sentence came to say what it says, and I agree that it's all consistent.
And what it's saying is saying that it's true and not provable. So at this point, I guess I sort of agree with Penrose. At that point, I go, OK, there's something beyond the notion of proof, beyond the notion of derivation that's going on here. There's the looking at analogies and understanding analogies.
that where we go, this sentence is clearly true, and it's also by its own statement, its own declaration, that it's not provable within this finite computational system. Yeah. Peros is fascinating. He thinks that our brains are physical systems, and he also thinks that our mental processes are generated by the brain, probably, but that our brains can do mathematics that go beyond the mathematics that computers can do.
That is a very specific statement that is more concrete, I think, and specific than what you've said so far. And it leads him to a weird spot, which he's quite lonely at the moment. But I find this nevertheless a very interesting argument to make. I'm afraid we will not be able to resolve it today because I have to drop now. But I found it very interesting to see that you are a penrosist at the end of the day.
Well, I don't like the microtubules theory, and I don't like the non-computational collapse of microtubules theory. But I think that he's not really to be blamed for this. I suspect that his reasoning is that since all known physics is computational, these basically takes a state and then there is a transition between the states, the resolution for what consciousness comes from
If consciousness is enabling us to do things that computers cannot needs to be in an unknown area of physics and the unknown area of physics that's left.
reasoning in the same way as Sherlock Holmes, if you actually exclude all the possibilities, the only remaining thing must be the truth, right? That's quantum gravity, because there is no generally accepted theory of quantum gravity. And then it just so happens that Hameroff has this beautiful psychedelic theory of how to get the microtubulize to have non-local interactions that employ quantum gravities in a way that nobody really understands. And this might be in this corner. And so
They become friends. But I don't think that Penrose theory is exactly the same thing as Hameroff's theory. Right. Right. Right. And I'm not talking about that more general theory of consciousness. I'm just talking about his specific analysis of Gödel's incompleteness theorem and what it means for mathematics. Yes. And it's basically also something that Chomsky is a fume to in which leads Chomsky to a mysteriousism. So basically they were confronted with the same
insight or the same idea that they think that human brains can do things that mathematics cannot, that mathematicians can make proofs that computers in principle cannot make, that they discover that certain statements are true, that in a computable axiomatic system cannot be derived. And this was also what my question was pointing out, at how do you know that something is true there if you cannot go show me a sequence of steps that does it, right? And so Penrose and
Right. I guess we will have to go. I'll just say our basic understanding of the axioms itself.
How do I understand the basic axioms that are the foundation of the computational system? Where does that understanding come from? Is that from within the computational system or does that escape the computational system? From my own perspective, it's the case that my mind is constructing a model of reality. The reality that I found myself to be in is something like a physics engine in which my own conscious self
acts as a puppet, as a simulacrum that is being used to tell the story about an intelligent agent. And I don't see any limitations in my ability to make models that could produce such an agent that would find itself in this world and associate a set of valence precepts with a garlic and another one with sunlight and
that happens entirely through the relational nature of my unified model of the universe that is being derived by completely non-inferious computation that are approximated in nervous systems. So I don't see where I currently stand that this doesn't work out. And I'm very sympathetic to when you don't see this, that it doesn't work out and that you have to think that you have to find the truth elsewhere.
and it could be that I am going to change my mind in the future when I stumble on something that basically shows to me that what I'm intellectually trying doesn't work so far it seems to work and I appreciate that we have this difference in our perspectives because it's a very productive and useful one to have. Absolutely, I've really appreciated the the tenor of the conversation too, very much so. I would just say my last thought on this would be that
What I would love to see from a computational system on consciousness is the association you just talked about between the computation and, say, the taste of garlic. Is it principled or is it arbitrary, that association? If it's arbitrary, then I'm not... Yes, it's not arbitrary. It is related to the valence of the taste receptors that you have. So it might be arbitrary in the sense that some people hate garlic and other people love garlic. So the garlic will taste different to them.
This means they will have a different experience when they taste garlic because the relations of the taste of garlic will be different to the entire world model that they have than they are to other people. So basically the types of receptors that we have and the valence that they imply and the type of self-model that we have. So in which way has the mind constructed itself that is entangled with its universe around it? What is that
So there will always be the question, why should this computational process, independent of valence, be the taste of garlic? Why couldn't it have been the taste of chocolate?
I would want a principled answer to why is this computational process necessarily the taste of garlic? Why isn't it the taste of chocolate? Because one is affiliated to garlic and the other one is associated to chocolate. But I'm talking about the conscious experience of the taste of... Oh well, chocolate is sweet for the most part and garlic is not.
So this is one of the dimensions in which the features vary and sweetness is perceived as pleasant under some circumstances when you need certain types of nutrients and the soreness and bitterness and sharpness of garlic is associated with other things that you might need or dislike at certain moments. So the valence is crucial that you get and there are basically hundreds or thousands or tens of thousands of valence dimensions that specify how we perceive this texture of the pattern.
This is round one. Take care everyone. Thank you so much. Thank you too. Good talk. I really enjoyed this. Thank you very much. It was plenty of fun and the audience is all saying thank you as well. I think there were about a thousand people. Well, thank you very much.
Thank you, Yoshi. Please send me the MP3, if you don't mind. And Don, I don't know if you still are recording yours. Bye bye. Okay. Bye bye. Take care. Thank you all. Thank you all. Thank you all so much for being here. It was plenty of fun. There's plenty to talk about for round two, whenever that occurs, maybe toward the end of the summer or the middle of summer. We'll see people's willingness and ability.
The podcast is now finished. If you'd like to support conversations like this, then do consider going to patreon.com slash C-U-R-T-J-A-I-M-U-N-G-A-L. That is Kurt Jaimungal. It's support from the patrons and from the sponsors that allow me to do this full time. Every dollar helps tremendously. Thank you.
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"text": " okay this should be live if you can see this type in animaniacs into the chat animaniacs great there are already 275 people watching firstly it's a distinct honor to be here thank you both don and yosha i appreciate it tremendously and the audience does as well this theories of everything"
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"text": " Don, why don't we start with your definition of free will as well as how you view consciousness, and you mentioned that you would like to give an overview of your point of view on science and theories of everything in general."
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"text": " And then Yocha, you'll join afterward and commend Donald or amend him. And then I'll pretty much shut my mouth and allow you both to speak to one another, interjecting only seldom. Okay, thank you, Kurt. And good to see you, Yocha. My attitude about science is sort of like what Newton famously said, right? He said toward the end of his career that he thought of himself as like,"
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"text": " We've really not even begun to explore the possibilities of truth. And what's interesting is that Newton's followers famously didn't follow him on that. In the late 19th century, a lot of Newtonians thought that it was pretty much over. They had a theory of everything. There were a few little wrinkles. You know, there was the problem of Michelson-Morley experiment and"
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"text": " that we will always be on Newton's seashore. We'll always be like Newton, the little boy playing with pebbles and shells while the vast truth lays undiscovered before us, the ocean of truth. And it's for a principled reason that scientific theories, if you look at how they're structured, we start with a good scientific theory tells you exactly what its assumptions are. This is what I'm assuming."
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"text": " These are the derivation rules that I allow, and then everything about the theory follows from that. But that theory doesn't explain its assumptions. The assumptions are what's assumed. So Einstein, in his special theory of relativity, assumes that light travels at the same speed for all observers in all inertial reference frames. But that theory doesn't tell you what light is."
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"text": " As valuable as it is, it's one of the most important advances that humanity has made. We'll always and only scratch the surface beyond the seashore with Newton while the vast ocean lays undiscovered. So when we talk about theories of consciousness and free will and so forth going forward, I do it with sort of a very modest look at my own ideas. The ideas are going to be very much"
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"index": 26,
"start_time": 612.022,
"text": " In the framework of these are the best ideas we've come up with so far, of course, there's going to be much, much deeper work ahead and much more to discover ahead. So we just have to, as scientists, be precise about the current assumptions we're making and why we're making them and what follows from them, but be completely open to radical transformations in knowledge and radical new understandings. Your view on consciousness and free will."
},
{
"end_time": 670.401,
"index": 27,
"start_time": 642.91,
"text": " So in a nutshell, my views on consciousness are not physicalist. So physicalist approaches will say that we will start with space time and some of its contents, particles, neurons, neural systems, neural networks."
},
{
"end_time": 700.657,
"index": 28,
"start_time": 670.896,
"text": " Those will be, so that's a scientific theory in which those are our assumptions. Space-time and its contents are fundamental. And particular contents may be very, very important. For example, dynamical systems on neural networks, for example. And from that, we're going to try to boot up subjective experience. And that's perfectly a fine project to try to do. What I would want from that physicalist approach would be"
},
{
"end_time": 721.834,
"index": 29,
"start_time": 701.254,
"text": " not a hand wave but but a specific accomplishment so how do we start with dynamical systems of neural networks and come up with the taste of chocolate or the smell of garlic or something specific some specific conscious experience where we say my my scientific theory says why this"
},
{
"end_time": 752.295,
"index": 30,
"start_time": 722.415,
"text": " Dynamical system of activity in neurons or in computer system or something like that must be the taste of chocolate. It could not be the smell of garlic. And these are the principled reasons why. If something like that were on the table, I would be impressed. Until then, I'm not impressed. And there's nothing on the table yet that can do that. So that's one reason why I've been casting around and looking for a different direction. It's not starting with the physical"
},
{
"end_time": 780.401,
"index": 31,
"start_time": 752.739,
"text": " But starting somewhere else, and partly because, and we can talk about this in greater detail, because our best scientific theories right now, namely quantum field theory and general relativity on the one hand, and evolution of a natural selection on the other, both entail that space-time is not fundamental."
},
{
"end_time": 810.657,
"index": 32,
"start_time": 781.783,
"text": " Our two or three premier scientific theories really tell us their limits. They tell us that space-time cannot be fundamental and that therefore the contents of space-time are not fundamental. And so if we're going to look for a theory of consciousness and we start with something inside space-time, we're already starting where our best scientific theories tell us it's not fundamental."
},
{
"end_time": 839.855,
"index": 33,
"start_time": 811.63,
"text": " So as a result, I've been trying to then say, well, if space-time isn't fundamental and we don't yet know what's more fundamental, why don't we first start with trying to get a mathematical theory of consciousness on its own terms? What is consciousness? What kinds of assumptions can we make about it? And then we can ask the question, is consciousness more fundamental than space-time? What is the relationship between consciousness and space-time?"
},
{
"end_time": 869.804,
"index": 34,
"start_time": 841.305,
"text": " So I can go into some of the details if we want to on that model, but the big picture is that I'm taking very seriously that evolution of a natural selection entails that none of our sensory systems tell us the truths about objective reality, and that therefore space-time is not an objective truth, it's just a representation of fitness chaos, and that"
},
{
"end_time": 898.848,
"index": 35,
"start_time": 871.118,
"text": " Physicists are finding the same thing that Nima or Connie Hamed for example at Institute for Advanced Study at Princeton basically has lectures where he says space-time is doomed and here's why and The best physicists are now trying to figure out what's next space-time has had a good run for several centuries and it's over space-time is not fundamental and the contents of space-time are not fundamental and so we need to figure out and he's got things with you've working with Juan Maldacena on things like cosmological polytopes and"
},
{
"end_time": 929.172,
"index": 36,
"start_time": 899.343,
"text": " They're finding structures beyond space-time from which space-time can emerge as a projection, as a special case. But in these deeper theories, there is no time and there is no space. But there are symmetries that are true of, for example, scattering amplitude's data that are true that you can't see in space-time. They can predict the data, but they don't use space and time as the fundamental concepts. And I think that"
},
{
"end_time": 959.787,
"index": 37,
"start_time": 930.367,
"text": " As we start to go into scientific theories of consciousness, we cannot ignore what our physicist colleagues are telling us. They're telling us, if you're looking for something fundamental, it's not space-time, and in particular, it's not time. And that is a real show-stopper. It's for the physicists, too. I mean, trying to think outside of the time box is not easy for the physicists. And so what do we do if we don't have space-time, if we don't have"
},
{
"end_time": 988.336,
"index": 38,
"start_time": 960.299,
"text": " So I think that that's one of the interesting questions that we have to face. If we're going to come up with a theory of consciousness, what do we take as fundamental in our theory? If we take anything inside space-time, we're already sort of cutting ourselves off because we know that as physics progresses, things inside space-time will just be shown to be secondary. So we can go into my details on"
},
{
"end_time": 1005.538,
"index": 39,
"start_time": 988.797,
"text": " Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?"
},
{
"end_time": 1027.449,
"index": 40,
"start_time": 1006.049,
"text": " Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal. Rankings based on root metric true score report dated 1H2025. Your results may vary. Must provide a post-paid consumer mobile bill dated within the past 45 days. Bill must be in the same name as the person who made the deal. Additional terms apply. Sure. And Yoshua, please."
},
{
"end_time": 1059.923,
"index": 41,
"start_time": 1030.247,
"text": " It's interesting that you start outing yourself as a Mysterionist in a way, right? Mysterionism being the position that human minds are basically not equipped to understand how they work or how the universe works that they are embedded in at a very deep level. And I sometimes joke that Mysterionism is the position that something cannot be understood if it cannot be understood by Noam Chomsky. Noam Chomsky is a Mysterionist with respect to the mind. At the Science of Consciousness conference, he once"
},
{
"end_time": 1088.746,
"index": 42,
"start_time": 1060.282,
"text": " gave a presentation where he talks about Descartes and then mentions that Descartes was actually a very smart fellow because he could already anticipate stuff that would only be discovered much, much later on. And I was perking up and wondering, my God, Chomsky is giving this guy credit. And it turned out what he anticipated was that we would later like Chomsky discover that the mind is unintelligible. Right, so this"
},
{
"end_time": 1116.715,
"index": 43,
"start_time": 1089.258,
"text": " It's fascinating, of course, if you are one of the smartest minds of your own generation and you see that other people don't understand things and that you understand. And there is a boundary where nobody seems to have an understanding and you crash against it. You might think, okay, maybe there is no way that humans can do it. Not convinced that this is the case. I'm not a mysterious at this point in my intellectual career. And that's part because I come from the other side."
},
{
"end_time": 1146.783,
"index": 44,
"start_time": 1117.142,
"text": " So many of the things that people took as a given for a long time, like space and time, appeared to me in the beginning quite mysterious. So basically the dissolution of space and time was not that mysterious to me. Basically, I'm a computer scientist. I started very, very early on in my life to program before I properly understood mathematics and before I understood physics. And I understood how to make things in a computer."
},
{
"end_time": 1162.534,
"index": 45,
"start_time": 1147.039,
"text": " and Einstein's watch that is taking away and you can observe its movements and so on, but you cannot open it and you can come up with theories what's happening inside. To me, this watch was the screen of a computer."
},
{
"end_time": 1193.37,
"index": 46,
"start_time": 1163.422,
"text": " And I understood that there is no limit to what can be put into the computer if it has enough resources, right? So if the computer is fast enough and has enough memory, there is no pattern that cannot be shown on the screen. There is no limit to the sequence of patterns that is to be shown on the screen. So any observation that I am making, if I understand it as a pattern on some kind of screen that is visible to me, I will always be able to construct something, a mechanism that is on the other side and produces the sequence."
},
{
"end_time": 1221.305,
"index": 47,
"start_time": 1194.292,
"text": " And now the question is, can I produce an elegant sequence? Can I produce a minimal pattern? Can I produce something from which I think it's plausible that it emerged by itself? And that is, to me, this big important question of physics. The idea of physicalism to me is the notion that we live in a reality that is fully emergent over a causally closed mechanical layer. And we are in that base reality that emerges from it."
},
{
"end_time": 1249.48,
"index": 48,
"start_time": 1222.073,
"text": " And the alternatives to physicalism is that the space layer is somewhere else. Because even if we live in a simulation that is created by some kind of supernatural being, something must have created the supernatural being and its parent universe. Right. So ultimately every supernatural event is going to have some kind of natural course, some kind of prime mover that is taking away in the void and producing the patterns that you observe. And the patterns that you observe are so damn regular."
},
{
"end_time": 1274.753,
"index": 49,
"start_time": 1249.957,
"text": " There is all this conservation going on of information that doesn't seem like a conspiracy to me. It seems that we're not in a simulation. It seems that the idea that consciousness could be primary to our reality is not true, because consciousness being primary means that you would have to live in somebody else's mind, that we live in some kind of conspirational simulation that somebody has set up for us."
},
{
"end_time": 1296.766,
"index": 50,
"start_time": 1275.145,
"text": " Well, that is possible and I can principle not exclude it because there can be no evidence that can ever be fully conclusive if somebody sets it up to deceive me. There is no reason for me to believe it because they're not enough things happening in my reality that counteract the notion that I live in a mechanical universe. The few things that pop up, I can still explain this by faulty memories and psychosis."
},
{
"end_time": 1326.647,
"index": 51,
"start_time": 1298.012,
"text": " So the only thing that needs to be explained, that was puzzling people like Turing and other thinkers, is there's a possibility that telepathy is true. If that would be true, it would not be compatible with the way in which we understand physics right now. And there's this question, is there a point at which we have to discard physics fully and accept that you live in some kind of simulation, in some kind of dream universe that somebody has set up, like a computer game where you can arbitrarily break causality when it's convenient?"
},
{
"end_time": 1356.783,
"index": 52,
"start_time": 1327.022,
"text": " Or is this something that we need to extend physics? Or is it just something where our minds are playing tricks with us? And we know our minds are playing lots of tricks with us. So Turing considered the possibility that telepathy exists as very real to the point where he included this in his 1950 paper, Computing Machinery and Intelligence, where he sketches out the Turing test and seriously asked what a Turing test would have to involve with such a system, the ability to be telepathic."
},
{
"end_time": 1376.732,
"index": 53,
"start_time": 1357.244,
"text": " And if it's not, what difference would it make? Doesn't get to the point where you assess out loud that if telepathy is possible, you cannot be sure which of your thoughts and feelings originate in your own brain. They could come from somewhere else, right? So this opens up the door to lots and lots of things. But for the time being,"
},
{
"end_time": 1406.425,
"index": 54,
"start_time": 1377.244,
"text": " I think that the evidence for telepathy is weak. And if telepathy would exist, I would be seriously willing to consider this together. This is not clear by whether we cannot find a mechanical explanation for it. There's always going to be some kind of computer program that explains the patterns on the screen. Now, if we think about space, to me as a kid that was programming, the notion of a continuous space never made sense."
},
{
"end_time": 1429.036,
"index": 55,
"start_time": 1407.329,
"text": " Because it's not computable. I cannot write something that is continuous space. And when I tried to wrap my mind around the mathematics, the language broke. I was not able to understand how to make a point that is infinitely small, yet fits together. If you add infinitely many of these points into a continuum, this doesn't work, right?"
},
{
"end_time": 1446.032,
"index": 56,
"start_time": 1429.309,
"text": " It's not a problem to make something that exactly looks like this. It's not a problem to make a computer game that looks continuous. It's not a computer game that produces physics that looks similar to what we can observe, at least in the simplification. Of course, our computers are extremely inefficient when it comes"
},
{
"end_time": 1475.384,
"index": 57,
"start_time": 1446.032,
"text": " to simulating the substrate layer, the quantum mechanics that we can observe or a layer below the quantum mechanics, because quantum mechanics is probably not the lowest layer in which physics plays out. It's just the lowest layer in which we can currently make observations that we can conceptualize. And this leads us to what you also mentioned, what is a photon? I don't think that Einstein started out with the assumption that the speed of light is fixed. I think it was a derivation that he made."
},
{
"end_time": 1504.053,
"index": 58,
"start_time": 1475.776,
"text": " He concluded that the speed of light is fixed. And he basically, once he had this conclusion, he had implications for the possible descriptions of space-time that emerged. Because when the speed of light is fixed, you end up with some very interesting paradoxes if you stay in a Newtonian universe, right? You have this issue, imagine you fly in a very fast spaceship and you are lighting, putting light out of your flashlight inside of your spaceship."
},
{
"end_time": 1534.258,
"index": 59,
"start_time": 1504.48,
"text": " wouldn't the speed of light necessarily add up to the speed of the spaceship to an external observer, right? So wouldn't this external observer not need to observe a different speed of light than the person traveling in a spaceship? And if the speed of light is constant always, it means that the thing that now has to change is time or space or both, right? You can still fix this if you make sure that the speed of time runs in a different way. And this leads us to the insight that"
},
{
"end_time": 1563.643,
"index": 60,
"start_time": 1534.684,
"text": " The time and space that we observe from our own perspective as emergent observer and whatever universe produces us are interdependent. They're not independent of each other. The speed of light depends on the trajectory that the speed of time depends on the trajectory that you are taking through the universe. And if you want to think about something that could be more fundamental, we would say that the photon is a carrier of the electromagnetic force. It's a type of boson, which means that"
},
{
"end_time": 1590.64,
"index": 61,
"start_time": 1563.899,
"text": " can be described as a certain pattern that has an integer spin, and it has the property that it is describing the potential value for measuring some electromagnetic interaction. So if we take space time from the perspective of the observer, it's the set of locations that can contain information and the set of trajectories that the information can take. And the photon is a model of information traveling through space time."
},
{
"end_time": 1613.541,
"index": 62,
"start_time": 1592.5,
"text": " And what we have discovered and what Einstein also sometimes suspected is that space itself cannot be fundamental. And there were concrete reasons to see this, because what was discovered during Einstein's career even, and he was aware of this discovery, was that there were singularities in space-time."
},
{
"end_time": 1639.343,
"index": 63,
"start_time": 1613.968,
"text": " which means points at where the mathematics of continuous space breaks down. So your mathematics doesn't work anymore. You have some kind of a division by zero, something unpleasant happens where your mathematics is no longer valid. And what Einstein saw is that he can fix this by shifting the singularities around in our spacetime model. And we can basically put them below the carpet. You can put them in centers of mass,"
},
{
"end_time": 1668.319,
"index": 64,
"start_time": 1640.128,
"text": " So in the center of mass, there is basically something like a little black hole where mathematics doesn't work anymore. The mathematics of space-time where your mathematical description of that world doesn't work anymore. And what could be more fundamental than space-time? I think it could be transitions. So you describe the universe as some kind of state vector, a set of information, and this information is dynamic. You have the way in which information moves between the locations. And in this paradigm, the speed of light,"
},
{
"end_time": 1698.285,
"index": 65,
"start_time": 1668.951,
"text": " could be the rate at which information propagates between locations. And this would be an upper limit of all interactions that you observe within this lattice, where stuff is densely connected. What would be necessary if you have a set of locations, some kind of graph, a causal graph and information flowing between them to understand that there is causal structure? Well, you need to understand where the information comes from to understand what it signifies so you can model it."
},
{
"end_time": 1724.599,
"index": 66,
"start_time": 1698.916,
"text": " How can a single bit mean anything to you if it's just a single bit, if it's not attached with the source, with the type, with the context? So what could be a way to figure out where information comes from? Well, it needs to have some kind of momentum, some kind of direction to carry information about direction. And you send this to a graph that by itself just has just locations, connections. The only way that you can do this is if this thing is"
},
{
"end_time": 1748.49,
"index": 67,
"start_time": 1724.838,
"text": " extended if it's not just a single location to which the information propagates, but if it's neighboring connections and you get information that verifies it. So you need to be in some kind of densely strung lattice for information that you can pinpoint. Basically, you need to have something that looks like a continuous space. So you can identify controllable structure that you can identify where stuff comes from, like a photon."
},
{
"end_time": 1775.35,
"index": 68,
"start_time": 1749.121,
"text": " And if there is information that is traveling across distance, so to speak, that is not local, that is not going through densely connected local connections, but that is going over individual long-range links, this information will look like a random fluctuation or a distant entanglement that you can no longer track if you don't know where it originated. And this will look like something like indeterminism from your local observer perspective."
},
{
"end_time": 1805.657,
"index": 69,
"start_time": 1776.015,
"text": " Still, it would not be in contradiction to the preservation of information. It would still be a universe in which information is not invented, but in which the amount of discernible information is constant. And if the universe was not in such a way that information would be preserved, of course, it would not be learnable, because it would mean that the present state of the universe is forgetting what happened before in the universe. It gets disconnected. The world line of the universe just gets disconnected."
},
{
"end_time": 1829.462,
"index": 70,
"start_time": 1806.032,
"text": " And so from an epistemological perspective, we can only learn the aspects of the universe that look like they are conserved. If there are things in the universe that are not conserved, then they will not be intelligible to us. And of course, it's conceivable that the universe is some kind of automaton that forgets information. Another thing that shows us that space-time cannot be fundamental besides"
},
{
"end_time": 1851.766,
"index": 71,
"start_time": 1829.787,
"text": " about theorem which destroys the notion of locality is the notion of the collapse of the wave function basically this collapse of the wave function is the point in the history of an observer beyond which we cannot obtain a model of locations of events in time and space right beyond that point it's no longer not just"
},
{
"end_time": 1874.821,
"index": 72,
"start_time": 1852.142,
"text": " that we don't have enough information to construct it, but it makes no sense anymore to assume that the photon was at a particular point when it went through the double slit. At this point, the space-time model breaks down. The space-time model is a mathematical abstraction that works relatively well to look at things happening in the limit, but it's not a model that can be fundamental, I think."
},
{
"end_time": 1899.991,
"index": 73,
"start_time": 1875.896,
"text": " And but I'm not a physicist, so I'm not actually qualified to have these opinions. This is just what it looks like to me as a computer scientist who tries to understand the mind and things like Donald that we have to understand a certain degree of physics to make sure that our theories of consciousness are tight and that that makes sense. And we have to understand in which way they could possibly relate to physics."
},
{
"end_time": 1930.469,
"index": 74,
"start_time": 1900.64,
"text": " I'm less convinced that a deep understanding of physics is necessary or that physics is going to teach us about consciousness, in part because I don't think that consciousness is that mysterious anymore. I spent a lot of time in my life thinking that it was mysterious, but it seems to be a riddle that can be solved. And basically, I think that there's some aspects to consciousness, for instance, that you're observing yourself to be observing, but consciousness is"
},
{
"end_time": 1957.022,
"index": 75,
"start_time": 1931.561,
"text": " Something that is entirely virtual. It's not a physical thing. Electrons, photons, physical entities, neurons, brains cannot be conscious. They're just mechanisms. And what we can see is that the elements of our consciousness are not mechanical. They're magical somehow. There is magic happening. And if there is magic happening, it means that it's an a causal structure. It's something that has been made on some kind of causal loom."
},
{
"end_time": 1978.422,
"index": 76,
"start_time": 1957.346,
"text": " but that is not necessarily built in the same mechanical way as physics is built. It's a story. It's a, it's a tale being told by a physical system to itself. And if you think about organisms, you often think of them as physical systems and then neither, right? The organism doesn't exist. It's not the same if you think about it."
},
{
"end_time": 2005.964,
"index": 77,
"start_time": 1978.899,
"text": " What exists are cells that interact with each other. And even the cells don't really exist. What exists are molecules. And even the molecules don't really exist, right? They're all layers of descriptions. They're models that we can make because they are coherent. They hold to some degree. It might be freshening out at the boundaries, but there are ways of thinking about the flow of information in the universe. And the organism is a coherent pattern that you observe in the interaction between cells."
},
{
"end_time": 2034.855,
"index": 78,
"start_time": 2006.613,
"text": " And the cells have been set up by evolution to interact in this coherent pattern, because when they interact as if they were driven by a single spirit, by a single target, by a single telos, and if their behavior is coherent and consistent, that a state building, then they have an advantage over cells which don't do that and just fight for themselves, because together they can play longer games. By playing longer games, they can occupy a niche in nature that cannot be occupied by control systems that play shorter games."
},
{
"end_time": 2062.449,
"index": 79,
"start_time": 2035.35,
"text": " This is the benefit that organisms have, these coordinations between cells. And an organism is a function that describes this pattern in the cells. And the organism is facilitated by information processing across cells, among other things. To coordinate its interactions, the organism needs to have something like a telegraph network by which it's able to make models of reality and coordinate them between the cells and coordinate the behavior of the cells."
},
{
"end_time": 2089.275,
"index": 80,
"start_time": 2063.012,
"text": " And in animals, this telegraph system is facilitated in large part by the nervous system. It would not be necessary that the nervous system, basically every cell type can do this. But if you want to make it fast, you need to have specialized cells that have a very quick, expensive metabolism and can send information over very long distances very quickly, which other cell types cannot. So humans are a specific type of cells that allow particular kinds of information processing."
},
{
"end_time": 2112.244,
"index": 81,
"start_time": 2089.94,
"text": " And this information processing has the property that it can put stuff on the screen. So it's some kind of computer. It's the thing that can produce arbitrary sequences of patterns if it discovers a suitable function to produce them and implement them in the distributed networks of cells. And part of what they're doing is that they create a story about a being that lives in the outside world."
},
{
"end_time": 2141.766,
"index": 82,
"start_time": 2113.251,
"text": " And in our culture, we have difficulty understanding how that is because we, in our culture, as a default, teach our kids that what they see is the physical world, that the physical world has sounds and colors and so on. Only much later we tell them, well, it's slightly more complicated and sounds and color are not actually in physics. Everything that you consider to be sounds and colors is photons. Photons make electromagnetic interaction, which let air molecules push against each other so they can form regular waves."
},
{
"end_time": 2170.572,
"index": 83,
"start_time": 2142.159,
"text": " And colors are local dimensions that you get by measuring sampling the frequency of the electromagnetic spectrum using different receptor types and making a model of them using polar coordinates. Right. So this is something that we don't tell the story fully to our children, which makes it even more confusing. And then we tell them photons are actually not little billiard balls, but there are regions in the space time that have a potential for an electromagnetic interaction."
},
{
"end_time": 2199.121,
"index": 84,
"start_time": 2171.135,
"text": " And this space that you're talking about is the photonic space. It's the space where you can possibly have photon interactions. For some reason, it's three-dimensional. And maybe there are other spaces that are not three-dimensional. And maybe in these spaces, you cannot have interacting matter in the same way. Because maybe in order to get stable objects, you need to make little knots in the electromagnetic structure or in the spatial structure. And you cannot make knots in 2D and in 4D, they fall apart."
},
{
"end_time": 2228.541,
"index": 85,
"start_time": 2199.411,
"text": " So maybe that's the reason, or maybe there's another one and we haven't completely figured it out yet. And there are some candidates that explained by the space that you're in is three-dimensional. So why is it that we are interacting with the photonic space and not with the others? Why are the others not seeming to form a connected space? And this is connected letters. But we don't know the answer yet. At least I'm not aware of the work that is sketching out the answer. And if I stumbled on it, I pray that I understand it."
},
{
"end_time": 2251.596,
"index": 86,
"start_time": 2229.172,
"text": " But I think that there are other cultures that have a better intuitive understanding of what consciousness is. And if you look around, you find that some cultures don't find consciousness mysterious. I even suspect that in the core of our own culture, before the Tower of Babel that destroyed the shared understanding, it's still in there. So a little bit obsessed these days with thinking about"
},
{
"end_time": 2281.527,
"index": 87,
"start_time": 2251.8,
"text": " Genesis in the Bible and read this epistemologically correct, not as a myth that is a stand in for an origin theory until real science comes along, but as something that is literally true. So what would that mean? You know, I'm talking about the first book, I'm talking about the book that starts out with the creation of sky and darkness and heaven and earth and so on. And the thing with this story, if you take it literally the way in which Christianity interprets it,"
},
{
"end_time": 2307.125,
"index": 88,
"start_time": 2282.022,
"text": " It's a story about a supernatural being creating a physical universe. And what's wrong with the story is that whoever tells it to you had no evidence that it was true. So there is no claim. If somebody makes a claim without evidence, you don't have to listen. It could be interesting as a story for cultural reference, or it could be interesting as an idea for something that you could test. But if it's in principle not testable, this person cannot have that evidence."
},
{
"end_time": 2337.5,
"index": 89,
"start_time": 2307.654,
"text": " There is no secret source of knowledge that this person had. There is, in principle, nothing that some other person can have with some kind of backchannel by talking to a burning bush that would constitute a valid experiment. So this reading makes no sense. It would never make any sense, but it could make sense, especially if you understand that sky and ground and light and sound and plants and animals and their names don't actually exist in physics."
},
{
"end_time": 2368.183,
"index": 90,
"start_time": 2338.37,
"text": " They only exist in our mind as a division of the universe into separate objects, so they become intelligible to us. And the way in which we construct these objects is inside of the mind. So the creation of the universe that is being described in Genesis is not the physicalist universe with quantum mechanics. It's the creation of the experiential universe in which we are actually in, in which we find ourselves to be in. And the first thing that the mind is discovering when it creates this universe is how to make light."
},
{
"end_time": 2397.858,
"index": 91,
"start_time": 2369.377,
"text": " How to create neural oscillators that are creating a contrast between light and darkness. So separate the light from the darkness and then organize this into multiple dimensions until you get a space. And then you align the space with the information from your vestibular organs and what you get is the two-dimensional plane of the ground and the three-dimensional space of the sky above it. So after you create light and darkness, you create"
},
{
"end_time": 2423.524,
"index": 92,
"start_time": 2398.114,
"text": " Literally every mind does this in their cognitive development, the sky and the ground. And then you discover the objects in it. So you basically learn how to model materials in your mind. So you have solids, and you have liquids, and you have organic shapes, and you have animated agents. And then you discover features that you cannot interact with, like celestial bodies, and anchor them in the world, and you learn how to navigate this world."
},
{
"end_time": 2453.712,
"index": 93,
"start_time": 2424.104,
"text": " And then you discover all the plants and the animals and you construct them in your mind and you associate them all with their names. Again, of course, not a feature of the physical world. They are socially exchanged, these names and so on. We create this world together. And then last but not least, we create a person. So the thing that creates it is not a person yet. It's a mind that exists before a person is around. We don't remember how we made light. We don't remember"
},
{
"end_time": 2482.841,
"index": 94,
"start_time": 2454.121,
"text": " how we discovered the sky and the ground in the first space. This was another observing agent in our own brain. And this observing agent in our own brain at some point discovers the needs of a person, of the needs of an organism, the organism that its brain is embedded in. And it creates a model of that too. So it creates an agent that is observing this universe, that is embedded in this universe, because this first observer in our own mind,"
},
{
"end_time": 2508.695,
"index": 95,
"start_time": 2483.439,
"text": " is discovering that such an entity exists. It's a useful model to describe reality, that there is a person that has needs and desires and social embedding and dreams and hopes and memories and expectations. And it will create a story of that. And that story is just as real as the trees that exist in our mind as imaginations or the trees or that in the forest and beyond the horizon."
},
{
"end_time": 2539.087,
"index": 96,
"start_time": 2509.172,
"text": " and as real as the sky and the clouds and the colors and so on. But they're all virtual. They're all simulacra. They all exist to tell a story to the organism that is useful for the organism to model the world. And this part where we become a person seems to be happening, I think, around the age of one and a half to two and a half, roughly, in most children that I observed. And at this point, a person that is different from before emerges in their mind. It's not that there is nobody there before. It's just that the thing before is different."
},
{
"end_time": 2562.585,
"index": 97,
"start_time": 2539.616,
"text": " You notice that there's a gap in their memories. They have memories when they're in the first year when you talk to them, where they remember what happened and have expectations already. But later on, there's this point where they don't remember these things anymore. It's very weird. And most people, when they think back, don't have memories that they can consciously access before they're like two and a half years old."
},
{
"end_time": 2589.087,
"index": 98,
"start_time": 2563.2,
"text": " And so I wonder if this transition is the result of just a re-indexing of memories due to our newfound linguistic ability, so we can later on no longer access these memories, or if it's really just basically a new agent that is created by the first agent in its own image as an observer that is aware of the fact that it's observing. But in a different way, as men and women, as something that thinks it's a person, that thinks it's a human being."
},
{
"end_time": 2606.869,
"index": 99,
"start_time": 2589.565,
"text": " And I'm not a human being. I realized it at some level. I don't have an identity as a human being. This is a story that my mind tells itself as an additional thing. My consciousness doesn't have an identity. My consciousness is also not of the nature that it's the same as everybody else's consciousness, right?"
},
{
"end_time": 2625.486,
"index": 100,
"start_time": 2607.244,
"text": " The question, do we all have the same consciousness looking through different eyes or we separate consciousnesses is in some sense as meaningless as the question of asking is the text editor that you're running onto your computer, the same text editor that everybody else runs on the computer, or is it a different one."
},
{
"end_time": 2653.763,
"index": 101,
"start_time": 2626.886,
"text": " The program vert is in some sense a natural law. If you put the circuits of your computer in the same functional configuration, then those things are going to happen with the circuits of your computer and they will afford the following interactions. But the program vert doesn't have an identity and it's also not that it has no identity in the sense, it's just not a meaningful category to apply to it. In the same sense, my consciousness is not in this category that would have an identity or none."
},
{
"end_time": 2678.217,
"index": 102,
"start_time": 2654.787,
"text": " So it's not something that is shared with others, and it's not something that is separate from others. It's a principle that applies to the observation. And when the consciousness gets tied to a self model, then it becomes perspectival and I have an identity and so on. But this identity is a particular kind of model that my organism tells itself by changing certain factors in my own brain."
},
{
"end_time": 2696.954,
"index": 103,
"start_time": 2679.155,
"text": " Razor blades are like diving boards. The longer the board, the more the wobble, the more the wobble, the more nicks, cuts, scrapes. A bad shave isn't a blade problem, it's an extension problem. Henson is a family-owned aerospace parts manufacturer that's made parts for the International Space Station and the Mars Rover."
},
{
"end_time": 2725.452,
"index": 104,
"start_time": 2696.954,
"text": " Now they're bringing that precision engineering to your shaving experience. By using aerospace-grade CNC machines, Henson makes razors that extend less than the thickness of a human hair. The razor also has built-in channels that evacuates hair and cream, which make clogging virtually impossible. Henson Shaving wants to produce the best razors, not the best razor business, so that means no plastics, no subscriptions, no proprietary blades, and no planned obsolescence."
},
{
"end_time": 2741.8,
"index": 105,
"start_time": 2725.452,
"text": " It's also extremely affordable. The Henson razor works with the standard dual edge blades that give you that old school shave with the benefits of this new school tech. It's time to say no to subscriptions and yes to a razor that'll last you a lifetime. Visit hensonshaving.com slash everything."
},
{
"end_time": 2769.77,
"index": 106,
"start_time": 2741.8,
"text": " 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 dot com slash everything and use the code everything. OK, let's let Don respond. Well, there's quite a bit there. So on the. The nature of"
},
{
"end_time": 2799.343,
"index": 107,
"start_time": 2770.367,
"text": " the physical world and computation and the finiteness versus continuity of space-time and so forth. I think that the work, you know, the Gödel's incompleteness theorem is very relevant here, that the notion of truth is far deeper than the notion of proof. There are any system"
},
{
"end_time": 2829.189,
"index": 108,
"start_time": 2800.282,
"text": " Any computational system will have things that it can prove, but there will be truths that that computational system cannot access. And if you add those new truths, add a new truth of, you know, a girdle statement to your set of axioms, then there will be yet more truths that cannot be accessed from that. And so what you can compute is always going to be trivial to what is true."
},
{
"end_time": 2854.36,
"index": 109,
"start_time": 2829.991,
"text": " There will always be, as far as I can tell, again, it's sort of like Newton's notion of we're at the seashore and the vast ocean of reality, of the truths. He actually used the word truth. The vast ocean of truths is out there beyond what we can compute. And every truth that you add to your base for computation doesn't solve the problem."
},
{
"end_time": 2883.422,
"index": 110,
"start_time": 2854.684,
"text": " And you might say, well, that's true of abstract mathematics, but that's not true of physics. I mean, physics itself is computable. But there's some recent work suggesting that that's not the case. So Tony Kubit, a physicist, and his colleagues have recently proved that a very important problem to condensed matter physicists"
},
{
"end_time": 2910.657,
"index": 111,
"start_time": 2883.882,
"text": " called the spectral gap problem is not computable. And that's a stunning result. And they also suspect, and they're working on this, they haven't proven this yet, but that something that's a big open problem, I think the Millennium Prize committee has is this is one of their problems is to understand the Yang-Mills gas gap problem, which is, you know, why do"
},
{
"end_time": 2937.824,
"index": 112,
"start_time": 2911.578,
"text": " Photons and gravitons have no mass, but the carriers of the strong-weak force do have mass. And Kubit and his collaborators think, again, that we're going to find that something non-computational is going on here. It's not decidable. And my guess is that this is just the beginning, that we're going to find that as powerful as computation is, and I"
},
{
"end_time": 2967.244,
"index": 113,
"start_time": 2938.609,
"text": " I was in the artificial intelligence lab at MIT for my PhD and I'm all for AI and for computation and I, you know, I think it's fabulous what computation can do and the naysayers who think that the computation can't do amazing things and artificial intelligence can have, you know, important limits that I think that I disagree with the naysayers. On the other hand, I do believe Gödel's incompleteness theorem is correct and I do think that"
},
{
"end_time": 2995.981,
"index": 114,
"start_time": 2967.807,
"text": " The notion of truth is just vastly, the notion, the set of truths, I'll put it this way, the set of things that we can prove from any system is essentially probability zero in the set of all truths. In other words, we're always going to be, as Newton said, on the seashore with computation and is for principled reasons. So it's not a mysteriousism that's not founded, it's saying our best theories tell us"
},
{
"end_time": 3013.848,
"index": 115,
"start_time": 2996.22,
"text": " The truth and proof are not the same thing, and that proofs will always only leave you on the seashore. And so that's why, I mean, I didn't like that conclusion, but, you know, Gödel proved it, and now physicists are finding it in the spectral gap."
},
{
"end_time": 3043.985,
"index": 116,
"start_time": 3014.565,
"text": " As much as I like computation, I'm a computer scientist myself, as much as I like computation, I have to defer to the mathematical proofs that say computation goes thus far and no further. Then ask myself, okay, how can, so my conceptual system then is itself just a symbolic system with derivation rules. So what I can compute by my thought,"
},
{
"end_time": 3073.114,
"index": 117,
"start_time": 3044.309,
"text": " is also going to be limited, which is why I was saying upfront what I think about scientific theories, right? Scientific theories are going to have these limitations. We will put down a set of axioms. Each theory, a good scientific theory, will tell you exactly what it assumes. And it will also give you a hint about the kind of derivations that you can give from those assumptions. And then you use, you find what that theory will entail. But our best theories, like"
},
{
"end_time": 3102.278,
"index": 118,
"start_time": 3073.968,
"text": " quantum theory and relativity and evolution with natural selection. The best theories will also tell you where they stop. They will say we go this far and no further. And for example, physics tells us that space time itself cannot be fundamental, that the very notion of space time cannot be fundamental, which is stunning because physics for several centuries has essentially been the study of what happens in space and time."
},
{
"end_time": 3132.91,
"index": 119,
"start_time": 3102.944,
"text": " And so to say that space-time is not fundamental means that the physicists have to redefine what physics is about. And that's what, for example, Juan Maldacena and Neymar Condejamed are trying to do with things like the cosmological polytope and amplituhedron and so forth. They're finding structures where there are no Hilbert spaces. So there's no quantum theory. There is no time. There is no space. There are these positive geometries. And what you find is you can predict"
},
{
"end_time": 3151.869,
"index": 120,
"start_time": 3133.899,
"text": " events in space time like scattering processes that you see at the Large Hadron Collider, you can predict them and in fact you can actually compute them in some sense better than if you assume space time. So they're finding that if you use Feynman diagrams and try to compute"
},
{
"end_time": 3173.046,
"index": 121,
"start_time": 3152.227,
"text": " Scattering amplitudes for two gluons coming in and four gluons scattering out using the standard quantum field theoretic approaches where space and time is assumed. You get hundreds of pages of algebra and it's a mess. Whereas if you let go of space-time and look at these structures with symmetries that cannot be expressed in space-time, dual conformal symmetry"
},
{
"end_time": 3189.957,
"index": 122,
"start_time": 3173.49,
"text": " Then you find that the same scattering amplitudes can be processed in just two or three terms that you can write down pen and paper on a sheet of paper. So all of a sudden, so what they're seeing is space-time has had a good run, but"
},
{
"end_time": 3217.773,
"index": 123,
"start_time": 3190.145,
"text": " If you force yourself to stick with space-time, then the math is ugly. You get hundreds of pages of algebra to compute scattering amplitudes. You can't see the symmetries that are there, like dual conformal symmetry. If you let go of space-time, you're finding these amazing structures that they don't know what they're about, but all of a sudden you see the right symmetries and the computations become trivial. So there's some big hint that I think on a couple fronts, from Gödel"
},
{
"end_time": 3241.032,
"index": 124,
"start_time": 3218.302,
"text": " And from the work by Tony Kubit and his team that the computation is as powerful as it is, and as much as I love it as an AI person and a cognitive scientist, it's always going to be on the seashore with Newton. And when we let go of space time, we're still, of course, as theorists, always going to have"
},
{
"end_time": 3264.087,
"index": 125,
"start_time": 3241.544,
"text": " A finite set of axioms and derivations about the cosmological polytope and so forth that Neema and Juan are finding. We're still going to have a finite set of concepts and derivations, so we're not going to get around Gödel's incompleteness theorem, but at least we're going beyond the notion of time, which is really critical."
},
{
"end_time": 3287.415,
"index": 126,
"start_time": 3264.701,
"text": " And that also cuts at the computational issues pretty interesting computational complexity is is about a lot of it about time complexity and what physicists are telling us is that ultimately we're gonna have to let go of the notion of time and so as computer scientists we're gonna have to rethink complexity issues when the very notion of time itself isn't fundamental."
},
{
"end_time": 3314.787,
"index": 127,
"start_time": 3287.944,
"text": " So that's going to be a real kicker for us in computer science. How do we think about complexity issues when time itself is not the right way to think about things? And therefore, the sequence of computations in time is not the right way to think about things. We have some really deep thinking to do ahead. But where I think we share some common ground, Yosh, is I think a lot of"
},
{
"end_time": 3345.503,
"index": 128,
"start_time": 3315.657,
"text": " Our experiences and so forth are models that we build. I think that we are building internal models. But the question is, what is the apparatus that's building those models? And I'm saying it's nothing inside space and time. So in particular, I'll be very, very explicit. I don't think that neurons exist when they're not perceived. I don't think space time exists when it's not perceived."
},
{
"end_time": 3374.991,
"index": 129,
"start_time": 3346.135,
"text": " I think neurons and space-time and even particles are simply data structures that we use. And there is a formulation of quantum theory that's very similar to this. It's called cubism, quantum Bayesianism, Chris Fuchs and David Merman, where they take this point of view that it's the every act of observation"
},
{
"end_time": 3402.125,
"index": 130,
"start_time": 3375.418,
"text": " In physics, every experiment that you do is an act of fact creation, right? That it's not that there are pre-existing particles with pre-existing states and you're measuring those states. Rather, they're subjective basions. So all the probabilities in quantum theory are subjective probabilities. They're not objective probabilities. And every outcome is a"
},
{
"end_time": 3429.104,
"index": 131,
"start_time": 3402.756,
"text": " a fact creation. And they do have, I mean, Chris Pukes has a very interesting 2010 paper called Cubism that I highly recommend. And in that paper, he actually points to a very interesting quantum discovery that there's a sequence of, what's proven is that even if you know what the outcome of your experiment is going to be with probability one,"
},
{
"end_time": 3459.701,
"index": 132,
"start_time": 3430.503,
"text": " That does not entail that the outcome is there and exists independent of your observation. That's a stunning thing to say. You know with probability one what you're going to measure, and yet you can prove with quantum mechanics that it's impossible that the outcome was there, the value existed before you made the measurement. So it's really the case that the acts of observation are fact creations, not fact discoveries."
},
{
"end_time": 3489.838,
"index": 133,
"start_time": 3461.305,
"text": " So most of the work that's done in consciousness assumes, and I would say this is 99% of the theories that I've seen in consciousness, assume that space-time is fundamental, assume that physical particles are fundamental, and that somehow neural activity in humans and perhaps other kinds of more complex activity in AIs creates consciousness."
},
{
"end_time": 3516.186,
"index": 134,
"start_time": 3490.333,
"text": " But the very founding assumptions that space-time is fundamental, that neurons exist when they're not perceived, contradicts our best physics. It also contradicts evolution of natural selection, which is very, very clear. Natural selection makes it very clear that the probability is zero, that the sensory systems of any organism tell them any truths about objective reality."
},
{
"end_time": 3546.51,
"index": 135,
"start_time": 3516.817,
"text": " They tell what they tell organisms, sensory systems evolved to tell organisms how to behave in order to stay alive, period. That's it. And so that gives you a user interface for staying alive, but gives you no access to the truth. And that fits with what physics is telling us that space time is a user interface, but it's not the final truth. And so what I want from a theory of consciousness as a scientist"
},
{
"end_time": 3568.626,
"index": 136,
"start_time": 3546.834,
"text": " I want a clear statement of what am I assuming? What are the exact things that my theory takes as primitive? What are the exact rules that allow me to derive things from those primitives? And how exactly do I get the taste of chocolate from that? That's what I'm looking for from the theory of consciousness."
},
{
"end_time": 3595.469,
"index": 137,
"start_time": 3568.899,
"text": " precise statement of exactly what i'm assuming upfront with mathematical precision and then precise derivation if i'm not taking the taste of chocolate as fundamental if i'm saying that somehow some dynamical system is going to give it to me that i want to know exactly which dynamical system is giving me the taste of chocolate and why that dynamical system could not be the smell of garlic i want to know exactly otherwise there's no there's no real science on the table"
},
{
"end_time": 3625.282,
"index": 138,
"start_time": 3596.015,
"text": " at all. So that's what I'm looking for is theories that say exactly what the assumptions are and tell me exactly for at least one specific conscious experience, how that conscious experience must be derived in that way. And so that's where I'm coming from on those. Now, in the case of cells in the brain, I would just mention something that's very interesting that you probably know about Mike Levin's work. Right. And he's finding that"
},
{
"end_time": 3638.746,
"index": 139,
"start_time": 3625.981,
"text": " that cells, not just neurons, but any cell in animals that in fact outside of the brain, they can learn and they can compute"
},
{
"end_time": 3665.486,
"index": 140,
"start_time": 3639.445,
"text": " and they can do morphogenesis of the cell's body. They use gap junction, communication, electric. So they're effectively doing what neurons do, but in a very, very different way. And this is all cells can communicate in this way with gap junctions and so forth. So I suspect that we're going to find that"
},
{
"end_time": 3694.548,
"index": 141,
"start_time": 3666.391,
"text": " Neurons aren't special in the sense of being information processors, that information processing, and this seems to be where Mike is heading, is that information processing is happening in what he calls these bioelectric fields, even if there are no neurons. And they can learn, they can retain memories, and they can be very intelligent. And so even as neuroscientists, we may find that we'll have to expand our horizons beyond neuroscience,"
},
{
"end_time": 3720.009,
"index": 142,
"start_time": 3694.991,
"text": " Understand if I were reductionist and trying to do biological reduction, I would at this point with Mike Levin stuff be interested to say, well, maybe I wouldn't necessarily reduce consciousness to neural activity. Maybe these gap junctions and the computations that cells can do would also be a suitable format. But again, I'm not a reductionist in that sense, but I'll stop unless you respond. Yes, sir."
},
{
"end_time": 3752.312,
"index": 143,
"start_time": 3722.619,
"text": " Thank you. You went very far and wide and try to be a little bit more concise. Let's start out with Gödel. Gödel's proof had a very profound and not necessarily very positive influence on philosophy. And basically, Lukas and others in philosophy opened up a tradition where the underlying current is that what Gödel has shown is that mathematics is impotent to describe reality."
},
{
"end_time": 3782.637,
"index": 144,
"start_time": 3753.695,
"text": " And therefore, reality can only be described by people who don't really know mathematics, that is philosophers. So philosophers like that intuition, but it implies that there is something beyond mathematics that allows you to make sense of things that assign truth. And slightly deeper, when you say that you like computation and you value it and so on, and you see its limits, it implies that you see what comes beyond these limits and you're using that thing beyond the limits to think."
},
{
"end_time": 3811.766,
"index": 145,
"start_time": 3783.626,
"text": " And I don't think that you are. Everything in my own mind that I can observe, when I observe myself perceiving, when I perceive myself reflecting, when I perceive myself reasoning, is computational. It means that I go from state to state in a somewhat deterministic way. The random parts are just deleting bits that I computed before, so I have to do it again. The randomness and determinism doesn't help me. So the part of my mind that is relevant to my thinking"
},
{
"end_time": 3841.51,
"index": 146,
"start_time": 3812.193,
"text": " is fundamentally computational. What Gödel discovered and is often misunderstood and also by Gödel himself is a very important thing. What Gödel has discovered is not that truth is deeper than proof. That was, in some sense, the suspicion which he started with. He knew that, in his view, that truth is platonic, that things can be true or not, regardless of whether we find out or whether it can be found out. And he hoped"
},
{
"end_time": 3871.869,
"index": 147,
"start_time": 3841.954,
"text": " to find a notion of truth, of proof that could reach truth. And he found that it couldn't, and he found this in a devastating way. And he drew the conclusion that there is truth that cannot be found with mathematics. And the opposite is true. There is no deeper notion of truth than proof. You see, perception cannot be true or false. Perception just is. Physics, physical events out there in the universe"
},
{
"end_time": 3876.988,
"index": 148,
"start_time": 3872.108,
"text": " cannot be true or false, they just are. A pattern that you observe is not true or false, it just is."
},
{
"end_time": 3907.125,
"index": 149,
"start_time": 3877.688,
"text": " You could be erroneously thinking that you're perceiving a pattern when you don't because you're suffering from false memory or a delusion or whatever that makes your thinking or perception inconsistent. But the pattern itself is not true or false. It's an interpretation that can be true or false. And the interpretation has to be in a symbolic language to have the property that can be true or false. A perceptual interpretation by itself is not true or false. It just is. So in order to be true or false, you need to have a language."
},
{
"end_time": 3931.63,
"index": 150,
"start_time": 3908.063,
"text": " The language needs to be defined in such a way that truth can be established and the process of establishing truth is a computation. There are two types of languages in which truth can be defined. The language of classical mathematics is a stateless language. It's one where time doesn't exist, where everything happens all at once or in some kind of eternal moment."
},
{
"end_time": 3962.278,
"index": 151,
"start_time": 3932.278,
"text": " So if you want to go from state to state in this language of eternal mathematics, in the stateless language, you just assign an index and then you iterate over the index and you do this in a single instant in one moment. And the stateless mathematics has a very beautiful property. It allows you to deal with infinities because you can now construct functions that take infinitely many arguments in a single step, perform an operation over them in a single step and give the result back in a single step. It's a language in which you can assign a value to pi."
},
{
"end_time": 3990.845,
"index": 152,
"start_time": 3963.575,
"text": " In the computational system, you cannot really assign a value to pi. You can have a function that gives you digit by digit, but you never get to the latest last digit. It also means that pi can never be written down in such a way that you can have a process that relies on knowing all the digits of pi and consumes them to tune the outcome of some physical process. If you make the switch to a stateful language, in which you can only go from step to step,"
},
{
"end_time": 4020.964,
"index": 153,
"start_time": 3991.305,
"text": " You're losing certain things. You're losing the ability to treat pi as a value. Pi is now suddenly a function that you can only approximate to a certain degree. And many other things stop being values. You get a fundamental difference between a value and a function. A value is something that you have already computed, that you know how to compute by extension. And this means that also the truth changes. Truth is no longer this platonic thing that precedes mathematics and where we can use mathematics as a tool to figure it out."
},
{
"end_time": 4041.408,
"index": 154,
"start_time": 4021.544,
"text": " It has to be contingent on the language in which you use it. If your language has internal contradictions, then truth becomes impossible to determine. You get into areas in this language where it falls apart. You can no longer use it to express coherent thoughts about reality and coherent models about reality."
},
{
"end_time": 4070.401,
"index": 155,
"start_time": 4042.142,
"text": " You can never make statements in the language that you can prove outside of the language. So you cannot use your language to prove things that cannot be described in the language. Your only hope to prove statements about the universe that you exist in in the language is that you are able to recreate the observations that you make inside of the language, which means you recreate a model of the universe that is so good that it gives you what you observe currently."
},
{
"end_time": 4094.753,
"index": 156,
"start_time": 4070.794,
"text": " And then you can hope that the statements that you make in your language capture something about the reality outside of you that gives rise to your observations. Of course you cannot know because it could also be different. But if your language is not able to produce what's on your screen, then your language is wrong. And Hilbert basically gave out this task to mathematicians to find a machine"
},
{
"end_time": 4119.565,
"index": 157,
"start_time": 4095.64,
"text": " any kind of structural sound language that is able to run the semantics of mathematics without breaking. And what Gödel discovered is that the semantics of stateless mathematics cannot be recovered. If you assume that there is a solution to get stateless mathematics to work, you will run into contradictions of the way that Gödel discovered. But there is a way out. You just"
},
{
"end_time": 4145.691,
"index": 158,
"start_time": 4120.367,
"text": " drop the notion of truth that is independent of the sequence of operations, the number of the set of steps that you took, the algorithm that you took to get to your result. It means that when you have a self-referential statement, like this sentence is false, right? This is a sentence that of the type that Gödel has shown leads into contradictions. If you assume that there is a stable notion of truth that is stateless,"
},
{
"end_time": 4174.411,
"index": 159,
"start_time": 4146.476,
"text": " If you accept that truth is not necessarily a stable value and you look at the sentence, then as long as you look at it, the truth value will fluctuate because the assumption that the sentence is true will lead to the sentence being false and vice versa. So suddenly you have no longer a stable truth predicate. And it just means that the property of the languages in which you can actually deal with truth and assign it is that under some circumstances, the truth predicate will not be stable."
},
{
"end_time": 4205.998,
"index": 160,
"start_time": 4176.084,
"text": " And it's fine. There's nothing wrong with that. And the same thing applies to the Entscheidungsproblem that Turing was dealing with when he came to the Harting problem. He defined originally the Turing machine in such a way that we could translate stateless mathematics into algorithms. And this might require that you have to go through an infinite sequence of steps. And if you make this assumption that you sometimes, in order to get to a truth, you have to go through an infinite sequence of steps, you run into contradictions."
},
{
"end_time": 4236.698,
"index": 161,
"start_time": 4207.551,
"text": " So you might use an unbounded sequence of steps that gives you continuously results. That's fine. But you cannot accept that anything exists in any kind of universe that has causal structure that is going to produce you a solution to the heartache problem, which would give you back stateless mathematics. So basically what Gödel and Turing have shown is that stateless mathematics doesn't work. And when we look back at the history of mathematics, mathematicians have never used stateless mathematics. They only pretended to."
},
{
"end_time": 4258.848,
"index": 162,
"start_time": 4237.125,
"text": " Whenever they actually wanted to compute something with mathematics, they under the hood use stateful descriptions. They never took in infinitely many arguments and performed infinitely many operations on them. And the intuition that stateless mathematics makes sense is because we had this intuition that continuity, that space and time in a continuous fashion exist."
},
{
"end_time": 4289.548,
"index": 163,
"start_time": 4259.838,
"text": " Why do we have this intuition? Well, that's pretty easy to answer, right? The number of things that we interact with, if we zoom in, we find that they are discrete. All our observations have a discrete resolution in time and in space. All our knowledge that we store about these observables has a discrete number of bits that we can assign to them. There is only a finite number of information that we can access and that we can deal with as an observer that is embedded in this universe. So everything was discrete to begin with."
},
{
"end_time": 4317.654,
"index": 164,
"start_time": 4289.906,
"text": " But it's too many parts to count. If you deal with too many parts to count, the insight that the number of atoms that you are in an ocean is a finite bounded number doesn't help you at all because it's still almost infinite from the perspective of an observer. So when you want to describe what the ocean is doing, it doesn't help to count the molecules in it and to assign locations to them and model the interactions. It doesn't work. There is too much"
},
{
"end_time": 4346.34,
"index": 165,
"start_time": 4318.131,
"text": " So when you look at the dynamics of too many parts to count, you're looking for operations that converge in the limit, which means they behave quite similar, whether you're using a trillion or 10 trillion or a gazillion particles. Once you have these operators that give you the same dynamics under all circumstances, when you take more and more elements to them, this part of mathematics that describes the convergent operators, that's geometry."
},
{
"end_time": 4374.599,
"index": 166,
"start_time": 4347.517,
"text": " And some of geometry is uncomputable, so you can only approximate it. But our brain has discovered geometry to deal with a world of too many parts to count. And this plays into what you're pointing out when you say that our perception doesn't give us reality, it gives us something that we can work with. Of course, the reality that we are embedded in has too many parts to count. We need a different reality. We need one that you can actually handle, even if it's not computable and can only be approximated."
},
{
"end_time": 4401.032,
"index": 167,
"start_time": 4375.316,
"text": " And this experiential reality is a very coarse simplification. It's about as coarse as a gaming engine is when you play a computer game as compared to real physics. It's not much better than that. In many ways, it's even worse, which you can verify if you put yourself into a lucid dream and look at the fidelity of what your brain is able to generate. Light switches will usually not work. You will not be able to read the same stuff twice on the same page and you imagine it and so on."
},
{
"end_time": 4428.729,
"index": 168,
"start_time": 4401.357,
"text": " There's only so many bits in your working memory. The fidelity of what your perceptual system can track and imagine is limited. It's relatively easy to overcome that. Don't really know what the number of bits in my working memory is, and I would be very curious to find out. But it's not as big as I thought when I was a child. It's not infinite. It's not unlimited. Perception of infinity is super easy to generate when your mind is very finite. Super easy to overwhelm my finite resolution mind."
},
{
"end_time": 4459.906,
"index": 169,
"start_time": 4430.333,
"text": " So this deep thing that Gödel is misunderstood, that Gödel has not discovered that mathematics cannot reach truth, but that truth is no more than the result of a sequence of steps that is compressing a statement to axioms losslessly and doesn't go beyond that. That was the deep insight and it's one that basically has not percolated in most areas of philosophy and even physics yet because the physicists have checked out the code base for mathematics before that result was obtained and understood."
},
{
"end_time": 4488.695,
"index": 170,
"start_time": 4460.384,
"text": " So basically that we need to switch from continuous stateless mathematics to constructive mathematics that was not understood back then. And it needs to be understood now. So basically my question to somebody like Donald would not be so much how to explain the spectral gap from because I think problems of this case of this type are with the result of using continuous notions of space time and infinities."
},
{
"end_time": 4518.166,
"index": 171,
"start_time": 4489.172,
"text": " and assuming them as given. So that's a statement about certain theories that are expressed in a language that has inconsistencies. In this language, with these inconsistencies, you get to the point that you cannot get certain results. There's also an issue of computational irreducibility, which is difficult to understand in stateless mathematics. Computational irreducibility is a property of a system that means that you cannot obtain the state of the system without running the system to that point."
},
{
"end_time": 4546.186,
"index": 172,
"start_time": 4519.224,
"text": " There is no way to predict the system except by taking the system with all its detail and fidelity and going through the sequence of steps. So you cannot predict what the universe is going to do when the universe is computationally irreducible. You're going to predict some things, but not all of things. Indeed, some things only with a certain degree of certainty because you can often not insulate them from the parts that you cannot predict because they are computationally irreducible."
},
{
"end_time": 4573.285,
"index": 173,
"start_time": 4546.834,
"text": " In a universe that is played out and implemented in a stateless language, that is a confusing property, because the cost of computation doesn't play a role when you are in a stateless universe. In a stateful universe, the number of state transitions that your model needs to make plays a certain role, and this specter of computation irreducibly is large. It means that you cannot compute things for practical reasons."
},
{
"end_time": 4599.582,
"index": 174,
"start_time": 4573.848,
"text": " because you don't have enough information yet and you cannot have information to make that prediction. But there is no deep miracle that is not caused by the language when you discover that the spectral gap problem is incomputable. So my question to Donald would be, if you think that there is a limit to computation that you can see, and you would still do something and make statements, what is it that you use to make statements beyond the limits of computation?"
},
{
"end_time": 4627.261,
"index": 175,
"start_time": 4600.077,
"text": " What parts of your mind are you drawing from when you make statements beyond what a computational system can derive? Right, so one way of trying to focus this would be to talk about the integers versus the real numbers and the rational numbers. So from your point of view, Josje, do you think that"
},
{
"end_time": 4652.039,
"index": 176,
"start_time": 4628.251,
"text": " For example, if we look at just the set of all functions from the integers to the integers, it's trivial to show that that's not countable. Turing showed that the set of computable functions is countable, the set of Turing machines is countable. In that simple example, just to make things very, very concrete,"
},
{
"end_time": 4674.889,
"index": 177,
"start_time": 4652.91,
"text": " The set of all functions from the integers to the integers isn't countable. The Turing computable functions are countable, and so there's a sense in which the Turing computable functions have measure zero. They're probability zero in the set of all functions. So do we want to conclude from this computationalist point of view that"
},
{
"end_time": 4699.787,
"index": 178,
"start_time": 4675.265,
"text": " that all those other functions don't exist? So you're saying those functions, so real numbers don't exist? Yes, for something to exist it has to be implemented. If something is not implemented anywhere it doesn't make sense to claim that it exists. I think it's a confusion of the notion of existence to say that something that is not implemented and is not implementable could exist."
},
{
"end_time": 4729.104,
"index": 179,
"start_time": 4700.52,
"text": " the things that produce patterns that we observe in order to exist and need to be implemented. So you could say, does the financial system exist? Well, it exists to the degree that it's implemented. There are some boundaries where we project it, and it's not actually implemented, where it doesn't actually exist, only at some course of approximation. But by and large, something exists. Some causal structure is implemented here. The set of all the functions between the integers is not implementable. Therefore, it doesn't exist."
},
{
"end_time": 4749.974,
"index": 180,
"start_time": 4729.445,
"text": " It's something that you can specify and this difference between specification and existence is something that is very obvious to a computer scientist and sometimes not obvious to a traditional mathematician. There is stuff that you can specify that makes no sense. It is only specifiable in your language, but that's because your language is much more permissible"
},
{
"end_time": 4766.698,
"index": 181,
"start_time": 4750.247,
"text": " Then the set of things that can exist and computation is less permissible. Computation only permits you to build things that can actually exist. If you can build things that cannot exist, it's a problem of your language in which you're building things. It's not a problem of reality, just confused."
},
{
"end_time": 4792.585,
"index": 182,
"start_time": 4767.585,
"text": " I have a comment. This one's from Professor Edward Lee of Berkeley, and it may provide some insight and you both can tell us your thoughts on this. So this is from Professor Edward Lee of Berkeley. This question is a major theme in the second half of my book, Plato and the Nerd. UTMs, so universal Turing machines, have the following properties. Number one, their operation is a sequence of discrete steps. Number two, the data comes from a countable set. Number three, that sequence terminates."
},
{
"end_time": 4821.374,
"index": 183,
"start_time": 4792.961,
"text": " It is a huge leap of faith to assume that physical processes have any of these constraints. I show in Plato and the Nerd that the hypothesis that physical processes all have these properties is actually untestable. I remember earlier, Josha, you mentioned that if it's untestable and you can't provide evidence for it, then perhaps it shouldn't be talked about. So this reminded me of this. And he says in brackets, this follows from an information theorem due to Claude Shannon, known as the channel capacity theorem."
},
{
"end_time": 4850.265,
"index": 184,
"start_time": 4821.766,
"text": " The converse hypothesis that the physical world is not so constrained is also untestable by experiment. But I argue, in Plato and the Nerd, that the converse hypothesis leads to simpler models of the universe and therefore is a better choice by Occam's razor. My claim is that universal Turing machines as realized on today's computers are simulations, quote unquote, of a process that is fundamentally non-algorithmic. So I just want to place that out there and perhaps you can use that as a jumping off board, Donald and then Yoshi."
},
{
"end_time": 4875.589,
"index": 185,
"start_time": 4851.937,
"text": " I'll be interviewing Edward at some point in the next few weeks as well. Oh, very good. That's really quick because these are very, very deep issues. It seems to me that this also interacts with what the physicists are telling us that there is no time fundamentally."
},
{
"end_time": 4905.196,
"index": 186,
"start_time": 4876.715,
"text": " So if time is not fundamental, then these computational issues where there are fundamental limits to what can be computed because we're assuming time. So in computer simulations, computer algorithms, we're assuming a sequence in time of computations that can be, and the kinds of limits that Yoshi was talking about,"
},
{
"end_time": 4927.159,
"index": 187,
"start_time": 4905.64,
"text": " It seems to me are a consequence of assuming time to be fundamental. And if we have to go to a physics in which time is not fundamental, then that places this whole conversation in a completely different context. And so what we may be pointing to is time has"
},
{
"end_time": 4955.077,
"index": 188,
"start_time": 4927.637,
"text": " been a very useful and helpful thing for physics for several centuries. And now the hard work that we have to do is to understand how to go beyond the notion of time. And when we go beyond the notion of time, will the kind of discussion we're having right now be fundamentally revised? The computational versus non-computational notions, we may have to really revise how our whole conversation here is going. I'd be very interested in what Yoshi has to say on that."
},
{
"end_time": 4986.493,
"index": 189,
"start_time": 4957.21,
"text": " Thank you. Also thanks, Edward Lee, for your argument. I concur with you that it's in principle not testable what physics is really like. What we can only say is which theory that we can come up with is more elegant. For a small thing, I think that this notion that the Turing machine has to get to result after a finite sequence of steps might be a mistake."
},
{
"end_time": 5008.131,
"index": 190,
"start_time": 4986.783,
"text": " in the sense in which two machines were originally defined. So basically, a computer that can be built is not a Turing machine in this sense, but it's always a finite state machine. And in a finite state machine, you can have a sequence of steps that is unbounded, that doesn't stop."
},
{
"end_time": 5031.323,
"index": 191,
"start_time": 5008.507,
"text": " And that gives you more and more digits of pi while you're looking at. In a sense, it doesn't come to a conclusion if you want to compute physics, but it's not the problem to build a computer that as long as it runs gives you more digits of pi. And so I think from a formal perspective or from a, it doesn't make much of a difference because you can easily fix it, but it's important if you think about hear that sound."
},
{
"end_time": 5058.439,
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"start_time": 5032.312,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 5084.48,
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"text": " There's also something called Shopify Magic, your AI-powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level. Join the ranks of businesses in 175 countries that have made Shopify the backbone"
},
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"end_time": 5107.875,
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"start_time": 5084.48,
"text": " of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothies, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com"
},
{
"end_time": 5135.913,
"index": 195,
"start_time": 5107.875,
"text": " Your intuitions about how things work or the proofs that you make in other contexts that the value of computation doesn't hinge on there being a finite number of steps until a computation that is going to give you a result that was formulated in classical mathematics terminates."
},
{
"end_time": 5163.695,
"index": 196,
"start_time": 5136.34,
"text": " But it means that everything that you get is the result of finite interactions. And if you assume that infinite interactions are possible, you run into the difficulties that Gödel and Turing have discovered, which means that your theories no longer work, they no longer make sense. And different from Edward, maybe doing him injustice here, I have not read this book. So I would say that"
},
{
"end_time": 5188.097,
"index": 197,
"start_time": 5164.121,
"text": " It's much more elegant from the perspective of Occam's razor to describe reality in a language that doesn't break. Because if your language breaks and you still try to make a model of reality, it's going to be arbitrarily expensive. It doesn't work. You have to find a language that works. So if we find that the languages in which we can describe reality have to be computational languages, because the others lead into contradictions."
},
{
"end_time": 5217.585,
"index": 198,
"start_time": 5188.507,
"text": " Then we have to use the computational languages. That's the situation that I find myself to be in. This doesn't mean that I can know what physics is like. It just means that all the physics that I can talk about without my language breaking has to play out in this way. The notion of what is time, so coming back to Donald, is very important. There are two notions of time. One is this intuitive notion that we have as human beings, which is basically this Newtonian time."
},
{
"end_time": 5242.875,
"index": 199,
"start_time": 5218.029,
"text": " This time which clocks run the same speed everywhere and so on, and it describes the transition of the universe from the past into the future via the present. And this notion of time is somewhat similar to the notion of the state transition in your computer, except that the state transition in the computer has some kind of global clock where everything in the computer goes from state to state all at once and"
},
{
"end_time": 5270.128,
"index": 200,
"start_time": 5243.097,
"text": " goes or progresses to the next step. But what we see in our universe that it only makes sense if we assume that it's dynamic. If the universe would just be a decoupled sequence of states without a transition function, there would not be any law that we can discover. There is nothing that we can control. Organisms would not exist in the way in which they do. So from the observations that we make, we have to assume that the transitions in the universe are somehow fundamental, that the universe is moving."
},
{
"end_time": 5298.251,
"index": 201,
"start_time": 5270.93,
"text": " And state transitions seem to be crucial in order to be able to understand the universe. There is some notion of transition and this notion of transition is much more basic than time. And the time that we are talking about when we see that time is not fundamental in the notion of space time is relativistic time. The relativistic time is what the universe looks like to a relativistic observer. And we can obtain relativistic time if we understand that"
},
{
"end_time": 5325.964,
"index": 202,
"start_time": 5298.882,
"text": " What we perceive as time is basically the speed of the clocks in our environment. And the speed of the clocks that we observe depend on our own speed. So if I move you through the universe and you are a supervenient pattern on the structure of the universe, imagine the universe is something like an ocean. And the present is the crest of a traveling wave through that ocean. And there are"
},
{
"end_time": 5352.142,
"index": 203,
"start_time": 5326.425,
"text": " waves maybe in front and behind us, but they're not our future, they're past, they're different universes that just happen to be a little more long or a bit less along. The future and past would require you to leave the crest of the wave and you can't because you're always traveling with the wave. So there is no way to leave that present because only the present exists from the perspective of that crest. And you and me, we are vortices inscribed on the crest of that traveling wave."
},
{
"end_time": 5377.79,
"index": 204,
"start_time": 5353.336,
"text": " And the rotation that the vortex is doing when it updates itself to observe the universe, to form a memory and so on, and to register its perceptions and so on, will depend on the speed in which this vortex rotates. Right? And so if the vortex is moving along with the wave, then the updates in the vortex are a function of the movement in the wave itself, the basic parasitize on the movement of the main wave."
},
{
"end_time": 5401.22,
"index": 205,
"start_time": 5378.916,
"text": " And you cannot, as this vortex traveling with the wave, ever leave the wave. You can move a little bit in the wave to the left or to the right. Moving to the left or to the right would be movement in space. You cannot move in time. You just move with the time. And the faster you move to the left or to the right, the less there will be updates available for interning your internal state."
},
{
"end_time": 5432.108,
"index": 206,
"start_time": 5402.773,
"text": " So the fluctuations of the vortex becomes slower and slower, the more the vortex moves in space. And this leads to relativistic time. It means that from the perspective of the vortex, when it looks at its environment, the environment gets distorted in time and space. So in this notion, we realize why something would look like to a vortex that moves like this, like relativistic time. And we understand that the relativistic time from the fundamental perspective, how to make all this happening, how to build a system that functions like this,"
},
{
"end_time": 5460.538,
"index": 207,
"start_time": 5432.466,
"text": " cannot be fundamental. It's a result to the observer. It will be what the universe looks like to the observer of the observer screens as we always do, right? But it is not fundamental, but fundamental are the state transitions. So what we need to do is basically replace the physicalist time that is relativistic for good reason in the frame of certain models by something that is more fundamental and allows us to derive the relativistic time. And this would be state transitions."
},
{
"end_time": 5490.367,
"index": 208,
"start_time": 5462.705,
"text": " Very interesting. In that spirit, or at least in that kind of direction, there's work by Marcus Mueller and Philip Hohn, and then also some more recent work by Fabio Mercati and Giovanni Emilino Camiglia, where they're showing how relativistic spacetimes can be constructed."
},
{
"end_time": 5512.756,
"index": 209,
"start_time": 5491.152,
"text": " from exchange of quantum information so you don't assume it upfront but you try to get a dictionary to that allows different quantum agents to send information back and forth and it turns out if you send enough information back and forth and try to set up a dictionary to make everything consistent you will get"
},
{
"end_time": 5541.766,
"index": 210,
"start_time": 5513.131,
"text": " Einstein's special relativistic space time coming out of us. So that's an interesting direction to go. Another interesting direction to think about, just a simple notion, time and entropy are, at least physical time and entropy are deeply connected. And so we would like to have some way of getting entropic time coming out of"
},
{
"end_time": 5572.875,
"index": 211,
"start_time": 5543.012,
"text": " a deeper system in which there is no entropic time, right? And there is a, I'm not saying this is the deepest way of doing it, but an interesting, simple way, just in the case of Markovian dynamics. So if I have a Markovian system, homogeneous, and it's in a stationary, then the entropy of that system doesn't change. So if for state X sub n and Xn minus one and so forth,"
},
{
"end_time": 5602.585,
"index": 212,
"start_time": 5573.353,
"text": " the entropy h of x of n equals h of x sub n minus one for all n. So there is no entropic time. But it's trivial to prove that if you just do a simple conditioning, if I look at xn given x1, or xn given, then it turns out that h of xn given x1 is greater than or equal to h of xn given"
},
{
"end_time": 5632.619,
"index": 213,
"start_time": 5602.79,
"text": " In other words, the very fact of doing conditioning, which is projection. So you can think about, I take this dynamical system, which has a notion of state transition, this Markov chain, but it doesn't have any entropic time. But as soon as you start projecting that non-entropic system onto different perspectives by conditioning H of Xn given X1, all of a sudden, now you have entropy."
},
{
"end_time": 5662.261,
"index": 214,
"start_time": 5633.422,
"text": " And so now you have that kind of notion of time. So is that a direction that we could go where we could still have, in some sense, a dynamical system, but it's not an entropic time system, and show how we get space-time arising from that in the way that some of these physicists are trying to do. I think that will be interesting. I think that it's a separate question whether the real numbers exist versus..."
},
{
"end_time": 5692.517,
"index": 215,
"start_time": 5663.49,
"text": " It's a pretty strong statement to say that real numbers don't exist. That's really quite interesting to say that they don't exist. But I guess that's where you want to go anyway. Yeah, well, I agree with Patagoras that real numbers don't exist. And the time was not right back then. So real numbers are actually functions. And you can give you this function instead of a real number. And it can give you as many digits as you want, or as you can afford to compute. But this is it."
},
{
"end_time": 5720.06,
"index": 216,
"start_time": 5692.91,
"text": " It's fine. So basically real numbers can be derived in a deterministic fashion. They are predetermined in this sense, but you will not know the billions digit of the square root of two unless you find a procedure to compute it and the energy or the neck entropy to actually get there."
},
{
"end_time": 5740.725,
"index": 217,
"start_time": 5720.52,
"text": " And this derivation of a result via using apnic entropy, I think, relates to our perception of time, this causal error of time, which is aligned with the entropic arrow. Eric Drescher finds a very good metaphor in his book Good and Real, I think, to give an intuition how a symmetric system"
},
{
"end_time": 5766.527,
"index": 218,
"start_time": 5741.015,
"text": " where the transitions are symmetric in both directions, is still not going to be symmetric at scale when you look at it. So he takes as an example, a ball that is made of large and small billiard balls. And you put one of these billiard balls in motion and the transaction between the billiard balls are all symmetrical, which means if you take a movie and you play it forward and backward,"
},
{
"end_time": 5796.271,
"index": 219,
"start_time": 5767.329,
"text": " will see for the every interaction between two billiard balls that it's the same if you go the movie backwards or forwards. It's a simplified model where you have no friction and so we have no thermodynamic stuff going on. We look at the universe at the level where thermodynamics doesn't exist yet because this maybe the stuff is too small to have these losses. So we just look at the billiard ball universe where everything is deterministic and without noise and in this model what we see is"
},
{
"end_time": 5825.384,
"index": 220,
"start_time": 5796.544,
"text": " that when we zoom out, there is something that is happening at scale, and that is some balls move after they have been hit and keep moving, hitting other balls. And if you play the movie backwards, it looks as if some balls are anticipating that they are going to be soon hit and start moving as a result, as if they would be hit, right? So there is this asymmetry that your balls leave a vague behind them."
},
{
"end_time": 5850.06,
"index": 221,
"start_time": 5826.63,
"text": " And this vague is describing, in some sense, the entropy that we are looking at in our universe. That's the direction in which you can, as an embedded observer, form memories. Because in order to form memories, you rely on the dissipation of information between locations. And so whenever there is a way to form memories, it means that you are aligned with some kind of entropic arrow."
},
{
"end_time": 5879.275,
"index": 222,
"start_time": 5851.084,
"text": " If you zoom out, it means that you can now sort the states of the universe in such a way that you discover the concentric waves that you are part of, and our ocean-like universe has a point of origin. And this point of origin is a construction that you make. You discover this by the wave expanding, and you discover it by information moving, diffusing across the locations in the wave. So there is a hypothetical point in the middle"
},
{
"end_time": 5905.879,
"index": 223,
"start_time": 5879.718,
"text": " where the information is not diffused yet. And this hypothetical point is what we imagine to be the Big Bang. Right, and it's a mathematical singularity in a way, because if you are in the Big Bang, you don't know which direction to go unless the Big Bang is not completely perfect and symmetrical. And the interesting thing about this before the Big Bang means it's the wrong question to ask, because"
},
{
"end_time": 5930.879,
"index": 224,
"start_time": 5906.101,
"text": " Sorry to interrupt, is this related to the Janus point? Have you heard of Julian Barber's theory of time?"
},
{
"end_time": 5962.005,
"index": 225,
"start_time": 5932.312,
"text": " No, but it's an artifact of a certain description. Basically, we create a certain mental model in which we describe the entropic arrow of time as the diffusion of information across locations in the universe. And then we imagine that there is a single point where this ends up and we go through this point. On the other side, we go back into another future. So the further we go away from this point in any direction, the further we go into a future in which systems could form memories of the past."
},
{
"end_time": 5990.077,
"index": 226,
"start_time": 5962.346,
"text": " And to form memories of the past, you need to have some kind of reservoir of neck entropy that you can tap and some kind of puddle of neck entropy. And then you can reason about the conditions, how such puddles of neck entropy could form under which conditions and how long they might last. I would like to get to the topic of free will as well. And then also some audience questions. So why don't you, Donald, outline your views on free will? OK, yeah."
},
{
"end_time": 6020.947,
"index": 227,
"start_time": 5994.189,
"text": " If in a physicalist framework, which so now I'll just talk about what most of my cognitive neuroscience peers think, right? Most of them assume that physical systems are fundamental. Neural activity causes all of our behavior. And in that case, there can be a fiction of"
},
{
"end_time": 6044.565,
"index": 228,
"start_time": 6021.254,
"text": " a useful fiction of free will, but it's really just going to be a useful fiction. If I do something, it's really my neurons with the neural activity that did it. And there is a sense in which you can say I chose to do it because actually neurons are part of me. So I think that's the point of view that Dan Dennett takes, for example, on this. And"
},
{
"end_time": 6076.323,
"index": 229,
"start_time": 6046.92,
"text": " And Sam Harris replies on that. He says, well, yeah, I also grow my fingernails. I'm not sure that I'm doing that by free will. So it's not real clear that just because my neurons are doing it, I have free will, just in the same sense that I'm not using free will to grow my fingernails. So Sam would say there's no such thing as free will if you're a physicalist. Dan Dennett would say I'm a physicalist. And there is this important notion of free will."
},
{
"end_time": 6108.968,
"index": 230,
"start_time": 6080.213,
"text": " I think that, of course, space-time isn't fundamental, and so that we have to completely think outside of that box altogether. And as scientists, we have to say upfront what our hypotheses, what our axioms or fundamental assumptions are, and be very clear about them upfront. These conscious agents, in the mathematics, they get certain inputs. We call them experiences that they have."
},
{
"end_time": 6132.363,
"index": 231,
"start_time": 6109.48,
"text": " And then there's something called the Markovian kernel that describes what actions they take, and those actions affect the experiences of other conscious agents. So that's just the mathematics that my team has written down. It's a very simple notion of Markovian dynamics of conscious agents interacting. And it's not in physical spring work. We're assuming that this is"
},
{
"end_time": 6162.534,
"index": 232,
"start_time": 6132.824,
"text": " you know, in its own world, right? These are conscious agents, and that's the foundation. Space and time are not the foundation, conscious agents. So conscious experiences and interactions of conscious agents are the foundational notion. And so then the question is, how shall we understand the probabilities? So if I get a particular experience that comes into a conscious agent, and it then probabilistically affects the experience of other agents, how shall I"
},
{
"end_time": 6190.879,
"index": 233,
"start_time": 6162.824,
"text": " understand that probability that it shall understand it as as a free will choice or or what and you know I could say you know I refuse to answer the question I just there's a probability there and that's that's as far as I go with with a theory there you know this agent so I leave that probability as just where my theory stops right I say"
},
{
"end_time": 6216.681,
"index": 234,
"start_time": 6191.271,
"text": " In some sense, wherever we see a probability in a theory, that's where explanation stops, right? That's basically saying, I don't know. So I always say this, whenever in a scientific theory, you see probabilities coming up, you're seeing the theory say, this is where I halt. This is where my explanation stops. And there are two major"
},
{
"end_time": 6246.817,
"index": 235,
"start_time": 6218.78,
"text": " approaches toward understanding those probabilities, the objectivist and subjectivist to probabilities, right? So objectivists say that these probabilities are pointing to some real thing in the world. There is some real random generator in the world. And subjectivists say, no, these are just degrees of beliefs. Whenever you see probabilities, you're only talking about"
},
{
"end_time": 6273.558,
"index": 236,
"start_time": 6247.79,
"text": " degrees of belief. But in either case, explanation stops, right? How do I come to that belief? Well, I can only tell you probabilities. What is that random objective process? I don't know, but I can just tell you probabilities. And so really, whenever you see probabilities in a scientific theory, and they're all over the place, I read that as saying, here's where explanation stops."
},
{
"end_time": 6301.749,
"index": 237,
"start_time": 6273.916,
"text": " And our theories our theories halt and and if we want to go further we're gonna have to unpack that probability into some some deeper deeper theory, so If I say that it's free will in the case of the conscious agents Then I mean in some sense that's just words what theory has is the probabilities and"
},
{
"end_time": 6320.145,
"index": 238,
"start_time": 6302.056,
"text": " And it has no further explanation so if i say if i call the probability of free will that i can call it that but but i haven't really done much to. Give much insight into the notion of free will free will then becomes a primitive and maybe that's what i want to do i want to say this is where explanation stops."
},
{
"end_time": 6344.224,
"index": 239,
"start_time": 6320.469,
"text": " And so free will is primitive. So these probabilities are free will and I agree to that that's where my theory stops that I can do no further. Now what's interesting in the conscious agent dynamics that we're working on is that any group of conscious agents"
},
{
"end_time": 6370.043,
"index": 240,
"start_time": 6345.845,
"text": " together also satisfy the definition of a conscious agent and so they are a conscious agent so any conscious agents interacting are also conscious agents so they're in the third there's one conscious agent because if you take all of them together they form one conscious agent but then there are as many if you're computational there's only countable number of them or in my case i don't know if it may be an uncountable number of conscious"
},
{
"end_time": 6398.899,
"index": 241,
"start_time": 6370.316,
"text": " agents but what's interesting is that the you unpack this probability in the Markovian kernel there could be one big probability for the one agent but you can unpack that into all these dynamical systems that are interacting conscious agents with their own probabilities in their own kernels and what's what's interesting is that you could then give in some sense an unpacking of the notion of free will in that way you could say well yeah the the one agent has free will in this this probability but i can actually"
},
{
"end_time": 6427.056,
"index": 242,
"start_time": 6399.309,
"text": " do some non-trivial unpacking of that notion in this sort of recursive unwinding of those probabilities throughout the network. So there is the possibility here of, I mean, ultimately there will be a primitive notion of free will that is just primitive and not explained. But given that one, I can explain all these other free wills sort of interacting, arising from this most primitive notion of free will in a non-trivial"
},
{
"end_time": 6455.913,
"index": 243,
"start_time": 6427.773,
"text": " non-trivial way. But once again, I would point out something that I see all the time in scientific theories. No theory in science will ever explain everything. And I would love to see if Joscha agrees or disagrees. I will just state, to make a strong claim, there cannot be a theory of everything because every theory has to make assumptions and those assumptions are not explained, they're assumed."
},
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"text": " It's just that simple. A KFC tale in the pursuit of flavor. The holidays were tricky for the Colonel. He loved people, but he also loved peace and quiet. So he cooked up KFC's 499 Chicken Pot Pie. Warm, flaky, with savory sauce and vegetables. It's a tender chicken-filled excuse to get some time to yourself and step away from decking the halls. Whatever that means. The Colonel lived so we could chicken. KFC's Chicken Pot Pie. The best 499 you'll spend this season."
},
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"end_time": 6487.654,
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"start_time": 6484.65,
"text": " Prices and participation may vary while supplies last. Taxes, tips, and fees extra."
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"text": " Okay, am I correct in my summary of your views on free will that if in a physical theory you have probability, now some of that probability is just due to our ignorance, but if there's a fundamental probability, you can just say, well, that's indicating that the theories break down, we just don't know. Or you can say that there's something underneath producing those and that which is underneath the probabilities is what you're calling free will. Is that correct? Or is that off?"
},
{
"end_time": 6542.398,
"index": 247,
"start_time": 6516.698,
"text": " Right. So if I'm a physicalist, I'll say that that probability is due to some process that I can say no more about, but there's some process that generates this stuff. It's not free will. It's just a physical process that I don't know. But if I'm taking consciousness to be fundamental, then it's an interesting move to say that that probability can be interpreted as free will. Now, of course, I'm not explaining anything. I'm not, I mean,"
},
{
"end_time": 6568.66,
"index": 248,
"start_time": 6542.773,
"text": " I'm just putting the notion free will, the word free will on it, right? And free will becomes just a primitive notion as well. So that's where my explanation stops. And the most unpacking I can do is that recursive unpacking that I mentioned, which is an interesting unpacking. But ultimately, there's this primitive notion of free will that I have nothing further to say about. But I think that that's not"
},
{
"end_time": 6599.087,
"index": 249,
"start_time": 6569.309,
"text": " a problem specific to this theory. The last thing I was saying was that that's endemic to all scientific theories. Every scientific theory will have miracles at its foundation. By miracles, I mean assumptions that are taken for granted and not explained. If you explain them, then you have a deeper theory with new assumptions that explain those assumptions, but the new assumptions aren't explained. And so in this sense, science can never have a theory of everything because science theories always have"
},
{
"end_time": 6623.933,
"index": 250,
"start_time": 6599.275,
"text": " Assumptions and the assumptions are what you don't explain. Yoshi, I know Donald said quite a few, there are quite a few elements to pick from there. So we interlocking claims, but let's address them. First of all, I don't know whether there can be one theory of everything, because my reasoning is not tight enough to make that proof one way or the other."
},
{
"end_time": 6652.654,
"index": 251,
"start_time": 6624.497,
"text": " So at this point I have to remain agnostic, because from various stand it seems to be possible that there can be a theory of everything and it seems to be possible that there cannot. From a computationalist perspective, whenever you have a set of observations that is finite, you will be able to construct a computational model that explains how to make such patterns. So in principle, there can always be a theory of everything that you observe."
},
{
"end_time": 6671.493,
"index": 252,
"start_time": 6653.882,
"text": " This is something that I cannot, they don't see a way around this. So this seems to be sound to me, and I think that can be formally proven, but it seems to be almost trivial that it's proven. So it's more interesting. The question is, can you narrow this down to a single one, to one theory of everything?"
},
{
"end_time": 6695.93,
"index": 253,
"start_time": 6672.176,
"text": " You will be always stuck with infinitely many theories of everything, where most of these theories will be super inelegant and redundant and basically recordings of your observations. Or will there be one theory that is the most elegant and explains everything deeply and wraps it up? And of course, if you think about the space of all theories and think of them as things that you can do in a language and"
},
{
"end_time": 6707.125,
"index": 254,
"start_time": 6696.305,
"text": " in which you can define truth. And if you realize that the languages in which you can define truth consistent, these are the computational languages, it turns out that all your models are going to be automata."
},
{
"end_time": 6728.319,
"index": 255,
"start_time": 6707.5,
"text": " And that you can sort the space of automata by the length of the definitions. So it also seems that in principle, it should be possible to find the shortest automaton between to every pair of automata that you can construct and can up this. And now the question is, what's your search procedure for all the possible automata? Do you have a search procedure that you can hope that terminates?"
},
{
"end_time": 6751.34,
"index": 256,
"start_time": 6729.189,
"text": " And this is not a question of whether it's mathematically possible, but whether it's efficient. So is there an efficient strategy to find the theory of everything that is the shortest one? And so far we haven't found one. And it relates to what AI is doing in machine learning when it tries to identify what's going on in the domain."
},
{
"end_time": 6781.527,
"index": 257,
"start_time": 6752.073,
"text": " So in principle, we can always be sure that we could be a brain in a vat and everything is just a nefarious conspiracy that is playing out. And because we cannot exclude this, we can never be sure that our theory of everything is the best theory that could exist of things. So that's obviously the case. But if we take out this single thing and make the assumption that reality is not a conspiracy, I think then it starts to look a lot brighter."
},
{
"end_time": 6812.432,
"index": 258,
"start_time": 6782.807,
"text": " Let's get to the notion of free will. I think that free will is tied into the notion of agency. And the best explanation of what an agent is that I found so far is that an agent is a control system that is intrinsically combined with its own set point generator. A control system is a notion from cybernetics. It means you have some system like a thermostat that is making a measurement using sensors, for instance, the temperature in the room."
},
{
"end_time": 6826.118,
"index": 259,
"start_time": 6812.705,
"text": " And that has effectors by which it can change the dynamics of the system. So the effector would be a switch that turns the heating on and off. And the system that's being regulated is the temperature in the room. And the temperature in the room is disturbed by the environment."
},
{
"end_time": 6853.097,
"index": 260,
"start_time": 6827.278,
"text": " And a simple thermostat will only act on its present measurement and then translate this present measurement using a single parameter into whether it should switch or not. And depending on choosing that parameter well, you have a more efficient regulation or not. But if you want to be more efficient, you need to model the environment and the dynamics of the system and maybe the dynamics of the sensory system and the actuator itself."
},
{
"end_time": 6874.94,
"index": 261,
"start_time": 6853.882,
"text": " When you can do this, it means that you model the future of the regulation based on past observations. So if you endow the controller with the ability to make a model of the future and use this control model to fine tune the actions of the controller, it means that the controller now is more than a thermostat. It's not going to just optimize the temperature in the room in the next frame."
},
{
"end_time": 6898.985,
"index": 262,
"start_time": 6875.35,
"text": " But it's going to optimize the integral of the temperature over a long time span. So it basically takes a long expectation horizon, the further it goes, the better probably. And then it tries to minimize all the temperature deviations from the ideal temperature from the set point over that time span. This means that depending on the fidelity and detail of the model of its environment and its interactions with the environment in itself,"
},
{
"end_time": 6907.329,
"index": 263,
"start_time": 6899.838,
"text": " It's going to be better and better if it assumes that there are trajectories in the world that are the result of its own decisions."
},
{
"end_time": 6932.79,
"index": 264,
"start_time": 6908.131,
"text": " By turning the temperature on and off at this particular point in time, I'm going to get this and this result, depending on the weather outside, depending on how often people open and close the door to the room at different times of the day, depending on the aging of my sensor or the distance of my sensor to the heating, and depending on whether the window on top of the sensor is currently open or closed and so on."
},
{
"end_time": 6960.486,
"index": 265,
"start_time": 6932.79,
"text": " I get lots and lots more ways to differentiate the event flow in the universe and the paths that the universe can take and the interactions that I can have with the universe that determine whether somebody will open the window and so on and so on. So you have all these points where the controller is a very differentiated model of reality where it's going to prefer some events of others and is going to assign its own decisions to these trajectories."
},
{
"end_time": 6983.729,
"index": 266,
"start_time": 6961.715,
"text": " This decision-making necessarily happens under conditions of uncertainty, which means the controller will never be completely sure which one is going to be the right decision. The controller will have to make educated guesses, bets on the future. This even includes the models of itself. The better the control system understands itself and the limitations of its modeling ability,"
},
{
"end_time": 7012.517,
"index": 267,
"start_time": 6984.138,
"text": " the better its models are going to be. So at some point of complexity, this thing is going to understand its own modeling procedure to improve it and to find gaps in it and so on. And this also means that when it starts to do this, it is going to discover that there are agents in the world, other controllers that have set points generators and model the future and make decisions. For instance, people that might open the window when you make the room too hot and you lose energy because of that. So maybe not overheat the room and people are in the room."
},
{
"end_time": 7041.203,
"index": 268,
"start_time": 7012.841,
"text": " This means you have to model agency at some point and you will also discover yourself as an agent in the world as a controller with a set point generator and the ability to model the future and you will discover this before you understand your own modeling of the future works. So you also have to make bets on how you work before you understand yourself. So you will discover a self-model. The self-model is the agent where the contents of your own model are driving the behavior of that agent."
},
{
"end_time": 7069.599,
"index": 269,
"start_time": 7042.09,
"text": " It is a very particular agent. It's one where your reasoning and your modeling has an influence on what this agent is going to do, a direct coupling. It's a very specific model, a very specific agent that you discover there. And so in some sense, free will, I think, is a perspective on decision making under uncertainty, starting from the point where you discover your own self model, up to the point where you deconstruct it again. And of course, you will deconstruct it again at some point."
},
{
"end_time": 7095.674,
"index": 270,
"start_time": 7069.923,
"text": " you will be able to fully understand how you're operating. And once you do this, making your decision becomes indistinguishable from predicting your decision. Because of computational irreducibility, often you will not be able to predict the decision before you make it, right? But as soon as you understand that it's just a computational process going on, and you understand the properties of that process, you will no longer experience yourself as having free will."
},
{
"end_time": 7115.52,
"index": 271,
"start_time": 7096.732,
"text": " Free will is a particular kind of model that happens as a result of your own self model being a simulacrum, instead of being a high fidelity simulation of how you actually work. And we are young beings, we don't get very old, it's very difficult for us to get to the point where we fully understand how we work."
},
{
"end_time": 7139.821,
"index": 272,
"start_time": 7116.203,
"text": " Except in certain circumstances, right, when we observe our children, very often we get to the point as parents that we fully understand what they will be doing in the given situation. We can fully understand their own actions and anticipate their decisions and the child might experience that it has free will. We experience that the child has free will up to the point where we suddenly understand, oh, this is what's going on. And at this point, I can completely control the child because it can outmodel it."
},
{
"end_time": 7169.48,
"index": 273,
"start_time": 7141.101,
"text": " And it's only to the point where this system is going to introduce levels that are, again, reaching my own level, that decisions become unpredictable. But if I am a few levels of monitoring depth above the other agent that might think that it's free will, the free will starts to disappear from my own perspective and also happens in my own mind. There's many things that I do, but I thought as a child I'm acting out of my own free will and now I understand how mechanical it is and I can deal with myself."
},
{
"end_time": 7186.783,
"index": 274,
"start_time": 7170.333,
"text": " By controlling myself, by outmodeling myself successively and becoming one more complex in this way. And all that, the computational process, the probabilities in the transition rules, you would view those as objective probabilities."
},
{
"end_time": 7217.363,
"index": 275,
"start_time": 7188.899,
"text": " Yes, so there is also this issue that I don't actually exist in the way in which I model myself. I only exist to some degree of approximation. I'm not this big tree that is strictly implemented in physical reality. I'm more like a bunch of shrubbery. And some of the shrubbery is tasked with making a model of myself as a tree. And that model is going to be a coarse approximation. So the fact that I am unable to follow up on my plans means that I'm only approximately implemented."
},
{
"end_time": 7242.995,
"index": 276,
"start_time": 7217.91,
"text": " The rubber hand illusion is a good example of how we're continually redefining who we are, right? Where you tap and drag on a hand at the same time you're tapping and dragging on a rubber hand. If you do it just right with a person, they'll take this rubber hand and incorporate it into their body image. So we're always learning who we are. But those probabilities in that learning process you would take as objective probabilities and not free will kinds of probabilities."
},
{
"end_time": 7273.387,
"index": 277,
"start_time": 7243.831,
"text": " What does it mean that a probability is objective? It only means based on the models in which which I have currently made. And if I go far beyond that, I cannot assign an objective probability to the probabilities that I am observing because they are contingent on the assumption, for instance, I'm currently not in a dream or that my memories are correct or that my data are correct or that the theories that event into establishing the relationships between my measurements and my data and so on are correct."
},
{
"end_time": 7302.5,
"index": 278,
"start_time": 7273.882,
"text": " So I do agree that at some point there are a lot of assumptions that go into this. And these assumptions, where I differ with you, are usually mild. Because I make so many observations that at some point the errors cancel each other out, or there's so many people that can verify my ideas and shut them down. And so my ideas don't exist in isolation. They are being shot against every philosophy and physics book that I can get my hands on and that I understand, right, in every conversation that I have."
},
{
"end_time": 7332.568,
"index": 279,
"start_time": 7302.858,
"text": " So that doesn't mean that I will discover the truth in this way, but it means that I discover many, many of the possible errors that I can make. And at some point, I realized that there is a finite space of theories that exists and that we are discovering the same things again and again. So when we ask ourselves, what are integers, for instance, or what are rational numbers? There are many ways of making theories about what integers are. For instance, we can say that there are the cardinalities of sets."
},
{
"end_time": 7353.524,
"index": 280,
"start_time": 7333.268,
"text": " So basically you count members of a set, and this is an integer, and all the numbers of members of sets that you can have are integers. Or you can say that there are a subsequent Lieberling scheme. That's the definition that I currently prefer. Or you can use Peano's axioms to formalize them. And it turns out that they all describe exactly the same thing."
},
{
"end_time": 7377.108,
"index": 281,
"start_time": 7354.138,
"text": " There are all different perspectives on the same thing, and once you understand the larger space that surrounds the integers, you also understand why there are different perspectives, because you understand how these perspectives are being constructed, and you can show that it's all the same thing. So in some sense, the integers are fractal, and you can describe this fractal using a generator function, and you can also describe it in many other ways."
},
{
"end_time": 7401.988,
"index": 282,
"start_time": 7377.773,
"text": " And it seems that mathematics or all the languages that we can use that work are usually small, relatively intelligible set of fractals. And there are the boundary of what is intelligible to the human mind, but not that far above it and probably still inside of it. So I'm more optimistic than you are. I have a question for the both of you."
},
{
"end_time": 7421.732,
"index": 283,
"start_time": 7402.449,
"text": " It's about your models. How much of it would have to change, let's say, Yocha in your case, if classical logic was indeed correct, if continuities exist? And for Donald, if the opposite was true, so continuity doesn't exist, intuitionist logic is primary."
},
{
"end_time": 7451.084,
"index": 284,
"start_time": 7422.602,
"text": " At some point in my life, I thought that continuity must exist because everybody was assuming that it did. Like most of the eminent physicists thought that the universe must be fundamentally continuous. Many of the foundational theories that we have in physics assume that there is continuity. And I thought that my inability to derive continuity to construct a continuous system is the result of my lack of understanding. And it took me quite some time to realize that"
},
{
"end_time": 7467.688,
"index": 285,
"start_time": 7451.698,
"text": " What Gödel has stumbled upon was actually the insight that continuity cannot exist because it's not constructive, cannot be implemented. So once you have the infinities, once you presuppose them, there are an amazing cornucopia, all sorts of stuff falls out."
},
{
"end_time": 7491.169,
"index": 286,
"start_time": 7468.302,
"text": " Like you have Hilbert's hotel that is completely booked out, but there's infinitely many rooms and then there are infinitely many buses coming on and you just ask everybody to move in the room with twice the number and then you fit in the infinitely many new people, right? This is not a feature. This is a bug. This shouldn't happen. I know how hotels work. No hotels work like this."
},
{
"end_time": 7513.848,
"index": 287,
"start_time": 7491.63,
"text": " This is not good if something like this happens. And it's not surprising that this blows up when you try to make proofs. And so I think that Hilbert's Hotel points not to a miracle in the universe that under certain circumstances, you get something for nothing, which is very nice if you want to derive the universe from nothing. But hear that sound."
},
{
"end_time": 7540.947,
"index": 288,
"start_time": 7514.787,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 7566.988,
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"text": " There's also something called Shopify Magic, your AI-powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level. Join the ranks of businesses in 175 countries that have made Shopify the backbone"
},
{
"end_time": 7590.35,
"index": 290,
"start_time": 7566.988,
"text": " of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothies, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com"
},
{
"end_time": 7605.964,
"index": 291,
"start_time": 7590.35,
"text": " It shows that your language can break."
},
{
"end_time": 7634.104,
"index": 292,
"start_time": 7606.442,
"text": " And so I don't see a way to get the languages in which continuity exists to work. And I cannot exclude that I'm wrong. And I might see a way in the future or somebody else does in a way that I don't. I just don't see a way how to make continuity work. But I get all the benefits from continuity for the description of practical systems using discrete logic. So in this sense, I would say that dynamical systems that are truly continuous don't exist."
},
{
"end_time": 7650.23,
"index": 293,
"start_time": 7634.565,
"text": " They're not causally existing. They cannot be causal. There are a layer of description that are used to deal with too many parts to count. And there are sometimes a very useful abstraction, but they cannot be used for a foundational theory. Because the foundational stuff"
},
{
"end_time": 7674.258,
"index": 294,
"start_time": 7650.623,
"text": " has to work. It has to be described in a language where all the elements, parts have to interface in such a way that your language doesn't blow up because otherwise the terms in your language don't mean anything. So what this means is that the word continuity does not actually mean anything in my world. It does not have a useful reference. I cannot point at anything that is truly continuous without my language breaking."
},
{
"end_time": 7684.206,
"index": 295,
"start_time": 7675.333,
"text": " So it doesn't exist. It's a word that only exists as a confusion, but it exists approximately. It exists as the dynamics of too many parts to count, which is fine."
},
{
"end_time": 7713.763,
"index": 296,
"start_time": 7685.486,
"text": " So I'm a confused man. And when you say that the language is breaking, I just see it as you saying that they're extremely unintuitive results that, well, they don't seem to make sense. But it doesn't mean that they don't make sense because you defined work as what's implementable. What it doesn't work means that you can no longer derive truth. It means, for instance, in axiomatic system, if you have a contradiction in your axioms, it means that you can suddenly derive everything and nothing."
},
{
"end_time": 7741.442,
"index": 297,
"start_time": 7714.292,
"text": " It just means that your fractal is no longer having a discernible structure. This is what it means that it's breaking. What is the exact contradiction in classical logic? Because it seems as though mathematicians are getting along fine, and it's difficult, extremely difficult to prove certain theorems. And it wouldn't be if there was a contradiction. Well, not necessarily, but you understand what I mean? Yes. So the issue is that the assumption of a stateless platonic notion of truth"
},
{
"end_time": 7769.957,
"index": 298,
"start_time": 7741.664,
"text": " that holds independent of the process by which you discover the truth leads into contradictions. And this was what Gödel had proven. It basically means that a sentence that is true under these assumptions is also false under these assumptions. So it cannot be true. And this is where undecidability comes in. It's not just about that some sentences are not reachable because you don't know whether they're true or false. It also means that there are some sentences that are true and false at the same time."
},
{
"end_time": 7795.964,
"index": 299,
"start_time": 7770.486,
"text": " But if you have to find truth in such a way that it can, that it includes false falsity, right? Something is either true or false. If you have an excluded middle, then this cannot be the case. So this is a very bad result. It just means that your language is not working. It gets to illegal states. It just means that the application of steps that you have prescribed in your logic, if you apply them properly, leads to an undefined result."
},
{
"end_time": 7825.691,
"index": 300,
"start_time": 7796.766,
"text": " It means that your language is sex faulting. It means your mind is breaking apart. It means that the thoughts that you are thinking no longer have meaning because they can no longer point to anything that could be implemented. Okay, so Don, the question that I asked before was, let's imagine the intuitionist logic is correct. How does your theory change? Well, yeah, so I mean, I could easily"
},
{
"end_time": 7857.449,
"index": 301,
"start_time": 7827.671,
"text": " Implement the theory of conscious agents in an intuitionist logic kind of approach and run it that way. So that wouldn't really change my theory of conscious agents fundamentally. But my own thinking on this, I guess, does differ from Yosh's in an interesting way here. And that is, I do take Gödel's result, not necessarily to show that the notion of continuity is"
},
{
"end_time": 7887.671,
"index": 302,
"start_time": 7857.892,
"text": " is nonsense or contradictory, but rather that if I have a finite system of axioms and derivation rules, then you can look at the set of statements that can be proven by that system, then you can find statements that are not provable within that system, so they're undecidable from within that system. But what Gertl did was to put a mapping"
},
{
"end_time": 7906.664,
"index": 303,
"start_time": 7888.131,
"text": " on to the language of the system so he could write down an analogy as Douglas Hofstad likes to talk about. He found an analogy that he could write down where there is this sentence I could write down that says I am true but not provable within the system."
},
{
"end_time": 7934.735,
"index": 304,
"start_time": 7909.104,
"text": " And that doesn't seem to me to require me going all the way off to uncountable infinities and continuity and so forth. It's just saying, I mean, here's a deflationary reading of Gödel. It's just saying, you give me any computational system, I'll find a statement that's true but can't be derived from within that system. Therefore, any computation that you pick isn't the final word. I don't have to go all the way to, you know,"
},
{
"end_time": 7965.64,
"index": 305,
"start_time": 7937.142,
"text": " uncountable sets and so forth. I can just use that to say that the computation can't be the final truth. And so that would be sort of the minimal way out. And that's why I think a lot of researchers have interpreted Girdle, but I guess Yosha disagrees on that. Okay, what would be the thing that goes beyond that? So what is the other language that you can use after Girdle's language broke?"
},
{
"end_time": 7988.507,
"index": 306,
"start_time": 7966.357,
"text": " Well, what you do is you take the new statement that you showed was undecidable within that computational system and you add it to your computational system. Every computational system has axioms. You don't compute without some assumptions, so your computation has to have certain axioms to begin with, so you add it to your axioms. It's now still a finite set of axioms."
},
{
"end_time": 8014.872,
"index": 307,
"start_time": 7988.814,
"text": " And now you say, OK, now I'm good. I took that undecidable sentence and I put it into my set of axioms. I'm good. Now I'm done. Well, no, you're not. Now because Gertl comes back and says, you know what, I just found another statement within your new system and that's not computable. So I'm not getting anywhere near to these uncountable infinities. No, wait, wait, wait. You are making a step too far here, I think. You have just found this procedure that discovers that something is true that is not true according to mathematics."
},
{
"end_time": 8044.428,
"index": 308,
"start_time": 8015.401,
"text": " So Gödel is trying to find a foundation for all of mathematics and he does this by reducing the mathematics that he's interested in to piano arithmetic and then computes all of mathematics in piano arithmetic and discovers that he cannot recover the semantics that he wanted to discover, which was a platonic notion of truth, one that is independent of the state sequence that he runs it through. This is the thing that he cannot recover and you try to recover the original mathematics by extending"
},
{
"end_time": 8072.449,
"index": 309,
"start_time": 8044.718,
"text": " the axiomatic system, Peano's axioms, with an infinite set of arbitrary statements. This doesn't seem to be very elegant. Also, of course, Gödel shows that it doesn't terminate. It doesn't work. It's not fixing mathematics in any way. So you still have the intuition here that you have a procedure that allows you to discover truths in ways that Gödel's procedure could not. And if you have that procedure, you should be able to prove that it's true."
},
{
"end_time": 8101.459,
"index": 310,
"start_time": 8073.797,
"text": " If you cannot prove that it's true, I'm not going to believe you. I don't think that the statements that you think are true, but my system cannot prove are true. Unless you can compute them. So you have to show a way that would force me as a rational observer and colleague of yours that is completely charitable and so on and reasonable and rational to follow you there. So if you can give me a rational procedure,"
},
{
"end_time": 8127.278,
"index": 311,
"start_time": 8101.954,
"text": " Then I expect that this procedure will be computational, that there will be a sequence of steps that I can follow to see why your claim that the sentence is true is actually valid. If you cannot make such a claim, I don't see how I can believe you. Well, so the way I understand Gödel doing it is that he comes up with this whole Gödel numbering approach."
},
{
"end_time": 8155.077,
"index": 312,
"start_time": 8127.944,
"text": " And he takes you through and shows you this mapping from the numbers into these girdle numbers that are making statements about the numbers themselves. And you look at that and you go, yeah, okay, I understand that mapping, that's perfectly fine. And now I can write down within that mapping, I can write down this number. And when I look at the interpretation of that number under this mapping, the number says,"
},
{
"end_time": 8184.07,
"index": 313,
"start_time": 8155.606,
"text": " I am true, but not provable within piano. And so now, at this point, I sort of agree with Roger Penrose. Penrose looks at that and says, OK, that means that there is something true here. I can see that it's true. I don't disbelieve. I mean, I saw the whole girdle numbering construction. I saw how the sentence came to say what it says, and I agree that it's all consistent."
},
{
"end_time": 8211.305,
"index": 314,
"start_time": 8184.548,
"text": " And what it's saying is saying that it's true and not provable. So at this point, I guess I sort of agree with Penrose. At that point, I go, OK, there's something beyond the notion of proof, beyond the notion of derivation that's going on here. There's the looking at analogies and understanding analogies."
},
{
"end_time": 8239.906,
"index": 315,
"start_time": 8212.142,
"text": " that where we go, this sentence is clearly true, and it's also by its own statement, its own declaration, that it's not provable within this finite computational system. Yeah. Peros is fascinating. He thinks that our brains are physical systems, and he also thinks that our mental processes are generated by the brain, probably, but that our brains can do mathematics that go beyond the mathematics that computers can do."
},
{
"end_time": 8264.428,
"index": 316,
"start_time": 8240.145,
"text": " That is a very specific statement that is more concrete, I think, and specific than what you've said so far. And it leads him to a weird spot, which he's quite lonely at the moment. But I find this nevertheless a very interesting argument to make. I'm afraid we will not be able to resolve it today because I have to drop now. But I found it very interesting to see that you are a penrosist at the end of the day."
},
{
"end_time": 8286.305,
"index": 317,
"start_time": 8265.009,
"text": " Well, I don't like the microtubules theory, and I don't like the non-computational collapse of microtubules theory. But I think that he's not really to be blamed for this. I suspect that his reasoning is that since all known physics is computational, these basically takes a state and then there is a transition between the states, the resolution for what consciousness comes from"
},
{
"end_time": 8295.776,
"index": 318,
"start_time": 8286.544,
"text": " If consciousness is enabling us to do things that computers cannot needs to be in an unknown area of physics and the unknown area of physics that's left."
},
{
"end_time": 8325.896,
"index": 319,
"start_time": 8296.357,
"text": " reasoning in the same way as Sherlock Holmes, if you actually exclude all the possibilities, the only remaining thing must be the truth, right? That's quantum gravity, because there is no generally accepted theory of quantum gravity. And then it just so happens that Hameroff has this beautiful psychedelic theory of how to get the microtubulize to have non-local interactions that employ quantum gravities in a way that nobody really understands. And this might be in this corner. And so"
},
{
"end_time": 8351.561,
"index": 320,
"start_time": 8326.084,
"text": " They become friends. But I don't think that Penrose theory is exactly the same thing as Hameroff's theory. Right. Right. Right. And I'm not talking about that more general theory of consciousness. I'm just talking about his specific analysis of Gödel's incompleteness theorem and what it means for mathematics. Yes. And it's basically also something that Chomsky is a fume to in which leads Chomsky to a mysteriousism. So basically they were confronted with the same"
},
{
"end_time": 8381.561,
"index": 321,
"start_time": 8351.903,
"text": " insight or the same idea that they think that human brains can do things that mathematics cannot, that mathematicians can make proofs that computers in principle cannot make, that they discover that certain statements are true, that in a computable axiomatic system cannot be derived. And this was also what my question was pointing out, at how do you know that something is true there if you cannot go show me a sequence of steps that does it, right? And so Penrose and"
},
{
"end_time": 8400.708,
"index": 322,
"start_time": 8382.193,
"text": " Right. I guess we will have to go. I'll just say our basic understanding of the axioms itself."
},
{
"end_time": 8427.073,
"index": 323,
"start_time": 8401.596,
"text": " How do I understand the basic axioms that are the foundation of the computational system? Where does that understanding come from? Is that from within the computational system or does that escape the computational system? From my own perspective, it's the case that my mind is constructing a model of reality. The reality that I found myself to be in is something like a physics engine in which my own conscious self"
},
{
"end_time": 8451.578,
"index": 324,
"start_time": 8427.312,
"text": " acts as a puppet, as a simulacrum that is being used to tell the story about an intelligent agent. And I don't see any limitations in my ability to make models that could produce such an agent that would find itself in this world and associate a set of valence precepts with a garlic and another one with sunlight and"
},
{
"end_time": 8477.039,
"index": 325,
"start_time": 8451.766,
"text": " that happens entirely through the relational nature of my unified model of the universe that is being derived by completely non-inferious computation that are approximated in nervous systems. So I don't see where I currently stand that this doesn't work out. And I'm very sympathetic to when you don't see this, that it doesn't work out and that you have to think that you have to find the truth elsewhere."
},
{
"end_time": 8501.954,
"index": 326,
"start_time": 8477.278,
"text": " and it could be that I am going to change my mind in the future when I stumble on something that basically shows to me that what I'm intellectually trying doesn't work so far it seems to work and I appreciate that we have this difference in our perspectives because it's a very productive and useful one to have. Absolutely, I've really appreciated the the tenor of the conversation too, very much so. I would just say my last thought on this would be that"
},
{
"end_time": 8531.63,
"index": 327,
"start_time": 8502.346,
"text": " What I would love to see from a computational system on consciousness is the association you just talked about between the computation and, say, the taste of garlic. Is it principled or is it arbitrary, that association? If it's arbitrary, then I'm not... Yes, it's not arbitrary. It is related to the valence of the taste receptors that you have. So it might be arbitrary in the sense that some people hate garlic and other people love garlic. So the garlic will taste different to them."
},
{
"end_time": 8555.555,
"index": 328,
"start_time": 8532.073,
"text": " This means they will have a different experience when they taste garlic because the relations of the taste of garlic will be different to the entire world model that they have than they are to other people. So basically the types of receptors that we have and the valence that they imply and the type of self-model that we have. So in which way has the mind constructed itself that is entangled with its universe around it? What is that"
},
{
"end_time": 8585.299,
"index": 329,
"start_time": 8555.555,
"text": " So there will always be the question, why should this computational process, independent of valence, be the taste of garlic? Why couldn't it have been the taste of chocolate?"
},
{
"end_time": 8608.234,
"index": 330,
"start_time": 8586.152,
"text": " I would want a principled answer to why is this computational process necessarily the taste of garlic? Why isn't it the taste of chocolate? Because one is affiliated to garlic and the other one is associated to chocolate. But I'm talking about the conscious experience of the taste of... Oh well, chocolate is sweet for the most part and garlic is not."
},
{
"end_time": 8638.353,
"index": 331,
"start_time": 8608.609,
"text": " So this is one of the dimensions in which the features vary and sweetness is perceived as pleasant under some circumstances when you need certain types of nutrients and the soreness and bitterness and sharpness of garlic is associated with other things that you might need or dislike at certain moments. So the valence is crucial that you get and there are basically hundreds or thousands or tens of thousands of valence dimensions that specify how we perceive this texture of the pattern."
},
{
"end_time": 8665.196,
"index": 332,
"start_time": 8638.353,
"text": " This is round one. Take care everyone. Thank you so much. Thank you too. Good talk. I really enjoyed this. Thank you very much. It was plenty of fun and the audience is all saying thank you as well. I think there were about a thousand people. Well, thank you very much."
},
{
"end_time": 8691.732,
"index": 333,
"start_time": 8665.64,
"text": " Thank you, Yoshi. Please send me the MP3, if you don't mind. And Don, I don't know if you still are recording yours. Bye bye. Okay. Bye bye. Take care. Thank you all. Thank you all. Thank you all so much for being here. It was plenty of fun. There's plenty to talk about for round two, whenever that occurs, maybe toward the end of the summer or the middle of summer. We'll see people's willingness and ability."
},
{
"end_time": 8713.251,
"index": 334,
"start_time": 8694.07,
"text": " The podcast is now finished. If you'd like to support conversations like this, then do consider going to patreon.com slash C-U-R-T-J-A-I-M-U-N-G-A-L. That is Kurt Jaimungal. It's support from the patrons and from the sponsors that allow me to do this full time. Every dollar helps tremendously. Thank you."
}
]
}No transcript available.