The Jordan B. Peterson Podcast - 244. Asking A Theoretical Physicist About The Physics Of Consciousness | Roger Penrose

Episode Date: April 15, 2022

Dr. Peterson recently traveled to the UK for a series of lectures at the highly esteemed Universities of Oxford and Cambridge. This conversation was recorded during that period with Sir Roger Penrose, a British mathematical physicist who was awarded the 2020 Nobel Prize in Physics for “discovering that black hole formation is a robust predictor of Einstein’s general relativity.” Moderated by Dr. Stephen Blackwood.___________Chapters___________[0:00] Intro[1:00] Is Consciousness Computational?[3:20] Turing Machines[6:30] Determinism & the Arrow of Time[12:15] Consciousness & Reductionism[17:30] Emergent Randomness & Evolution[23:00] The Tiling Problem, Computation, & AI[29:30] Escher, Brains, Bach[39:00] Pattern Recognition & Intuition[45:30] Mathematical Representations & the Physical World[54:00] Collapsing Schrodinger’s Equation[1:00:00] Consciousness-Independent Reality[1:07:00] Black Holes & Time Horizons[1:15:00] Einstein’s Biggest Mistake[1:27:00] Meaning & Consciousness[1:39:00] Hawking Spots: Potential

I'm Stephen Blackwood and I have the great honor today to be here with Sir Roger Penrose and Dr. Jordan Peterson. Let's get right down to it. Jordan, I know you have questions you're keen to pose to Sir Roger over to you. Yeah, well, I've wanted to talk to a theoretical physicist for about 30 years. And so I'm pretty happy that you're the theoretical physicist

that I get to talk to. I'm probably not representative, so you're... Well, that might be even better. So I want to jump right into it. I call a good friend of mine is a AI engineer and a computer engineer and he's built a lot of the world's great chips at iPhone chip. And first 64 bit chip, the alpha back in 1985. And we were having a conversation. I said I was coming to meet you and I don't want to put words in your mouth, believe me, but that you believed that consciousness is in some fundamental sense non-computational.

And I asked him what he thought about that. And part of the reason I asked him is, because he's of all the people I've ever met and maybe of all the people in the world. He's the person who's done most to build arguably brain-like algorithmic systems. And so I asked him if he thought that there was a distinction between the algorithmic computation of cognition per se and whatever consciousness might be. And he thought it was per se and whatever consciousness might be and he thought it was algorithmic all the way down. And I understand that you don't believe that. I also went with him a couple of times to a consciousness conference in Tucson where half of spoke. So we got familiar with that line of

reasoning. And I also understand, I believe that part of the reason that you think that consciousness is necessarily non-computational is because of Gidele's theorem. And so maybe we could enter theirs. What I'm very curious about your proposition that consciousness per se is non-computational and I'm curious about why you came to that conclusion, and if you think that's a warranted conclusion, what you think about that in relationship to these complex AI systems, and also in relationship to Goodell's theorem? Well, I've never seen the argument refuted. I've just talked to people who've never really understood it as far as I know. No, the argument goes back to when I was a graduate student

and I was doing pure mathematics, algebraic geometry. And I went to three courses, which were nothing to do with what I was supposed to be doing. One of them was a wonderful course by Herman Bondy on general relativity, which had a big influence on what I did later on. One was a talk by the great physicist Paul Dirac, and that talked me about quantum mechanics.

And the third one was a course by a logician called Steen. And he taught me about touring machines that notion of computability, what it is, and how you understand that. And the girdle theorem. And I had heard vaguely about the girdle theorem previously and had been rather worried because it seemed to show that there were things in mathematics

that you couldn't prove. What I learned was that it's not like that at all. Well, it is like that in a sense. If you lay down the rules of what you call a proof, and if those rules are such that they could be checked by a computer, checked whether they've been correctly applied by a computer. So computation rules in that sense.

Then you can construct a sentence. This is what Gerl did, which by the way, it's constructed. You can see that if you trust the rules, if you believe that the rules do, if they say yes, you've proved it, tick, then you believe it's correct. If you have trust in the rules, that trust extends beyond the rules.

In other words, you can see that a certain statement is true by virtue of your belief that the rules only give you truths, yet that statement is undenrivable, unprovable, using the rules. That statement of faith about the rules? It's not a statement of faith. I'm sorry, I didn't understand that. The faith is not a faith.

You understand the rules. You check them, you say, yes, that's okay. If that rule is correctly applied, I agree. It does, you know, it's a, it's a, it's a, a rule which is within something that you believe to be appropriate. And, and these rules, it's built up out of things like this, which nobody would dispute. So, okay, if you follow those rules, and it says, yes, that's a proof, then you believe that the thing that it says, yes, it's a proof, is actually a true statement. So, does a proof really mean that it's true? If you believe that, that conviction,

that the proofs actually do what they're supposed to do, gives you something beyond the rules themselves. That's sorry, that's what I was referring to with the word faith, is that the statement of belief, no question maybe you said you're wrong. Well, I guess I'm wondering what do you think it is that constitutes that belief? Okay, and why the word understanding, specifically, because that's the thing in some sense that's outside the system, the understanding?

Yes, it is, because you can see it is, because it's the understanding that the rules give you the only truths that enables you to understand that this girdle statement is actually true. And so is that belief in that truth of that proof, that is one of the things that Kudal pointed out would be necessarily outside any system that's both, what is it, formal, logical and coherent? What shows, it shows that the, I mean, I read it in this particular way, I don't just

think he said it quite like this, but I read it in the following way, that understanding whatever that word means is not computational. Okay, okay. That is what I... It's not the following of rules. It's something else. Okay, so let me ask you a question about that. So, this is a three-pronged question, let's say. Okay, yes. It seems to me that there's a high probability that the future is actually indeterminately different than the present and the past, that it's actually unpredictably different. Oh, this is a different question. Now you're talking about determinism.

Yes, yes, but I think it's, it seems to me that it's tied to this idea that computation can be complete and algorithmic. I don't think it can be because if the future differs in a fundamental manner, an unpredictable manner from the present or the past, then a deterministic algorithmic system can't maintain a grip on the horizon of the future. And I have another part of that question. But it's a different question. So I think it's important to distinguish these things. Yes.

Because up to this point, I was not talking about indeterminism. No, no, I was talking about rules. Well, just yes or no. And I mean, it's not a question of maybe you or I mean, it isn't even talking about the laws of physics at this stage, that's the second step you like. I guess I look forward to something like the potential necessary function of consciousness. So because one of the things consciousness seems to do from a neurophysiological perspective, for example,

we tend to become conscious of our procedural errors. And so consciousness becomes alerted to the errors and then zeroes in on the source of the error in some sense and corrects it. And so it looks to me like it's something like a correction system for underlying algorithmic systems. So for example, if you practice a motor routine for a long time, you build specialized algorithmic machinery and your brain that runs it. But maybe you've put in an error, you're playing a difficult piano phrase, for example, and you stumble over a note. You've automatized that.

You play it, you listen, and you hear the anomaly, which is the error. Your consciousness focus isn't on that. A large brain area will activate as a consequence of becoming aware of that error. Then when you practice the new routine that's corrected, the brain area will shrink and shrink and shrink until it's a small part of the brain, usually in the back of the left hemisphere. And now you've built another automated machine to play out that phrase. And consciousness, I think it was Whitehead who said that,

at least the purpose of consciousness, although he might have used thought, was to increase the number of things that we can do without consciousness or thought. But it seems to be this horizon phenomena. And the reason I was asking about the indeterminacy of the future was too full, is that if the future is deterministic, then an algorithmic system could in principle adapt to it. But I don't, it doesn't seem to me that the future can be predictable, and I think that that might be grounded in something like quantum indeterminacy,

because there isn't a fundamental determinism that propagates all the way up. So... Well, you see, I mean, we have to, that things I was talking about up to this point, but not to do, they weren't even to do with the laws of physics. So that's a separate question. I mean, it did relate to that, which is my own views. Certainly it did depend on that.

But the question of determinism is a separate issue. And the normal way we look at quantum mechanics is it does involve an indeterminism, which you can have a theory which does that too. But that's different. You see, if it's just indeterministic, it's not connected. The journal argument is to do things where you have definite rules. You can check whether these rules have been followed or not. And the question is whether it coincides with your understanding about what things are

true or false in mathematics. So that's what it's to do with. Now you see, you can question how you move from that into other aspects of what consciousness does. And also the question you were referring to is whether something's automatic in your penis can play things and obviously where the little finger goes next is not something that he or she decides to do. It's largely controlled by the cerebellum, probably, which as far as we know is entirely unconscious.

So the greater number of neurons in the brain, which are in the cerebellum, seem not to be acting according to conscious actions at all, or something completely unconscious. That's a very strange thing that people make the case as well that there's some simple relationship between neuronal function and consciousness, but as you pointed out, the cerebellar activity doesn't seem to be conscious at all.

And then there's a tremendous amount of neurons in your autonomic nervous system distributed throughout your body. And there may be some consciousness associated with that, but it's not particularly acute. And most of the time it's entirely unconscious. The autonomic nervous system is running your digestive system and your heart and all of these inner automated systems. It's interesting, too, because often becoming consciously aware of a highly functional unconscious system actually impairs its function rather than improving it. That could be, yeah. Sure.

I'd not quite sure what this tells us about consciousness. It just tells us that certain things are not conscious, which are controlled by neurons in the brain, and so it's a different issue. Right. My just to put it to ask, Mr. Roger, if you would say a word or two more about why it is that consciousness cannot be reduced simply to mechanistic processes. Well, you see, I'm very careful to say I'm not talking about consciousness in all its aspects. Yes. For example, I have nothing to say about the perception of the colour

green, for instance. I mean, sure. There's something going on which makes green have a certain impression on one. But this is not what I'm talking about. And probably most of the things that we think about when we talk about consciousness are not what I'm talking about. So I'm only talking about a very specific part of what consciousness does and the argument is that if this is something which is not a computational process, then it sort of sheds a question mark on the whole thing.

But it's only very specific to the question of understanding. So I tend to make that point clear. And understanding is something which in the certainly in the normal usage of the word implies conscious, and you wouldn't say of a device normally that it understands something without it being aware of something, and aware means being conscious of it. So that's just normal usage and I'm going along with that. So I don't know what most of these words mean, but I would say that understanding is something which requires consciousness.

Yes, it's one way into this. To speak about, I mean, so much of our thinking, of course, is Calculative. There's a goal there. We're calculating how to get to it. And so there's a huge amount of life that is like that. But to then ask the question about why this is a goal, or why this is worthy of being a goal, or what would make it worthy of being a goal, or what would make that worthy of being a justification

for that to be a goal, the kinds of thinking that you have to engage in in order to reflect upon the nature of the ends and purposes is distinct from the kinds of thinking you engage in to calculate your way to a goal, and that seems to point towards the realm or a kind of thinking or awareness that is clearly distinct from a simply mechanistic calculation. Yes, I mean, I certainly wouldn't disagree with that. It's just that it's hard to know whether those things could be put into a computational system. The reason for concentrating on this very specific area is that I can say something about it, that's all.

So the particular area is mathematical proof. They see most people don't bother themselves with mathematical proofs and they're conscious too, so I'm certainly not saying that, so an indicator of conscious, I mean I'm saying it is something which requires consciousness, but I'm completely accepted. There are also other aspects of consciousness, which are going on all the time in which you're much more important than going along with that too. But it's just that if you can find something

in what consciousness seems to do, which is demonstrably not computational, that's saying something. And that's the limited little thing I'm trying to say. Now, you started working with Hammeroff as I understand it, to try to provide something approximating a localization or a neurophysiological account of what this non-deterministic process might be. Ah, but I didn't say that's usually non-deterministic. That's different.

Okay. It's very easy to confuse the term. Well, and I am confused about them, apparently. You see, non-deterministic means that rules don't have a clear statement about what happens next. And maybe there is a choice about what happens next. And that choice might be random, or maybe choice in some more personal sense that you have a reason, I don't know.

But usually one talks about randomness there. You say that the theory does not have a complete description of what it tells you happens in the future because there is a random element in it. And the way quantum mechanics... In the future. Yes, in the future. That's what normally the way one talks about quantum mechanics... In the future, in the future. That's what normally the way in which one talks about quantum mechanics normally. And that's a truly random feature.

In current... In current quantum mechanics, that's correct. Yes. Okay, so that's what I was referring to when I was referring to the indeterminacy of the future horizon. It was that randomness that I was doing before. Yes, we see that. I mean, it is another question. You could have a random device which is otherwise computational.

I mean, it just, you put in at certain points, okay, do something randomly. Thing is that don't think, and it's just in question there, I don't think that gives you anything in the way of establishing results Which which seem to be a non-computational process like with the girdle thing? Okay, so so okay, so there's an evolutionary answer to the problem of emergent randomness and the answer is so I'm a skeeto. Miscito is a good example, any or fish, any animal that lays a tremendous number of eggs that could conceivably march to maturity.

So there's genetic mutation in all, so maybe let's say just for the sake of argument that a given mosquito lays a million eggs, fertile eggs in its lifetime. Now, there's variation in those mosquito patterns, and at least a certain amount of that variation is random, and that's a consequence. And it's actually a consequence, I would say, of events that are actually manifesting themselves in some sense at a quantum level, because at least some of the mutations are caused by solar, by radiation. And so there's disruption at a molecular level. And so evolution seems to be able to use the admixture of randomness into structure as a means of dealing with the interditermincy of the future. And to some

degree, it does that through death, right? Because of those million mosquitoes on average only one Managed is to propagate itself to reproduction or we'd be need deep in mosquitoes and like no, I'm saying Yes, but what I'm trying to say is that's what's going on with consciousness is different from that Because I don't see how this you know you're putting randomness and in the way you're suggesting and Clearly that says, is an important aspect to evolution and so on. It certainly wouldn't deny that at all. But it's not the same thing. Consciousness isn't producing randomness in response to indigency.

When I say non-computational, I don't mean that it's random at certain times. I mean, something quite different. So what, okay, let's zero in on that. So, because I'm very curious about what you do mean. I mean, this is obviously a tremendously important distinction between algorithmic, computational, algorithmic domain and something that's in some sense outside of it. And I'm struggling to understand at the most detailed level, let's say, how you envision the structure and function of consciousness or maybe just the function.

It's not producing mere random variants. And that can't be because random is too widespread. So at least at the very least. So for example, if you study creative people, we've done a lot of this. There is in some sense more randomness in their speech, because imagine that with, if you utter a given word, there's a certain probability that another word will emerge in a field around that. The creative people use lower probability concepts and words in their approach. So there's a kind of randomness. They go farther out into the word association field and that does help them generate more creative solutions. But that's not, if that becomes unconstrained to too great a degree, you get,

well, maybe like a manic creativity that's counterproductive and to random. People are jumping too much from disconnected point to disconnected point. And so consciousness doesn't seem to be creative consciousness, doesn't seem to be a mere random walk. So that's a psychological take on that. So what do you think is, what do you think? I'm still struggling to understand

what you think consciousness does. It does understand. Yes. You see, I think probably are trying to make me be more specific than I can be because I don't know what it is that how to make a device that can understand something. So I'm just trying to say that whatever understanding is, it's not a computational process, and that's the argument. Okay. Okay. I said, it's not. So you're not trying to specify what it might be. You're just saying it has to be something that's not a computation. Yes. Yes, that's right. Is there a fundamental link? I mean, when we say it is not non-computational, does that mean, or does that not mean, by definition, that consciousness

in some deep level is free? No, you see, that's right. These are open questions. I'm not saying that. I mean, it may be either as an aspect of indeterminism in it, and that could be. But that's not what I'm saying. And the trouble is, I think it's not a concept which people appreciate usually. So I can give you examples of non-computational things. And one of the examples I often give is if you take, you can take a, imagine a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a, a,'re given a finite set of these polyominoes, and the question is, can you cover the plane with those shapes, only those shapes, no gaps, no overlaps? Now that question, the answer yes or no, the answer is definite yes or no,

either you can or you can't. But it's not an algorithmic process. It's shown mathematically that there is no algorithm, which can tell you, yes or no, whether these shapes will cover the plane. Okay. So when I was talking to my brother-in-law, I was talking to him about these AI systems that learn how to recognize, let's say, cats from photographs. He told me there is no way of algorithmically determining the program that the machine

learning systems will eventually apply to the problem of identifying cats in a photograph, but if you let the AI neural networks run, and then you analyze their output, you often get something that resembles an algorithmic program as an output that you could have hypothetically calculated if you could have specified the search space. It's something like that, but there's no way of doing that

without letting the program do its walk through the domain of cat photographs with its differentially awaited neural network architecture. You can't A-priori predict it. Yeah, well, I still don't think it's the same thing. I mean, I could certainly give it different shapes, and you can say, tell a machine, you know, which of these will tile a plan which won't.

Now will that learn to give you correct answers? Well, probably usually it does. I suppose once it's tiled, you could formalize the process by which it was tiled, because you could describe the mechanisms or the order in which the tiles were located and the rotation of them. You could specify it after it had all been laid down. And I think that's analogous to what the AI system seemed to be doing when they're learning to perceive.

But the trouble is that it's not the message whereby you can tile a plane are, I mean, just a theorem, tell you that you can't put them on the computer. I mean, you might get the thing which works most of the time. Right. It's quite possible. So, in those tiling problems that you're describing. And so that's, that is, I see, I guess I kind of see why you're interested in the tiling issue.

So that has to do in some sense with the ability to map a surface with a certain representational form. And so if you have these tiles that you described and you're trying to completely cover a given surface, that's a mapping problem. I see what you're doing with that. Are there different ways that you could conceivably solve that problem? So you can solve. Okay, so so even if you do converge on a solution, you haven't converged on the only solution. Oh, absolutely. I mean, there wasn't an earlier result, which I would say that if it were true, that any way of tiling that plane with these shapes, with say some given set of shape, finite set

of shapes, if it tasked the plane, it can do it, it can do it periodically with a repeating pattern. If that were true, then there would be an algorithm. But it's not true because there are certain ways of tile and a plane which do not have repeating patterns. Oh, so now that's so cool because I was wondering today, I was wondering, why in the world is he obsessed with tiles? What's going on? Well, the fact that the tiles are, they're essentially mapping an area with a pre-determined concept in some sense. That's the tile.

Shake. Well, and you said it can be non-repeating and still solve the problem. You see the one in front of the mass building, that's an example. That's an example of a tile set, only two different shapes there. I mean, these aren't polyominodes, but never mind about that. Those two shapes will tie right out to infinity, but there is no way of doing this, which is periodic.

And you can see, it's almost, you can see this sort of piece of... So how do people actually do it then? There's another way of telling you how to do it. With the tiling. So you designed the tiling in front of the building. So do you actually tell the workman how to start the tile? And then how do they figure out how to do it?

They have a plan for the whole thing. And you devise the plan for the whole thing. So you provided the map. OK. How in the world did you get interested? Do you have any idea how you initially got interested in the tiling problem? Yes. When you say it, what certainly was this computability question, that is the connection. Yeah. I had learnt, I think I'd seen article in the maths reviews, this reviews, mathematical papers and so on. And I'd seen that somebody had produced a set of tiles which would tile the plane only non-periodic way.

And I hadn't seen what they were like. And there was a conversation. I think it was just, just after I'd been appointed And I hadn't seen what they were like. And there was a conversation. I think it was just, just after I'd been appointed to my chair here, the right-spot chair, but before I'd taken it up, and I had a conversation with an American mathematician, and he had told me in detail about, I think, there's a mathematician called Raphael Robinson who had got the number down to six and he'd got a set of six tiles, which would only tile the plane in a non-repeating way.

And he said that Raphael Robinson, this was Simon Coach and this is an American mathematician. And he said that Raphaaffa Robinson was somebody who liked to get the number, the smallest number, his sort of perfectionist in this way. And he said, he's got this run, at each side I would several thousand, you see, and he got it hundred and six. And he pretty pleased with that. And I said, well, I can do it five. I happen to know, I had a set with six, you see, but I knew that I could reduce it to five. How did you know?

How did I know that I said? Did you reduce it to five? Because the way that the... I mean, it's just a technical point. There was a certain shape for matching, and this shape only fitted into one other tile. So I could glue that, the ones with... It's just a slight detail point. I could glue some of the tiles together to make them five. And when you're mapping the plane, do you map it

to the precise borders of the plane, or can there be overlap? You know what I mean? Can it be messy on the edges? Or are you trying to precisely cover, let's say, a rectangle? It keeps on going beyond the edge, and then you cut it along the edge. Yeah, okay, that's right. Yeah, yeah. Okay. So now you also had some interactions, at least at arm's length, with Escher.

Oh, yeah, yeah. So what I read was that you and your father had been interested in Escher's work, and you worked out with him the ever ascending staircase which by the way seems to me quite similar especially to the music in Bach's third Brandenburg Concerto which and I talked to a musician this week about how Bach managed to make this continual ascending spiral that never really goes up. That's true. There is a thing like that. Yeah, right. Yes. So, and then you sent the drawings of the staircase to Asher?

Well, the story was a little bit longer than that because I had been at this, I was a graduate student. I think in my second year, I can't quite remember. And I and the colleague went to Amsterdam to go to the International Congress of Mathematicians, which happened every four years. And at this Congress, I happened to see one of my lecturers and he had a catalog which had one of these Escher pictures on one of the slides. And he said, well, there's an exhibition in the Fangok Museum. Well, this artist, MC Escher, never heard of him before. Now, we went to see the exhibition. I was absolutely blown over by these pictures. One in particular I think was called Relativity.

And I came away thinking, oh, that's amazing. I wonder whether I could do something a little bit different than I hadn't actually seen in the exhibition. And so I tried to make a construction with bridges and roads going in the possible ways. And I simplified it down to this thing. The people referred to as a tribear. I've seen the tribear. And I showed my father, I mean I didn't know that there's a Swedish artist called Oscar, right? A Svard who had done things very similar earlier.

But I actually didn't know about him either. But anyway, and there are other artists who have done things like, if you look carefully in the old, there's a Breugel which has a picture of gallows and they're joined up differently in the top. Yes, I've seen that. I've seen that picture. So there are other people who had played with these ideas, but I hadn't quite seen it in Escher.

And so my father and I wrote an article. He developed the staircase was his actually. He was designing buildings and then he produced the staircase which went around and around and we decided to write a paper on this. We had no idea what the subject was, what journal do we send it to. So my father said, well I happen to know the editor of the biggest journal of psychology. So let's call it psychology. So we sent it to them and they accepted it. He said he thought he could get the editor to accept it. They did and this was, we gave reference to Escher's,

the catalog of Escher's exhibition. And then my father had a correspondence with Escher with letters going back and forwards. Then I think it was driving in the Netherlands for some other, I was a conference I think. And I was curious. When I was reasonably close to Etchette, I phoned him up. I got the phone number from my father. He was very nice and he invited me and my then wife to tea and I just had a chat with him. He sat at one end of a long table, I was the other end, and

he had two piles of prints. He said, well, this pile, I don't have many left, I'm afraid, and he pushed the other part to me. Choose one. So I sort of went through these things, and I picked one out, pretty hard to choose one, I love all that. And I chose one called Fish and Scales, which he was actually rather pleased because he said, well, most people don't understand that one. So I thought it's bit excited by that. But this I then gave him a set of little pieces of just one shape. And I gave him a set of them and said, well, can you tile with those? And then a little while later he wrote to me and said, he'd seen how to do it, but he wants to know what the underlying principle was.

So I did. I was very bad correspondent. It took me a little while before I got back to him. But I showed him what it was based on. On the basis of that, he produced what I believe with his last watercolor, maybe even his last pictures, I don't know, I think called ghosts, which is based on this, it's the only tiling as far as I know that he ever did, which is what's called non-ISAHIDRA. You see, you usually did periodic ones, but they're periodic in a strong sense that if you find a shape,

the next time you see it, it has the same relation to the pattern as a whole. So you could move this one into that shape and the whole pattern goes with it into itself. But the one I showed him was what's called non-isahedra, that you can have different instances of the shape. So this one has a different relation to the pattern as a whole from that one. And so if I move this one into that, I can't bring the hope at him along with it. So you have two different roles of the shape plays. And the last one of his pictures showed this.

So I'm curious too. So this about two things now, I'm interested in why you're so fascinated by the relationship of a geometric shape that can be arrayed in a variety of different manners to this underlying problem of mapping. So you're reducing or establishing a relationship between the problem of mapping a large terrain to the utilization of very stringently defined, what do you call them, the representational systems, or that's a geometric form. What is the geometric form conceptually in relationship to the problem of mapping. Well, you had a shape and then you have certain rules about which pieces will fit next to it. But there's certain freedom in that rule. You could put this one that way or another way, you see. And you know, if it's a shape which very clearly has to fit that way next to it, then it just repeats. But if there's some freedom as to what the next one will do,

then you might have to make that choice. And certain choices will run you into difficulties later. And other choices maybe will allow you to continue. Is there a relationship that between that and what composers do with music? Because I mean, there's a certain, well, there's a certain repeating determinacy in music, but obviously a composer just doesn't take a pattern and repeat it indefinitely.

They take a pattern and the pattern seems to allow for some choice in movement from their pattern forward. Well maybe, I don't know. I mean, it's a, I mean what makes a piece of music into a good piece of music? I mean, I have no idea. That's a much deeper issue. Well, we do know a bit about it. We know that if it's too simple and repetitive, it, your interest gets exact, yes, exactly. It gets stale very rapidly. And then as it moves towards

purely unpredictable, it becomes indistinguishable from noise. So there's some place in between there and you could probably move on that place where you get some ultimately harmonious relationship of predictable form. And while something like the play of novelty that seems to me to be analogous to that possibility of shifting the shapes in this tiling problem, I mean, I think music is tiling something. It's a representational form. No, that's probably some connection. It's just that music, I mean, there think music is tiling something. It's a representational form. No, that's probably some connection. It's just that music, I mean, there's so much more freedom as to what you do. You see, with these tiling shapes, it's forced on you, either it fits or it doesn't, you see.

With music, it's much more subtle. Right. I would hate to make too much of a comparison between it. Elite. Yeah, yeah, yeah, yeah. Fair enough. One more question along that. Okay more question along that triangle you made. Yes.

Now, what's the relationship between those paradoxical forms and the tiling problem? Not much. Because they seem to be, there, I mean, there's a play of representation and image there. One of the things I've been wondering, I looked at all your diverse contributions. And I thought, wow, there's a play of representation and image there. One of the things I've been wondering, I looked at all your diverse contributions. And I thought, wow, there's a lot of things happening,

a lot of different places. But there must be something that's not random. There's something at work that's kind of a uniting principle that might be, I don't know, it might be the problem that you're trying to solve in some deepest way that's uniting all these elements of exploration and interest. I don't know, you're asking too hard a question. I don't know.

I mean, sometimes I don't see any overriding principle. I mean, there's a sort of thing, you know, something feels right. No, why does it feel right? I mean, that could a sort of thing, you know, something feels right. Now, why does it feel right? I mean, that could be something very subtle. Yeah, maybe wrong, too. Oh, maybe, maybe not wrong. Yes, yes. So you're saying that?

It seems to me that that also is related in some important sense, psychologically, to that notion of understanding, you know, the feeling that it's right. It's like, it's interesting that it can be wrong, but it's also feeling that it's right. It's like, it's interesting that it can be wrong, but it's also interesting that it can be a predictor of a guy as student. A student, she was very creative and she would come up with hypothesis that were damn good, but she was more creative than the typical psychologist, and I don't say that in a denigrating way. I mean, she was

more like an artist than a researcher. And then what she would do is spend like six months writing out the algorithmic pathway to that conclusion, even though that is not how she derived it. But she had a pretty unaring ability to jump forward to the right place with her intuition. And it's something like, I think it's something like a deep form of pattern recognition. You know, you don't need the full pattern to infer what the pattern might be. You can have a sparse representation of it, leap to what might be analogous to a tiling solution, I suppose. And that seems to be something related to the accuracy of intuition. I know when people become skits of typo, for example, they, and paranoid,

that also happens in paranoia. They have a lot of intuitions about patterns that might be there, but most of them are wrong. And so it's like their pattern recognition system has become, well, it's exceeded the limits of its capacity for accuracy and is starting to see pattern in what's truly random, prediction error. Yeah, well. May I ask, there's a, I think one important distinction here from what I can understand. So Roger is, with the nature of understanding is not to be simply reduced to belief or intuition, though it may be related to them, when one understands something, let's say, the simple equation that 2 plus 2 equals 4,

is not a belief that that is true. Understanding is operating at a level that is beyond belief. It has a certainty, an inner certainty certainty that is not subject to doubt fundamentally. And what I was wondering if it might be helpful, just for the sake also of the people who may subsequently watch this conversation, if you would be willing, Suraj, or to give us a sense of your your, the way you describe the three spheres of matter and mind and mathematics, is that might give us a basis for some quite rich conversation subsequently. Well, maybe. You want me to describe the picture. Please.

Well, this was just the way of thinking about the relationship between mathematics and the physical world and the world of conscious perception. And I was regarding each of these with a sort of world. I mean, whether that's a useful way or not, it was just helpful to me. And there is the mathematical world, and I take a very platonic view here, that the mathematical world exists independently of us. And so when we find a mathematical result, it's more like a discovery than an invention. So it's there already, and you find it. So it's certainly a feeling that, as far as I'm aware most mathematicians

have and the truths are there and they're there independently of us and if we're lucky we can find one of these truths and see why it is a truth. Now that's one thing. Now then there's the physical world and the physical physical world, the more we learn about it, the more we find that it operates according to very precise mathematical laws. But yet it's very small. You see if you look at a mathematical journal, you find it's almost entirely full of things which have nothing more so able to do with physical world. They're playing around with mathematics for its own sake. That part of the mathematical world, which actually does have direct relevance to the way

that physical world operates, is a small part of it. So I have a picture of this mathematical world and a tiny bit of that comes and imposes itself or whatever you like to explain or whatever you like to say, the physical world. So the more we learn about the physical world, the more we see it is driven or acts according to these very specific, tiny part of the mathematical world. And the second thing is, in that physical world, which seems to be operating according to mathematics,

there are entities which seem to be able to perceive and understand and have consciousness. So the acquisition of consciousness in whatever way is a small path, usually the world consists of rocks and things like that, which don't seem to have any of this quality. But there are certain creatures, things that just people in this room and elsewhere, and probably other animals, which may have less of it than humans, but on the other hand, I'd certainly think they have consciousness and some of them. So, but still it's a tiny part of the physical world which seems to have

access or whatever the right thing is, seems to be able to be, if it has a certain sense, this world of consciousness. So it's just again a small part of that. But it's only a tiny world part of the conscious activity which is concerned with mathematics. So I had this picture with this sort of meant to be slightly paradoxical than each world in a certain sense comes from a little bit of the world preceding it. And so it's drawn in a way which is like, like this impossible triangle, which looks like a paradox. That's only a little joke in a way. I don't know how much depth there is to that. But I'd rather like to depict it in that way.

So stop me when I'm wrong, okay? All right, so it seems to me that the mathematical reality is something like the observation of the patterned regularity between things. It's not the things themselves. The physical, which we're talking about. Well, I'm thinking about the mathematical representation of the physical world. So because things, there are things, obviously, but there are things in relationship to one another.

And the relationships between the things, like the pattern that your tiles compose is just as real as the tiles. But it consists of the relationship between the tiles. And is it the representation of the relationship between things that's part of that mathematical world, rather than, I know it could be past the world. You see that it's a physical thing, and that's just sitting in front of a mass building. So that's the physical thing.

But it represents a mathematical idea, which only gives you the idea. You could say, oh, these tiles fit together in such and such a way, and these are parts of a Euclidean plane, a Euclidean plane, is a concept. We don't actually have it physically. But you can see, by looking at the tiles carefully enough and see how they fit together, that this is a mathematical thing you're looking at in the way. And this mathematical thing would allow you to continue, if you understand what's going on indefinitely. So the entire Euclidean plane could be covered according to the rules at those shapes, you see.

Okay, so let me ask you another question. Okay, and so, is the physical world one tiling solution to the plane of mathematical possibility? I guess it, in a sense. I mean, it's slightly... You see, it's not really talking about the laws of physics there. It's only in the sense that Euclidean geometry is a pretty good approximation. That's what it's saying. I mean, there's not much physics going on there. You might say, well, what makes these tiles, some of them shine and some not shine or something

like that? I mean, it's more like physics. But the actual design that's being used there, it's been put there by human beings according to another human being said they should lay them down, and that was driven by a certain mathematical concept. But it's different from the way that mathematics underlies the laws of physics, and that's quite different. It might be if you took one of those thousands through it across, or how are you pretty hard to do because they're quite heavy.

But the way that would move in the air before it came down and crashed, that would be a clear indication of a physical law, where in which gravitation behaves. And then the way the thing holds together, the law that holds the… – Makes these tiles solid. – Be something to do with the… with quantum mechanics, to do with the ways that the atoms are constructed and how they connect with other atoms and what makes them solid rather than a fluid or something like that. So that would be the way that mathematics drives the physics. It's general laws rather than a specific thing. I think that's what I'm trying to say.

I'm curious to go do it, because in some sense, and I could obviously be wrong about this, but the physical reality seems to constrain the mathematical possibility, because there's only some mathematical rules that govern the behavior of actual objects,, because there's only some mathematical rules that govern the behavior of actual objects, even though there's all sorts of possible mathematics that could govern the action of all sorts of hypothetical objects. Right, so it's so mad if there's an underlying, I can't help but think that this is associated

with this many worlds idea, but if there's an underlying metaverse of mathematical possibility, you get the emergence of something like, well, what would you say? One concretized exploration of that possibility space, and that now establishes a relationship between one element of that mathematical possibility space and, well, in reality itself, doesn't exhaust the search space. But it seems to me that that's analogous to this tiling problem in some sense. I think it's, I don't know, I can count up saying I think it's really very different from what one is trying to do in mathematical physics. See, in mathematical physics, you're looking for general laws

which seem individual, instantivate, agree with this law. So that an object like one of the tiles that are being used outside mass building, I mean, the trouble is that it depends on detailed laws about the atoms which construct the tiles and so it's just nothing to do with what we're talking about here. I don't think it is. Well I guess I was wondering partly because there's these fine-tuning arguments, you know, and the question arises, well there's lots of ways these phenomena could be interrelated, but in reality it turns out that there is a very

finite and constrained number of ways that they are actually related. And those are the fundamental laws. And then the question arises, well, why that set of constraints and not, you know, some other set of constraints that seems equally, probably, probably statistically, you know, if it was a sample of the mathematical domain. Yeah, I guess I have to understand what you're saying a bit better. I mean, you can say, okay, there's this building, what the one we're in now, which has in the front of it a certain tiling. I mean, that's, if you're going to explain that, I mean, that's very different from what mathematical physicists do. I mean, they're just looking for that, I mean, that's very different from what mathematical

physicists do. I mean, they're just looking for general principles. And the as far as we're aware, those general principles are not violated in what's been going on in this building. However, that's not entirely what I would think, because what's going on in this building and so on is an implication of what's going on in people's heads. And this does have to do with consciousness. And what's going on in consciousness, in my view, is not yet part of current physics. So I am trying to say that although we have very good theories about

how things behave, bodies behave, they're not good enough yet to tell us how a conscious human brain operates. So do you allow your imagination to wander into the domain of metaphysical speculation about that? I mean, because you're making a case. I mean, I was talking to some divinity scholars the other day, and they were laughing, I suppose, about physicists who say, with regard to the big bang and the hypothetical emergence of everything out of nothing, that give us one free miracle and we'll proceed from there.

I mean, there is speculation among physicists that the laws of physics don't apply to whatever the state of existence was before the universe emerged into being. And you're making a case now as well that consciousness itself may not be able to be encapsulated within the realm of our current physical theories. So what do you think the metaphysical or do you or let me try and get I don't have to unpack something because we're venturing on a different topic. Yes, I know which is the question of the big bang Yes, which I have a different view on that from what you normally Okay, so but that's well that'd be fun to talk about that if you want to yeah, that's interesting topics to talk about

but that's really different. And as far as I don't even see a connection as things stand, from what I'm worrying about in consciousness. What I'm worrying about? I'm also wondering about both stand outside the laws of known physics in some sense. But let me say something else which outside the laws and known physics. And this is not something that people normally even recognize as a problem. I mean they do, but they shove it under the carpet. Which is what's known as the collapse This is not something that people normally even recognize as a problem. I mean, they do, but they shove it under the carpet, which is what's known as the collapse of the wave function. Now, you see, current quantum mechanics, strictly speaking, is an inconsistent theory. That's rather brutal way of saying what Einstein and Schrodinger and even Dirac said quantum mechanics is incomplete.

And the way to explain this is, okay, there's a wonderful equation which tells you how thing a state of all is in quantum mechanics, called the Schrodinger equation. Now the Schrodinger equation tells you, if you know what the state of a system is now, the Schrodinger equation tells you what it will be tomorrow, if you like. The evolution of that state is governed by this wonderful equation due to Irving Schrodinger. The trouble is that it doesn't. That's to say, the way physicists usually use the Schrodinger equation is to work out certain probabilities of what an observation on the system would

tell you. So what you have to do is you wheel out of the cupboard and a measuring device. In this measuring device, you set it on the system, which is evolving according to the short equation, and it measures it. And the process of measurement does not follow the Schrodinger question. It gives you a probabilistic answer, this or this or this. That's another outside the system problem. It's certainly outside the Schrodinger question. Right, right, right. As Schrodinger was terribly worried about this. I mean, he produced his cat in the box and all

sorts of things. He clearly realized there was a problem as did Einstein. There's no question about that. Some others didn't. Well, it took a different view. They said, look, we don't understand the theory well enough. That's more that we're saying. We're shorting, we're saying that. You're saying we understand it well enough to see that that's not the way the world operates.

When you make a measurement on the system, it does not follow the shorting of our equation. And that's what people understand about quantum mechanics. But it's a sort of vague set of rules about it doesn't tell you what constitutes a measurement. Right, that's a big trouble. That's a big trouble. Yeah, yeah.

They say if you do a measurement then it just becomes a probability for what they're sort of out of the other. But it doesn't say what kind of a desires makes a measurement. Now there's one school of thought You said been going on away from way back to the early days of quantum mechanics Vignore in particular promoted this point of view that it's a conscious being Observing the system and that makes a wheeler believed I believe I will am I to believe it quite a lot being observing the system. And that makes the... That's what we are believed, I believe. I believe. It was quite a lot of people believe that,

I think, Van Neumann had a similar sort of you. I'm not quite so sure about this view, but certainly Vignan. And I talked to Vignan about this. Yeah. I got the feeling from Vignan. He wasn't quite as dogmatic. He was made out to be on this issue.

He just thought this was a possibility, I think. But anyway, that's, people often refer to it as the Vigno view that is a conscious being who makes a measurement. That's not why I view. My view is that it's almost the opposite of that view. That there is an objective physical process which deviates from the Schrodinger equation in which the state does collapse so that it becomes one or the other with certain probabilities. And that this has to do with when gravity is brought into the picture. And there's reasons for believing this. I don't want to go into that. But there is reason. I'd like you to go into it if you wouldn't be willing to, because I mean, I'm very... Well, it's a very clear mathematical calculation.

There's not a question about it. It's quite what you do with it, you see. And what you do with it, according to me, is to say, okay, it tells you that this system has a lifetime, and it will, in that lifetime, become one or the other. Without a measurement? It sort of... That's right, yes, without a... Well, it's so interesting to me that you're interested in consciousness and you see the consciousness

in this Gidele theorem sort of manner. And I would think the most predictable thing for you to believe as a consequence of that would be that it is conscious measurement that collapses the quantum indeterminacy, the waveform, and yet you don't, you think that that statistical vagueness will collapse into something that's essentially, is it either or is it binary? Is it zero-one? The collapse?

No, there's a probability it'll do. Right, but when the probability collapses, it's a two-state system. You see, you might have an object which is in a superposition of here and here. There was the Brax first lecture, I remember, and he took out this piece of chalk and said, well, he was talking about atoms, according to quantum mechanics, or a particle.

So quantum particles are going to be here, or it can be here, or it can be in a state which is partly here and partly here at the same time. And then he took out a piece of chalk and people tell me he used to break it into. I can't quite remember, because my mind was drifting away from what he was saying, and I was looking at other wind-learn, thinking about something completely different. And unfortunately, it only came back after he'd gone onto the next topic, so I missed the explanation, which was probably a good thing, as I think back on it, because probably the explanation was something sort of to calm you down and stop worrying about the problem.

I suspect it was something like that. So you don't think that conscious observer per se is necessary to collapse the wave? Absolutely, that is what I'm agreeing with you. I don't believe that. But you do think that if I'm not mistaken that the presence of an observer in the universe, that is to say that the observation of the universe by us is that true to say is fundamental to the universe. Not really. That's an interesting question, but it's not part of my view.

The world would be there, but independently of whether there were creatures of consciousness walking around on them. So, can I ask you a question about that? So, it's related to this. So, it's my understanding, and I could be wrong about this too, because I'm way afield here, you know, I'm out of my depth and area of specialization, but my understanding is that in some sense as far as a photon is concerned that the universe is too dimensional perpendicular to its direction of travel. I don't see that there, but go on.

Well, I thought and I thought that this that there but go on. Well I thought and I thought that this my it's a consequence of the contraction of things as the speed of light is approached and so oh I say no no no no that's that's you're talking about the the rents contraction or do you know yeah yeah well I thought as part of that that part of the reason that no amount of energy can propel something past the speed of light is because in some sense the light beam is already where it is and at its destination at the same time and you can't get flatter than flat. Now the reason I asked you that though was because it pertained to this other question, which was,

if you could imagine what the universe might be like phenomenally from the perspective of a light photon, that's very unlike the universe that we perceive. I see, I mean, if you were riding on, well, I mean, I suddenly said, yes, I know what riding on a light, the trouble is that you can't sit on a light. Yes, that is a problem. If you were nearly going, yeah, very, very fast like that, the passage of time, you would think it hadn't taken any time at all. Right. Except, well, and that's the same as being at the starting point down the destination. That's. Yeah, it's okay, okay, okay. So that, now for us, we perceive things with duration and distance.

And so, but the photon is in the universe and we're in the universe, but the universe looks very unlike each of those situational positions. And so you said that there would be a reality independent of consciousness, but I'm curious when you think of a reality independent of consciousness? What are the attributes of that reality? Like is it is a field of quantum potential? Is it?

I'm not quite sure I understand the question, but I mean, classically there's no problem. I mean, this thing about the contraction and all that stuff, with it's going close to the speed of light and so on. This is classical physics, so we're not worrying really about the problems of quantum mechanics there. But they're already there in classical physics. But if you had a particle traveling at speed of light, let's say just less than the speed of light,

and if you could sit on that particle, it would seem as though you got to your destination almost instantaneously. That's correct. But that is nothing to do with quantum, well, not directly to do with quantum. Right, right, right. That's just that's relativity.

Right. Yes, sure. But the phenomenal universe at that speed is radically different than the phenomenal universe at our speed. Yeah, but the universe is there. It's just a question of I'm not quite sure I understand this you see I'm sure the universe I understand how it can be all of those things simultaneously like No, it's it's what that means. That's not a problem. It's just yeah Like, no, it's just what that means. That's not a problem.

It's just, yeah, when I say it's not a problem, what I mean is that there is a way of looking at relativity, which means special and general relativity, which is completely coherent and doesn't really worry about who measures what. It's just there. You have a space time, which is this four-dimensional structure, maybe hard to understand and visualize and so on, sure. But it's the thing which is there, people call it a block universe view. Well, I think about it as a whole symphony at once in some sense. Well, if you like, but it's all there. And what something measures in that system,

you have to go and ask the question. If you had a body traveling with a great speed and it was a clock on that body, you'd ask for how many ticks does it happen before one end in the other. That's perfectly well defined. If it was sitting stationary, it would have so many ticks between starting a thing. You could have one which goes out and comes back. You might say there are only about four ticks, where's this one? I had a thousand ticks. Well, it's the answer. It doesn't need the time. Right, and it's susceptible to all those interpretations simultaneously. Yeah, because each one is just, it's only measuring it with, it carries the clock with it and that clock ticks at a certain rate and that's fine.

There's no problem. Well, I say there's no problem. I mean, it's not a philosophical problem. There's a little bit of a problem. We're going to use to the ideas. Sure. No, I agree with that. Yeah. Yeah. That's not the issue. You can, once you've got use to the ideas and you, oh yes, you can see time is something which depends on how you're moving. Right. And the clock which is moving fast. Is there any difference between that statement and rate of change depends on how fast you're moving?

Like, is there any difference between time and rate of change? The rate of change is... because I think of time as the averaged rate of change. And so when you say that time slows down as you move faster, you're not saying much more than as you move faster, you're... That's just a question. You see, I think the mistake here is the think of time as an, as an objective thing. Yes. Which is attached to this mole and it's not. Right. Right.

There is no concept of when such an event happens. You say, you might say, well, is this event later than that event? Well, if they're what's called space like separated, then just to say, you'd have to go faster than that to get from one to the other, it's a meaningless statement, because there is no universal concept of time in this model.

It's not not there. I think, you see, that goes against what we normally feel about time. You think about time is progressing and somebody on the Andromeda galaxy. We experience duration, so. Yes, but you see, what about when is now? I often use this, I think I use this example of two people crossing the street and they're

walking, just walking the speed crossing the street. And the question is, according to one of these people, there is a, At the same time as they cross each other, there is an event on the Andromeda galaxy where space fleets has been launched and they're going to invade the earth. According to the other one, the decision has not even been made yet as to whether they're going to invade the earth or not. Now this is only because you're trying to transfer your local notion of what you mean by time to the Andromeda Galaxy. And this depends on what frame you're using.

So if you're using a one moving frame, it hasn't happened yet, and the other one, it has. You just have to get used to that idea. But there is no universal notion of time ticking away. Independent. Independent of the frame of reference ticking away. Independently. Independently. Of free reference. Yeah, that's right. Yeah, okay, okay.

Can we get you some of that? Can I go sideways one more time? Okay. Because I'd like to ask you, like I said, I've been wanting to talk to a theoretical person forever. I'm really curious about black holes. And so I have this idea. And so tell me what you think about this. So when a star collapses past the neutron stage into a singularity, is, and let's say there's

multiple black holes, are they all the same singularity? No, no. Okay, okay. Well, I mean, you could link up them somewhere, but no, we don't. Apart from saying we don't know, I would say no, there are different singularities. Well, I was, I was trying. In close that statement, we really know what we're talking about here, but go on. Okay, well, while I was, I thought about this partly, God, it was so long ago that I thought about this, that I can have her, do even remember what I thought. But I was trying to wrestle with the fact that you get this unbelievably intense,

not even single point gravitational field. And there are strange effects of time inside the event horizon of a black hole from the perspective of an observer. Now, if I remember correctly, if you were watching someone descend into a black hole from outside, don't they go slower and slower? They would see them hovering on the horizon and then fading away very quickly, actually. Okay, what? They just fade, yeah.

They would fade. What happens to their sense of time once they pass the event horizon compared to the sense of time, the framework? They would go right through and they wouldn't notice anything at the horizon. Right, and what would that look? And you wouldn't be able to see the big black hole. I was a little one. They would have been wrecked by the tidal forces.

But yeah, if it's a big enough black hole, you could imagine going through it. You wouldn't even know you'd gone through the horizon. If you could see someone descending into it, how long would it take them to arrive at the surface? Is that forever? Not for them, no. No, for you watching them. Well you just see them.

You don't ever see inside the horizon. The light can't get out. Right, right, right. So you never see that. That's right. So they could be watching their watches and thinking whoops, you'd gone through now and they would do that but you would if you could see that watch from outside you'd see that the hand slowing down and getting closer and closer to the moment when they cross the horizon but fading out. But it would be slowing down. Yes, You'd see it slowing down, yeah.

Okay. Then if you could see inside, would you see that continuing to slow? No. No. Sorry, I'll show what you mean by seeing inside. Once they pass the event horizon, you can't see them anymore. But as they approach the event horizon, if you were watching them, you'd see their clock slowing.

Yes. So if you were outside. If you were outside. Yeah. So if you're outside. If you're outside. Yeah. So then I'm wondering, you can't tell this, but their clock is going to slow the same way as they continue moving towards the black hole. And that's the troubling. See, it's the wrong way to think of it.

Okay. That their clock is, is there a time which their clock registers? That's going to saying there is a universal time, which everybody is supposed to respect in some sense. Relativity says no, there is no notion. But I'm assuming their clock would continue to slow relative to you. I'm not trying to assume an absolute time in the question.

I'm just, I'm wondering is that as they approach, I know, I know the problem that you can't detect it is the problem here, but as they're moving towards the star relevant relative to someone who's watching them their clocks are slowing. According to this frame of reference. Signals that you would receive, maybe that clock it emits a little flash of light. Yes, that's exactly. And you see look those flashes like a slowing down. flash of light. Yes, that's exactly. And you see, look, those flashes are slowing down. Getting farther apart.

Yes, that's right. OK, so then from the external perspective, I was thinking that it would take them forever to reach the singularity. And if it takes forever, then that would be the same amount of time that it would take everything in the universe to collapse back into the initial singularity if the collapsing universe theory is correct. And so the reason there's infinite gravitation in some sense at the point of the singularity

is because that's a point at which the end of the universe has already manifest in the current universe. And that seems to me that that would be what would you say in keeping with the idea in some sense of a block universe. It's not quite sure I see the problem here. You're thinking about the whole universe, a collapsing model. Yes, you could certainly. Yes, I'm also wondering if that's a model that you think is... No, it's not my model. It's not a whole new model that people consider, sure. And you might have a hundred-tie universe, which is collapsing in words, yes. And then you would hit the singularity before you see somebody else

sitting in it. In those models, you would find you're in trouble, your coach is getting too big, and you get killed by it. As you are watching somebody else and you see, no, no, they're happily not nearly there yet. Right, not nearly there yet. Yes, that's what you would say. That is what you would say. Okay, that's okay, okay. All right, then your model isn't,

is it a big bang model with an initial emergence out of nothing and then eventually it collapse back to that? No. So, okay, so how do you conceptualize that? Well, first of all, it is a big bang model. And in other words, there is a big bang, but the big bang was not the beginning. The model, the reason people have trouble with this model, I think, is you're probably having trouble with it, and you're not unique in this. You see, people tend to think that if you have a model in which it keeps on going in some sense, and your big bang is not the beginning,

that you've got to collapse back, so it expands, and it comes back, and then you're back with... But this model is simpler that way. Yes, but this model is not like that. That's where you've got to get your mind running. Okay. And it's, people have trouble, and I agree with it. It's a crazy idea. And I admit it's a crazy idea. The trouble is it seems quite likely it's true. From certain,

optional things. But it's crazy too. It could be crazy and true at the same time. Yeah, that's like a definition of light. Yes, but you see in this model, the universe expands and it expands and this exponential expansion we seem to see the stars seem to be going, starting to go away from us. These very distant stars that people look at with an increasing speed. Right. And it seems to be this exponential expansion. And I've really driven the dark energy hypothesis. That's what they call it. Really. Well, I claim it is absolutely nothing inconsistent with Einstein's 1917, wasn't it? In modification, if you say that he regards his biggest mistake,

but it's probably actually right. That's to say the introduction of a cosmological constant. Constantly right. He introduced it for the wrong reason. That's true. But he was right to introduce it, even though he regarded his biggest... Well, he needed to make things work, but he didn't have any real practical reason for assuming that it was true, apart from...

He wanted a static universe. He didn't like the expansion. No, this was a time before. I think Hubble had already seen the expansion, but it hadn't got through the Einstein, how convincing these results were. So he wanted a universe which is static and stayed there forever. Right, right. And then he needed the cosmological constant to do that. That's correct. He would need that. And he needed the cosmological constant to do that. That's correct, he would need that. However, he was wrong. When he got convinced that one of the universities

is expanding, sorry, he said, oh, that was a mistake, my biggest blender, he said, trouble is, his biggest blender turned out to be true. It's apparently, I mean, this is an argument, people don't necessarily think it was. People might not think it's the cosmological constant. I think it was, I think it's right. I have reason, internal reasons for that.

But let's say that this is right. It's a cosmological constant. The universe expands and expands exponential expansion. Now you might ask, who's in this universe, eventually? Not us. The black holes will all evaporate to the way by walking of apparition. There's swallow, galactic clusters.

What's left in the universe? Pretty well photons. Now giving the simplified version of the theory because there's some questions about it still. But let's say it's dominated by photons, which is pretty, pretty well true, but not, let's take that. Now the trouble with photons is that they don't fuel the passage of time. Right. And more importantly, the equations governing light are the wonderful equations due to James Clark Maxwell, the Maxwell equations. And the Maxwell equations have a very interesting property that they can't

tell big from small. They're what's called conformally invariant. But if you have a system which you've got some electromagnetic field and you could stretch this system to bigger or smaller. It doesn't notice the difference. The equations work just as well and you can squash them here and stretch them here. Well, is that in part because space really doesn't mean anything to a photon? In a sense, well, it's the scale of the space. You see, it's what we call, there's a term which I'll use here called conformal. Conformal means big and small. I very much like, we talked about Escheron a minute ago, there are these Escher pictures called circle limits,

where he describes what's called hyperbolic geometry, but don't worry about that. The most famous one is these angels and devils, and you see it, there's a circular boundary, and they look as though they get smaller and smaller and smaller as they get to the edge. Yes. Now as far as those angels and devils are concerned, the little ones are just the same as the big ones.

Right. They don't know that they're smaller towards the edge and that to them is an infinite universe. But to us we can see, no there's this infinity which is just sitting there. And these angels and devils, if they don't know big from small, I'm not sure I have a bit of trouble using this to explain things because the angels and devils do have a size in the picture. But you see, if they were made of massless material, that wouldn't know big from small.

So if they were made of just electromagnetism, then big and small are equivalent. And so you wouldn't know when you got to the edge of this universe. So that infinity is just like anywhere else. That's the difficult concept and this thing. That the photons reach infinity without realizing anything funny has happened. If you put it like that, infinity in this conformal picture is just like anywhere else.

It's the only mass that knows the difference. If you want to build a clock, you need mass. And this comes from the two most famous equations of 20th century physics. And the two most famous equations, one of them is Einstein's equals mc squared of course, which tells us that energy and mass are equivalent. And the earlier one was, it was Max Planck's e equals h nu or e equals hf, whatever I should call the frequency, which tells

you the energy and frequency are equivalent. But the two together, that tells you mass and frequency are equivalent. Now that means that if you have a mass, it is a clock. It has a frequency, simply determined by its mass. And this fact is really the basis of modern clocks, which are extraordinary precise. They don't directly give this because the frequency is much too high, you have to scale it down. It's probably the same idea. So clock, a mass is a clock. But the other side of that coin is if you don't have any mass, you don't have any clocks. If you don't have any time, you don't have any time. So you don't have any time, you don't have any time scale,

you don't have any distance measure. So if the world is inhabited only by massless things, say photons, then it doesn't know big from small, it doesn't know hot from cold. And so the idea is, and this is where you have to take a deep breath. The idea is, it's opposed to all the other parts of this conversation. The idea is, it's opposed to all the other parts of this conversation.

The idea is that the remote future is instinctual from a big bang. So long as there is no mass around. Now, the remote future, the reason you have no mass around is basically, well, listen, there's a complicated part of the argument. Yeah, let's say it's because of the mainly photons. That's good enough. Well, about the other way, what about the big bang?'s say it's because of mainly photons. That's good enough. What about the other way? What about the big bang?

What's a lot of mass there, surely. But the thing is that at the big bang, things get so hot, things are moving around so fast, if you like, that the energy, or the mass energy, mass-hyphen energy, the concept of mass, according to Einstein, is almost entirely in their motion, and that the mass becomes more and more irrelevant, the closer you get to the big bang.

So again, you have a situation where mass is effectively zero. So, are you, is it your claim, belief theory, that when things ground out in a universe that only consists of electromagnetic radiation, that that is now a precondition for an event like the Big Bang? In a sense, yes. I'm saying that the physics which is going on at the very end of the future is extraordinarily like the physics going on at the very end of the day. I'm going to say beginning. I only mean the big bang because it's not really the beginning. Yes. Well, it's such a lovely place to end and we have been going for an hour and a half and I don't want to wear you to a frazzle.

I'm not frazzled. Well, I think I might be. Do you mind if I just ask to have a question? Sure, go ahead and see, please. One of the things that I'm very struck by in your account of the three realms of matter, mind, and mathematics, roughly speaking, is that the realm of mind or consciousness is... The realms are not reducible one to another. So the realm of mind cannot be reduced simply to the realm of matter. Nor can the realm of mathematics be reduced simply to the realm of matter.

They each have their own existence. Well, you see, it's a picture which I've used. I'm not sure whether it completely concur with my current views, but go on with what I'm saying. What I wanted to ask you about is, and it's a two-part question, but I'll start with the first here. And that is that what is the relationship? It appears as though there's a fundamental intrinsic relationship

between the realm of our consciousness or thinking on the one hand, and the realm of mathematics or, let's say, intelligible reality. I'd like to hear you comment on, I mean, just to maybe see this a little bit. The philosopher Plato, as you well know, and you often describe this realm of mathematics

as a platonic realm, it had a theory of recollection. And we can regard that as a myth or whatever, but it does appear at some very profound level that it's true that we couldn't come to understand things that have an intelligible reality, like mathematics, if they were not already somehow in us, or potentially in us in the patterns or structures

of our own consciousness. So I'm wondering if you could say a few words about the relationship between our thinking or the realization of our thinking, its development, and the realm of the mathematical, or more broadly speaking, you might call it intelligible reality, or however you might want to construe that realm. I was talking about the perception of mathematics, so that's the possibility of understanding

mathematics. Yes, the possibility of understanding mathematics. Gosh. So, what I've lost the thread of the question. Oh, really the question is, do you believe there is, is there an intrinsic relationship that appears to be between our thinking, our realm of consciousness and the realm of mathematics or intelligible reality

independent of us, but intrinsic relate, are those realms intrinsically related? Well, I think I'm trying to say that we can access the truths of mathematics with our consciousness, how we do that, I don't know, I mean, but somehow we can access that world. And of course, some people find it easier than others, and this is a difficulty

in trying to talk about these things. It's a question for Richard Dawkins, lady. Yes, and the risk of going out too far, I want to just make it an effort at relating this question to the work of Dr. Peterson. One of the things that Dr. Peterson has clearly shown is that there are many, many people who are not, you know, it's called the, for some people, are as a shorthand who call us the meaning crisis. Many, many people who are finding they don't,

they simply don't have the resources to make sense of their lives in a way that seems to be adequate to the demands of their own self-consciousness. And so, you know, at the heart of human life as evolved, as creatures that are evolved to self-conscious, is clearly finding a way of understanding ourselves in the world that is adequate to the demands of that very self-consciousness. And life has no, what life is as meaningful as precisely to answer that demand of ourselves as a self-conscious creature. And one of the things that seems to me that very much is at work at this at least some

profound level is the idea that everything is reducible simply to materiality that as it were eliminates any substantial reality to our own consciousness, if that were true, it would just be a epiphenomenum. But it also denies the existence of an independent realm of spirit, as some philosophers would say, or of intelligible reality, or simply put it in terms of the mathematical. And so what I'm wondering about,

and it's maybe an outrageous question to have as a physicist, but you have written many and many beautiful books that are clearly related very much to this very question that has to do with the nature of human realization. That is to say how we come to understand ourselves in the world, and what I'm trying to drive to here is whether you have thoughts on the nature of the realization of our consciousness. We could call that simply human realization as a shorthand. And about the question like what might constitute the fact of intelligibility, right? There's a capacity for us to reflect this structure, the mathematical structure, the physical structure, and that seems to be part of what you described as understanding. It's like perhaps you're formulating a question about

the metaphysics of that intelligibility. Yes, or we could simply say, Sir Roger, in your observation and reflection, what are the forms of life and culture that appear to facilitate that deep human realization that appears to have a intrinsic relationship between our Cells as self-conscious creatures and the nature of what is independent of us and that does seem to be to be at the heart of the question of meaning that Dr. Peterson has been working on and perhaps helped others to think about I mean I

Not quite sure I've crossed the question here, but it has to do with people's I I mean, this relationship between conscious beings and this world of mathematical, platonic world, if you like. And it's certainly something which people differ very much in. I'm easily them, make that contact, if you like. And I certainly have made attempts to try and explain to people who are not used to thinking about mathematics, if you like,

to gain a little bit in that understanding of what's going on in mathematics. So that's how successful or not, I don't know, but at least to attempt to help. Thank you. Yes. As a follow-up to that question, do you intuit or think or believe that in that realm of the mathematics, as you might say, intelligible reality,

do you think other things might also be included in that, let's say, truth, or love, or beauty, because of course the dominant view right now is that these are simply constructs of the human mind, or culture, it's another way of saying the human mind, or material forces that are at work that have given rise to these constructs, but don't actually have any independent reality themselves. Do you think that there is a tinship or perhaps that mathematical reality or truth is part of around that exist as independently as mathematics do? I think there's a, I believe I have in some places that I have to think where it is, adorned this picture with the platonic world being part of a bigger picture,

which has to do with other things than, you see, that's to do with truth, if you like, but there's a question of beauty or other qualities. And I think that may be relating to the question you're raising here. I don't have much to say about it, but I do remember drawing a picture somewhere. I can't even remember where now, in which this platonic world was part of a larger body of things like beauty, for example, and qualities, or virtue, in fact, also,

things, qualities which are things that our consciousness is concerned with, and very important, but not quite what I've been talking about, which is a very specific thing. Yes, I understand. So I certainly would agree that there's more to it than that, and I think that's what you're telling me. And I'm going along with that.

It's just that I didn't know what to do with it, I think. That's a trouble. Well, the reason I ask is because it does seem to me that if these two things are connected, that is say the nature of what we are and think that we are, is somehow intrinsically, according to its own, let's say, structure or nature, connected. I mean, we might even say, I mean, if human beings don't have no nature, there's some sense of which mathematics itself is not even possible. I mean, certainly not for us.

I mean, it seems to me we have an innate capacity to varying degrees, as you say, to think these thoughts or perceive these realities. But if that realm is, say, the realm of mathematics is part of a larger realm in the way that you've just said, and it is related intrinsically to what we are, that our self-perception and self-consciousness has a structure such that it calls out for, in some sense, an understanding of these things, or an understanding of ourselves in relation to those realities. It does seem to me that human realization has to be thought very fundamentally through from that starting point. Yeah, I think all I can say here is that I have considered that in places I could probably find a transparency if I used to use a tool. Whether I can find a place

in something I've written, I'm not so sure. But I certainly do consider the platonic truth, if you like. It was really more like truth, beauty, and morality. In that order. That's a good question. I think I can find whether there was an order. And what would you say morality in that sense? I mean, truth and beauty, in some sense, I mean truth and beauty in some sense, that's more apprehensible than morality.

Do you have any idea why you're intuition, drove you to place morality at the, at the outermost part of that? I can't diagram. I don't know whether even I did or not. OK. So that, that, that I'd have to break, break through all the things I'd,

I suspect there must be an article somewhere where I did that, but I do remember using it in talks. Yes. So, this would be addressing the remark. It's more than I don't really have anything that I can say. I can say, okay, I like things. I like Bach, for instance. Very fond of that, very much.

And it's a certain, I think, particularly with music, there are things which I can relate to very much. But in order to make it anything that I can talk in a rational way about, I sort of give up there, because I'm good enough at arguing about these things. Right, right. Yeah. Oh, yes, we're doing this. I'm so happy that you agreed to talk to me. Well, I hope it was of some use to you. But some of you think that's very interesting.

I think that's difficult to describe. And clearly it's particularly these things with the big bang and all that, which is an idea which we do seem to see evidence for something. Signals, you see, there could be signals coming through from the previous eon, as I call it. I think we see them. The colleagues of mine. You'd have to throw that in at the end, wouldn't you? Well, what do you mean? Oh, well, yeah, I used to go around giving talks about this stuff very often. I thought, this is fine.

I can do this. Nobody will ever know whether I'm wrong or not, and so I can talk about this forever. And I thought, I wonder if that's right. And I thought, well, first thing I thought about was collisions between supermassive black holes. I mean, our galaxy is a collision course with the Andromeda galaxy. It has a black hole much bigger than ours. After we collide and set things down a bit, our poor little black hole got down by it. And there will be enormous gravitational waves going out, carrying away some proportion

of the significant proportion of the mass energy in the two objects being concerned here. And maybe they could be detected by different people. Maybe they could be detected in the next eon. Gravitational waves can get through from one to the next. This is clearly, according to the model they can. So various people tried to search for these things. Mainly my colleague, Vahegurza Jan, who was an Armenian and some other Polish people who later get on it. And they had a much clearer calculation of what they regard as the probability that these signals were really there.

In 99.4% confidence level, I think they got. Did they are? Yes, they're there. In 99.4% confidence level, I think they got. Did they are? Yes, they're there. Some people didn't believe it because they don't believe the model, of course. But then more importantly, more recently, this is a paper, mainly one which came out in the monthly notices of the Royal Astronomical Society, about a year and a half ago, and we claim that we see what we call Hawking Points. That would be, after one of these galactic clusters gets swallowed up by black hole, and there's nothing less, but this black hole, it evaporates away by Hawking evaporating. All that radiation doesn't even begin until so late, but by the time it comes into the next year on, it's a little tiny point.

That little tiny point over 380,000 years spreads out. It's a little bit of an argument about how far it spreads out, but what we seem to see is it spreads out to about four degrees across, which is about eight times the diameter of the full moon. And that's what we see. So we see with a now bigger confidence level. 99.98. There is an argument now which is to do with whether the actual size we see is consistent with expectations

and there's interesting questions about that. But ignoring that point we have a 99.98% confidence level. And there's interesting questions about that. But ignoring that point, we have a 99.98% confidence level. They're there. The spots, there's little spots, the raised temperature. And we see them. And why are they there?

What are they doing there? According to current theory, they shouldn't be there. According to the theme I'm put forward, yes, they should be there. And they're the result of the remote future of a galactic cluster. Probably, propagating itself into the next Eon. The radiation, yes. It's the radiation, the Hawking radiation probably, which comes from the black hole, and all

this mask, it's concentrated into that, and that comes through the little tiny point, which by the time you see it is spread out to about eight times the diameter of the moon. And we see these spots, and they're seen both in the more sophisticated Planck satellite data. And if you look at the, what is it now, the five strongest points in the Planck data, and look in the earlier WMAP, that's a different satellite, completely different. And you find these spots exactly the same places

in the WMAP data. There's a sixth one in the WMAP data, which is just about as strong as those five. Look back in the Planck data, and that's there too. So there's six points I claim are genuine Hawking points, as I'm calling them. And there's no other explanation for them that I know of. They're seen and they are independently confirmed by another group

who weren't claiming they don't see anything, but they do see the evidence for these spots too. You just look at the data. Okay, what's the reason for it? Current cosmology, I can't see any explanation for them. This model predicts them. I haven't seen any response from the after a year and a half from the established cosmology community, published in a very respectable journal, it's probably the leading journal for astrophysical processes. There is an error, but in this, which is rather curious,

but I don't want to go into that. But it doesn't much. Whether the confidence level should be reduced a bit, I think that's probably a case for that. But not much, because the signal is pretty strong. Thank you very much. That was something, man. Well, just to bring us to a close here, Sir Roger, it's been a great honor to speak with you today.

I know for both me and Dr. Peterson. Thank you so very much for your time. It's me, my pleasure. Music