The Origins Podcast with Lawrence Krauss - The Origins Podcast: Roger Penrose

Episode Date: March 24, 2022

Summary: Roger Penrose and I discussed his life and work in science, mathematics, art and beyond, including the work for which he won the Nobel Prize, and his recent highly controversial proposal regarding the beginning and end of the Universe.To get this episode into your RSS feed, please click the button below from your phone:Roger Penrose, who shared the 2020 Nobel Prize in Physics, for his 1965 theoretical demonstration that black holes are an inevitable consequence of Einstein’s General Relativity, something that hadn’t been widely accepted at that time, is known to his colleagues as a remarkable mathematical physicist, whose way of picturing things has changed the way we now picture many things. His use of what are called conformal diagrams, now called Penrose diagrams, allow us to intuitively picture processes in curved space, particularly around black holes in ways we couldn’t do otherwise. He also developed something called Penrose tiles, fill a two dimensional plane in a way that was previously thought to be impossible. He both inspired, and was inspired by the famous Dutch artist M. C. Escher, in his ‘impossible’ drawings. Most recently Roger has proposed an alternative picture of the evolution of the Universe called Cyclic Conformal Cosmology, which connects the distant past of the Universe with the far future. It is controversial, and few others have accepted his picture at this time. He and I spent almost 3 hours discussing all of these things, and also his early inspirations as a young man, the nature of mathematics and physics, and much more. I am extremely happy to release this episode with Roger Penrose as the first Substack-hosted episode of The Origins Podcast with Lawrence Krauss. I hope you enjoy it, and all the future episodes to come. Get full access to Critical Mass at lawrencekrauss.substack.com/subscribe

Hi, I'm Lawrence Krause and welcome to the Origins Podcast. Roger Penrose is known to the public as the winner of the 2020 Nobel Prize in Physics, which he shared with several astronomers who discovered a black hole at the center of our galaxy or at least demonstrated its existence by looking at the motion of stars. And we've talked to one of the Mandrages. Roger shared the Nobel Prize for showing 50 years earlier that black holes, in fact, were an inevitable consequence of general relativity, something which really hadn't been accepted at the time because black holes are so weird. But Roger is known to physicists for many other things as a remarkable mathematician who's developed techniques that have really changed the way we think of general relativity. so-called Penrose diagrams.

He's also discovered a fascinating aspect of nature called Penrose tiles, which he and I talk a lot about, which in some ways was sparked or sparked his interest in the art of Escher. And we had a wonderful discussion about very early experience he had as a young man talking to Escher and actually helping him in some sense with some of his images, some of his impossible images. Roger has recently promoted an idea in cosmology called conformal cyclic cosmology, which frankly, as I discuss in our dialogue, is a controversial idea which really hasn't been widely accepted in the community beyond himself and his colleagues. And I have several concerns and questions about it. He and I had a,

had a discussion we talked about his early life and science, his experiences having to do with general relativity, and what led him to his current work, which we discuss at length in the latter part of the podcast. I hope that this will provide a new glimpse into the way scientists can debate ideas, hopefully respectfully and fruitfully, and how ideas at the forefront of science can remain controversial and how most important. and as we discussed at the end, how scientists should be not happy to be wrong, but certainly willing to be wrong and proclaim their wrong and change their minds, because that's what differentiates science from, say, religion.

In any case, it was a true pleasure to talk to Roger, and I hope you will enjoy this in-depth discussion of physics and mathematics with Roger Penrose. This is a very special edition of the Orgence podcast as well. Because the Origins podcast video, no ad video, is moving today from Patreon to Substack, to my new substack page. And it will be freely, this video will be freely available as all things will be on the Substack page. But I hope, and the Origins Project Foundation's hopes that you will subscribe to Substact because the funds of subscribers to the Substack site

will go to help the foundation and to help make this podcast possible. Hope you enjoy it. If you don't watch it on Substack, you can always listen to it on a link through Substact at any of the standard listening sites, iTunes, etc. Or you can watch it on, as always, on the YouTube channel,

and we hope you'll subscribe to that if you watch it on YouTube. So once again, Roger Penrose. Well, Roger, thank you very, very much for taking the time out to talk to me. I really appreciate it. It's really good to see you again. And I know I think I emailed you, but now I can personally say also congratulations on the prize. Thank you.

And I was trying to remember the last time we were together. And I think, I don't know if you remembered this, but I think it was at Oxford at a debate with philosophers where you and I were partners. and I don't even remember what the context of the debate was, except that I remember that you and I won. I'm afraid I don't even remember it. Yeah, all I remember is a bunch of Oxford philosophers, and we were talking, I think it was about physics versus philosophy in some way. Which side were we on?

Physics or philosophy? Yeah, I think we were on the physics side, I'm pretty sure. Philosophy of science versus physics. And I remember, yeah, I just remember. remember you were my debating partner on that and it was fun to do it. And I actually mostly just remember the drinks afterwards. But in any case, I think that was last time we're together. I wanted to talk about many aspects of your science here and which we'll get to, including ideas about cosmology, which is an area we both have worked in, among other things. But this

is an origins podcast. And I want to begin with your origins, which are quite interesting. to me in a variety of ways. You come from a scientific family, in a sense. At least your father and your stepfather and I guess in some sense, at least grandparents as well. My mother's father, certainly, he was a scientist, physiologist, yes. Now, I'm just wondering where the, you know, in the context of growing up in that

household, where I, I, where the, where the, where the, where the, where the, where the, where the, influence was for you to want to learn about science or mathematics. Did it come from discussions with your grandparents or which of your parents would sort of encourage that? Mainly my father. Also, I should say my older brother, Oliver, who he was very precocious, much more, I mean, I wasn't at all, he was. And he knew a lot of physics. And I learned quite a bit from him, but mainly it was my father from whom I learned quite a lot of mathematics, actually. He worked in human genetics was his topic. Yeah.

He did quite a lot of mathematics. He certainly was interested and excited by mathematics as quite a lot of other scientific matters. And I learned a lot from him. Yeah, that's true. I knew your father was kind of worked in genetics. I don't know. Was your mother, was she educated in science at all? Yes, indeed.

She was medically trained. Well, I don't know what I want to go into this particularly. Okay. She was trained as a doctor. But my father had lots of positive qualities, but he had one big negative quality, which was for some psychological reason, which I could never get the hang of, he wouldn't let her realize herself. in her medical profession or in almost anything.

It was strange. We have a lot of good qualities, but I have to strike that one as a bad quality, I'm afraid. Yeah, yeah, no, it's unfortunate. I think it happened a lot, especially in an earlier generation. But that's unfortunate here. But did she play a role also in encouraging your interest? I think she did in a slightly,

how would I put it? She couldn't express herself in a sort of an independent way, but she had a way of relating to me, which was slightly kind of not quite direct. I kind of know how to say it exactly. I think I learned a lot of how to express myself from her. She was very, the use of language, I think. She had her skin and I got quite a bit from her.

on that, I think. And that happened, it's interesting to me, that often happens in, in, in my experience with, with mothers, in fact, in terms of language. The, did, did you read a lot? Did, do books influence you about your interest in science? Did you pick up books by the, you know, the standard, well-known, you know, James Jeans or whoever else with the, you know. Some of these things, but I would say I was not much of a reader. I was a very slow reader, I think. And I did not read a great deal. There were some things I did read some Bertrand Russell. Yeah.

There is, yeah, I read a bit. Yeah, well, I mean, you know, it's interesting to see, again, the differences in people. And in both, I love the fact that almost any stereotype of a scientist is wrong. And that it takes all types. And I think it's encouraging for young people to realize that. And, you know, in so many ways, not just, you know, some people read a lot, some people don't read. But people often assume, especially young people, that they're not good enough or capable enough because they don't have X quality. And it's really important to realize that people that who have been quite successful sometimes also don't have that quality, whether they're not a mathematical prodigy or they're not, they don't read or whatever.

It's science, when it's healthy, takes all kinds. I think that's really an important thing. I sort of read secondhand. You see, Oliver was a great reader. And somehow I got from him, well, certainly he read to me sometimes, and he read to me the Mr. Tompkins books. Oh, okay. Yeah, so I don't remember that and various other things to do with science, which he did.

So I think he had a big influence on my. He was your old. How much older? How much older? Two years? Yes. Yeah, my older, I've one brother who was older and I think certainly strongly influenced me when I was younger, although he wasn't, he'd give him a lawyer, but my interest in a variety of fields was certainly impacted. But Oliver did become a scientist. Yeah, he's a physicist, in fact, right? He became a member of the Royal Society and so on, fellow of the Royal Society. Yeah, no, well, I want to get to your siblings because you have a really interesting, there's something interesting about your background that seemed to encourage all of you to do, both to have, be very, very good. gifted in your own fields, but also to be interested in them. I think it's,

but, you know, I was going to, so when it comes to reading, I was going to say in some sense that one of the good things about science, mathematics and physics in particular, is that if you're good enough, you don't have to read at all, as Feynman used to kind of, I think, epitomize in some sense. That's true. That's true. Yeah. And I wanted, there are two aspects of your childhood. I wanted, I wanted to ask about your, your father was a mathematics. You have a stepfather who is a mathematician. I don't know whether there was any influence there too or not.

That came much later. You see, that was after my father died in his 70. Oh, okay. And when my mother married Max Newman, who had been a good friend of my father's way, way back. Oh, interesting. Apparently he'd had a crush on my mother, even way back there. after my father died, he sort of made a beeline for her. Okay.

But that was, okay, that was much later then. Okay. Now, the other thing I can't help saying, because behind me is a wonderful river. I'm now moved back to Canada where I grew up. I haven't been back here in 50 years. Yeah, that's a real background. That's my beautiful in Prince of Rhode Island, but it's a beautiful background. But it's, and I'm very happy to be here.

But you have a Canadian background that I didn't know of. spent some of the war years, I think, in Canada, in London, Ontario. What was your father doing there? Well, I was there from, well, I was in 1939, I guess, we went there. It was 1940. So my years are getting confused. 1939, that's right. I, I, 1939, I was seven years old when we went and I had my eighth birthday in Canada. Yes, we went first to the US. to Philadelphia. And then my father got his job at the Ontario Hospital

that's just near, just outside London, Ontario. And so he spent the war years there. That was a big influence on me. In what way? Well, I went to Ryerson's school and then to Central Collegiate for my final year.

It was curious. Now, my first year there, I had to teach her I couldn't get on with at all. She had what was called high grade two and low grade three. I was in low grade three. Okay. Now, she considered, because I was very bad at doing mental arithmetic, she used to have these things to add a number and then multiply myself. And it goes down too quickly for me.

I just got lost. I always got lost. And she thought I was too stupid for low grade three. It moved me down into high grade two. Wow. I was a little bit too good for high grade two, so she couldn't place me between high grade two and low grade three. However, later on she got rid of me.

I think by, just as a way of getting rid of me, I got moved up with some other people into high grade three. I don't think she thought I was good enough for high grade three, but since we never got on, I think she probably thought this was the way of getting rid of me. Ah. I did have a, I forget whether it was in high grade three or later, but I did have a very insightful teacher, Mr. Stonet.

And he used to have these mathematics tests, and I never did very well in these tests. But he noticed that the reason I didn't do well as I simply didn't finish the tests. And so he decided to let me have as long as I liked. So I could just go on and go on and the people were playing in the playground and I could watch them out of windows.

And I would just be slogging away through the test. And then I would do very well. I'd get into the 90s, you see. And he realized that it was simply that I was too slow. Well, this is fascinating. I mean, I've known of you as a brilliant mathematician since I started doing physics. And it's fascinating that in a sense, people didn't realize. It wasn't as if they recognized you as a mathematical.

prodigy or anything like that early on. No. Well, I used to make models and things with my father. So this was a separate thing. We did at home, yes. Well, now, when did you, so did that, did that, I was going to ask you, man, maybe this is relevant. I mean, good teachers are really, from some, again, it's not universal that it's important for people.

I know some people who said teachers never impacted on them their whole lives. But having good teachers, certainly for me and many people I know, has been a particularly good teacher can have a huge impact on a young person. And that's why I guess I give so much respect, especially for teachers of young children, because they can really, really change a person's trajectory. And this teacher had an impact. Did you, I was going to ask you, what got you interested in mathematics? Your father, of course, talked to you about mathematics, but when did you kind of get the sense, or did you get the sense that you wanted to be a mathematician early on, or did that just kind of happen? it's a good question too

I remember I mean there's a story I often tell you see my older brother was clearly going to be a physicist my younger brother was only interested in chess that's not quite true he was interested in all games and of course part of my

background I don't know you have this done but my younger brother Jonathan became which chess had been the record in minds In record time, how old was he when he became a chess master? Well, he didn't become a grandmaster, but that's a slightly complicated story. Okay. He didn't eventually become a grandmaster, but his, I can't remember.

He first won the British chess championship, I think, in his early 20s. He was in his 20s, but he entered for the British Boys championship, which he won, I remember. but he was good at almost all games. And I remember, this is a curious story, I remember he'd beat me at this game, you know, stone, paper, scissors. Yeah, sure. And he would completely wallop me regularly.

I thought, surely this is a game of chance. How can he beat me at this game of chance? And I think, I mean, this is sort of some, um, jinx or something like that. So what I did was I got out of table of logarithms, opened it in the middle. that Hughes, who sort of took these

random figures and translated the numbers into stone paper and scissors whatever they want and I made a long strip of this and I would follow this and then I broke even

so that was a really relief to me he was actually using psychology or something I mean he had an extraordinarily good memory just to play this game of people called

pears or pelmanism yeah put the cards and you see the back to the cards and he turned two over and when you put to them back, you see, all I see is the backs of the cards, but evident he still sees the fronts of the card.

And he absolutely bollered me in that kid. There was no question about that one. Go on, sorry. But anyway, the fact that he was so much better, obviously, than me, at chess, I'd never played chess. Well, that's not quite true either. I hated chess and tried not to ever to play chess. there was an occasion when I was at school in London,

university college school, when my younger brother Jonathan was the first board of chess, and my three Jewish friends were the board two, three, and four. And occasionally they needed the board five, and they put me on board five, I think just to scare the opposition that there were two penroses in the team. I never won a game, I have to say. I never played chess apart from that.

He sort of immunized me against playing chess, which I think was important. I don't know whether I would have ever got interested in chess, but I certainly didn't because he was much too good. Ah, that's, you mean, you think you might have gone to the dark side if he hadn't been? It's quite possible. We see, Oliver didn't play chess. And he was four years and four months over. And so he was able to keep, by really working very hard at it, he was able to

keep ahead for quite a while until they both played in the British chess championship and Jonathan came out ahead of him. Oliver was good enough to be Cambridge University champion, so you've got some feeling. Oh, wow. Okay. Well, look, let's let's let's um, it's it's interesting. I'm glad to see that you're, you know, it's another stereotype that you're not a, well, maybe you could have been a chess, uh, wonderful chess, but you weren't, but I'm happy to hear that. Although it is a game of people who like, well, the memory part is, I think, really obviously important to be a good, to be very good. He could remember, certainly up to the scale I ever knew. And that, when growing up. Yeah, I think that's really.

Remember every game you'd ever played. But in a sense, you like games. And we'll get to that, I think. Or like puzzles is perhaps a better way of putting it. Because we'll get to what I think are some beautiful, obviously beautiful puzzles that you've been involved in. And so that natural interest. But let's, let's, since you mentioned two of them, you're, you have this, the siblings are just amazing. As you say, Oliver, a physicist. Um, your sister, Shirley Hodgson's a geneticist, right? Yes. Yes. And, and one who followed in my, you see, I was supposed to be a doctor and family. This is, you know, you were aware of that. Well, I mean, my mother, I was, you know, a Jewish mother. I want, she wanted me to be a doctor. My brother to be a lawyer.

and he became lawyers, which put... Both parents being medically trained. Of course. He was going to do physics. He was a dead last. Jonathan was only interested in games and chess and stuff. He was a dead loss. Roger is the one who was going to follow up in there.

And I used to take these vocational guidance tests in Canada. And you sort of lined these things up this way and that way. And my came as a doctor. I was going to be a doctor in the family. And they were very relieved that they, you know, I was going to carry on the tradition. and the moment came when I was entering my last two years at school, University College School in London,

and each one of us had to walk up to see the headmaster and see what they were going to do in their final two years. So I walked up, I was going to be a doctor as I walked up to see him. And he said, well, what do you want to do in your final two years? And I said, I think I have this right, biology, chemistry and mathematics. And he said, no, you can't. do that combination. If you want to do mathematics, you can't do biology. If you want to do biology, you can't do mathematics, make your choice. So I said mathematics, physics, and chemistry.

Oh, wow. And there was my medical degree down the tubes. That moment. Oh, it's fat. This is again fascinating for me personally because I, I wanted to be a doctor. My vocational test had me be a doctor in Canada when I grew up. But I think, but you know, my, because my mother had convinced me. And I convinced myself, I wanted to be a doctor. And then for me, it was in the final years of high school when, yeah, when I guess my problem was that my mother had sort of convinced me doctors were scientists and I got fascinated with science. And at some point, I kind of had the realization that they weren't necessarily the same thing. That and the fact, and it may be different in Britain. And well, maybe it wouldn't, wasn't. But I actually did take a biology class. And at that point,

it was just memorization. It was just memorizing the part of the person. of a frog and that and I just said this doesn't interest me at all at that time of course biology's changed a lot yes but you see I think I mean my mother thought I would have had a good bedside manner or something I don't know about that but I would have been a complete disaster with drugs because I would never remember any of these names and so on so I shouldn't have been let loose on these things at all and so it's so it's interesting that you did it sort of was a choice to do you know, but mathematics, but it was biology or mathematics. So by then you kind of knew you wanted to do mathematics.

Yes. And of course you did do mathematics. And I wanted to ask you, it's jumping ahead a little bit. Do you think of yourself as a mathematician or a physicist, first and foremost? Often when I talk to people, I say, when I'm amongst physicists, I'm a mathematician. When I'm amongst mathematicians, I'm a physicist. That's an intriguing question. I think, you see, I'm very interested in the mathematics,

but it's got more and more focused as in the physics. I mean, the physics is the driving force, but the mathematics is the way you go. Okay, but so, okay, but the physics was the driving force, but it wasn't all, I mean, was it, but initially, I mean, your PhD was on tensor methods in algebraic geometry? Was it, was it motivated by physics, or, was it motivated by interest in do mathematics?

That was mathematics. Yeah, sure. You see all these stories, I have to tell you all these stories then. That's fine. It was one of the stories, I have to backtrack a little bit here. I think it was when I was at University College London doing mathematics. I should say my father was not keen on my doing mathematics and not something else. He thought if you could do other things, you should do mathematics.

On the side, like he did in some sense. Yes, that's right. And he was not keen on my just doing a mathematics course, but he got one of the lecturers, a man called Kesselman, who made up tests. I have a lot of respect for the Kesselman. He made up a special test. I can't remember whether it was six or 12 problems. And he said, look, you can do these problems. Take the whole day, if you like, do as many or as few as you like. If you only do two or three, that's fine. I did the lot. but these were all tests with sort of a twist to them they were not sort of straightforward he must have worked very hard on working this hour but anyway since I did so well on those tests my father sort of relented and said okay I'm doing that's going back a little further

but let's not go back quite so far there was some radio talks how by the way how how when was this what stage was this when you're an undergraduate or younger When I was in my, as an undergraduate, okay. Went to the University College for lectures and things there. I can't remember exactly which year it was.

Doesn't matter. I just wondered if it was before university or not. Anyway, I'm sorry I interrupted, but you were going to move on to. One could check this out because the Fred Hoyle radio talks were key. I remember racing home to hear these radio talks. There were five of them. I think they started with the, Earth and the atmosphere and then they worked their way out and solar system.

Yeah, sure. Galaxies. And then he talked about cosmology. And when he talked about cosmic, this was the Steadist state, the days of the steady state model. Sure. And he talked about the galaxy, which was seen faster and faster, at a certain point, they would reach the speed of light. And when they exceeded the speed of light, they would disappear, and you wouldn't see them. And I had drawn little pictures and things, and I couldn't quite get my mind.

mind around this. And I was visiting Cambridge and I visiting my brother, Oliver, for some reason which I've not forgotten. But I remember having this lunch with him in the Kingswood Restaurant. And we were talking away. And I said, I didn't quite understand. Trent was going to these very nice talks, but I didn't quite understand about these galaxies disappearing and so on. And he said, well, look, I don't understand much about cosmology. But sitting on the table over there is one of my good colleagues, Dennis Sharma. And he knows all about cosmology. He'll tell you.

So I went and sat down next to Dennis and explained my little problems and do my probably light clothes and things like I can't remember what. And surely they will just fade away. They don't disappear like that. So he said, well, if I don't really know about this, I'll go and ask Fred.

Anyway, I didn't hear what came out of that. But when I did go to Cambridge, eventually as a research student, no, yeah, a research student doing algebraic geometry, you say algebra, yeah, working other hodge. Yeah. And Dennis sort of took me under his wing. And he, we went on long drives to plays in Stratfuss, with Shakespeare. Sure, sure. And often stopping off in Oxford's one reason or another.

and driving at great speed around corners and things like that. That's the action of the distant stars. You think about Marx principle and things like that. And nobody discussed me. What happens? Well, suppose the Earth disappeared, but you still feel the accelerations and what about so on?

Suppose the stars are in moving. So we had these sort of conversations about it. It was very influential on me. So I learned from Dennis a great deal of physics. So I would say that my, early education and physics largely came from Dennis Dennis. Dennis Sharman. Sure. I would say there were also three courses I went to in my first, second, I can't remember

exactly which years at Cambridge, three courses, which had nothing whatsoever to do with my research. The three courses were one, Herman Bondi. Oh, wow. on general relativity. One was a man known Steen on mathematical logic. One was Paul Dirac on quantum mechanics. Not bad.

Not bad. They were all extremely influential on me in many ways. Steve one, because I learned about hurdles there. Analytical logic and that sort of thing. And the big effect, really my point of view that I later formulated more strongly came from Steen's lectures and understanding about touring machines and girdle serum. And he was very clear on those topics. Wow, this is fascinating. Because I knew, of course, Shiam had an impact, but I'd assumed it was after your, finished your PhD.

No. Before. Oh, okay. Now, it's interesting that Shiamma took you under his wing, his wing, when you were doing a student mathematics. But I guess, was it because of the introduction you had with your brother? Or how did you, or is it just a... Yes, that's how I knew him.

But I think it was my... Just the fact that I seemed to have some insights into cosmology, which he hadn't seen before. I think it was really just drawing light colors, which is not much of an insight, really. Well, we get to that. Well, it did say it changes the world in many ways. I want to get to that.

We'll get there eventually in the next five or six hours. No. But this is fascinating. Well, but I still want to focus on this sort of transition from mathematics, physics. So you knew you did your PhD in algebraic geometry. And tensors, of course, are highly relevant to physics, but it was really the algebraic geometry that fascinated you at the time. One of the reasons I'm asking is a personal one.

I did a degree in mathematics and one in physics. And what kind of a, surprised me is, you know, I was always very good in mathematics, but, but there were some really excellent mathematicians, young mathematicians who were, who I was with in my mathematics classes. And I just assumed that, you know, since, since mathematics, since physics was really mathematics to me, I mean, it was really, you know, it was the basis of physics, that these mathematicians would breeze through the physics classes that, when some of them did take with me. And what shocked me is that they were much better mathematicians to me, but they could, didn't have a, but they had a heck of a

hard time in the physics classes, which I shocked me because I thought it would, should be trivial to them. And at the same time, to me, what kind of I was trying to decide. And I saw that when I was in physics classes, I could see where we were going. In math classes, I could always kind of do everything. But I could never kind of see beyond the horizon, if you want to call it that. I couldn't see where things were going. And that's when I kind of realized I wasn't a mathematician. and I'm wondering if that kind of, but you, well, if that impact on you at all, but I mean, I guess it didn't because you kind of knew you were a mathematician, but I wanted to sort of ask in that sense about your experience as a mathematician who obviously, obviously had insights about

physics. I think there's something of what you say in me also, but it's a little bit different than it. Well, I should also, I keep telling you this little stories because they're very influential Well, no, I think it's really not only just interesting to me, but interesting for people are listening. The stories are a wonderful way to understand things. When I went to work with Hodge, I was one of four graduate students. One of them gave up after a little while. I don't remember how long. So then when they were three. One of them did go through, get a PhD, and he gave up mathematics

at that point and became interested in history and philosophy of, of physics, I guess. That was Michael Hoskin. Oh, okay. And he became a historian or a lot of them, I don't know, of physics, primarily. And the two remaining people were left. I was a little bit, I chose a topic,

I had a list of topics. I chose one of these. And I, I once decided that I looked at I wasn't altogether happy with this topic. And he said, well, perhaps you'd like to sit in on the other graduate students class, just see what you make of it. So I sat in on this undergraduate students class,

and I did not understand a single word of what's going on. And I thought, my God, if they're all like this, what am I doing here? That was Michael Atia. Oh, Michael Atia. Okay. It feels mentalist, I guess. You've got to respect each other in our different ways.

is just, yes, that was my dear. Wow, okay, well, that's a high bar to. I realize there was something a bit special about magnetia afterwards. Who, by the way, one should say, you had a huge influence on physics, and I used, I got to know him too, and he was, he was wonderful to talk to as a physicist to talk about mathematics. Yes, yes, yes, he knew all the mathematics. He had an extraordinarily broad, but not just as knowing. It was understanding what was wanted. Yeah, exactly, in a different sort of way. Yes, and there was a thing I remember this occasion. I had a problem.

I was just beginning to see the importance of certain things, to do with Twister theory and how it got developed in a certain way. And I talked to his singer, who was this great collaborator. Oh, yeah, another person I had that talked to. How do I solve this problem? He said, oh, that's not right. I'll tell you how much. You just solve these equations here, and then that tells me the answer.

Okay. Then when I got back to Cambridge, this was in the stage, I got back to Cambridge and I talked to Michael. I said, because I wasn't quite, I couldn't see quite a solve as a question. And I asked him the same question. And he said, oh, you're doing it like this. And he said, he blew a little picture. He said, it's this and this and this.

And then he said, well, you have to show that this thing is number of degrees of freedom of this or so on. And then you do it like this and you can't take a line in the number of the lines. And there's your answer. I'm like, wow. You know you should take this and let's bring these subjects together and out pops your answer. And that was my problem. Yes, Michael Atia. And it's interesting, both Singer and Atia, the Atia Singer Index theorem is incredibly important. This was an instance of the Aetia Singer.

Wow. Well, okay, so it was clear to you that there were, how can I put it, better mathematicians maybe around you. Those people who were much better at handling the mathematics. I felt I had some quality that was different in a way. Which is true. Yeah, well, I don't know what it was. But it was not the same as Michael's. You see, he had this great grass. And there were people talking about new ideas that were coming in using, as Max Newman, who became my stepfather, used to say, in his younger days, in topology, we're talking about triangles.

Now they talk about squares. Square. And soon they'll be pentagons. And you see. And this was going on. And people were talking about this abstract. very abstract ideas and I could never get my feeling, the proper feeling for those abstract things that people were going on with and had such fluency with. And I couldn't pick up on it so much.

I was much better at fiddling with the kinds of geometrical ideas. Well, speaking of geometrical ideas, I wonder, you know, I tend to think pictorially, and it seems to me you do too in many ways, in particular around the same time, I think I was I was amazed I didn't realize that Escher's influence on you and your influence on Escher which I should have known about I guess so I apologize for not but the the the geometric I mean you're obviously interested in geometry but the but it seemed to me that this fascination about impossible pictures combined in interest in puzzles and kind of games with an interest in in geometry

in a very pictorial way. And then we'll get to light cones, but would you say you think about mathematics pictorially? Yes, very much. I would say I'm much more visual than, I would always, see, when I was at school, I remember thinking, you know, that I maybe thought rather differently about mathematics and other people. And when I went to university, I would find people who thought like myself. It wasn't like that at all.

I found people felt more differently for me than I had experienced before. And I would talk to somebody and I didn't understand much of what they were saying and he didn't understand what my mind. But at the end, I could see what it was. And it was somehow, I think they were out of our class, I can't remember how many about 14 people. There were three, I would judge, who could think visually. One of them would good, but was not specifically visual.

one of them was more visual, and there was me, that was particularly visual. But on the other hand, most of the others were not visual. And I always thought that somehow, I don't know, that there's a kind of selection advantage not to be visual in mathematics. Yeah. I had this experience when I at University College school, no, university college when I did my undergraduate degree,

that the way they did it in UCS, in UCL, was to have the first two years, you would take your main exam at the end of the first two years, and then your specialist topics at the end of the third year. So I'd done my first two years, and then in the third year I was doing, two geometrical papers, you see. Now, as it turned out, as I found out later,

my best papers were not on the geometry. They were on algebra. And the thing is in algebra, you just, you don't have to, you see your equation, and then you go over to there. Whereas the geometry, you read the problem, you translated it into a picture, you solve the problem, and then you translate it back into words and write it down and a lot of words. And this sort of flipping backwards and forwards, I was, I didn't finish the papers, and it was like that, and that my slowness began to show itself. Oh, interesting.

So it was, but I've rather felt that there is. is a selective advantage in not being the visual type in mathematics. Yeah. Partly just because in examinations, it's selected against. But if you think about the mathematics in a geometrical way, you can't get it out so easily, as if you're directly doing this form. Yeah, you go off and then come back and...

Yes. I felt there was very much of that double translation in what I had to do. and this was slowing me down. And it's probably true in the classes too, that the people I taught, I remember lecturing, that I tended to be a bit visual in the way I taught. And often they didn't like it very much.

So they wanted me to write down equations all the time and not draw pictures. And that somehow it's only a rather small proportion of them who come through who do have these visual skills. And the best ones can do both, of course. I mean, Michael Oetia was very much. Yeah, sure.

He could do both. It's interesting. When you say that, it's interesting to me. I just thought of the history of physics. It was probably, Galaya was probably lucky that they didn't have algebra at the time, or at least because he thought in terms of pictures. And much of his, you know, which is now, much of what he did, which seems co-convaluted could be done in an instant algebraically. But he was, but he didn't have to do that translation. He was a good artist, too.

Yeah, he's a good artist as well. In fact, that, you know, you just hit me. back to where I wanted to go, which is, I mean, I'm, I, one of my big points throughout much of my career, especially my popularization of science is that is this connection between science and culture and this, this unfortunate, um, uh, branching, uh, of, of science as a separate area when it's not. It's a part of a culture in, in every way. And, and, and, and, and, uh, and I often say that, that, you know, that the purpose of the two is the same. They change our perspective of our, of our place in the cosmos.

And when you see a piece of art, it does that or a piece of music and listen to a piece of music. And same with science. But actually, the, the, the conjoining of art and science, I can't think of a better example in some ways than your experience with Escher. And I, and I, I want to have a number of questions about that. And we will get to cosmology eventually, but this is fascinating. And I think, I hope it's.

fascinating for others, but I don't care. It's fascinating for me. And were you interested in art? Or how did your thing with Escher come about? And maybe you could talk about that a little bit. Well, I had already been interesting. Of the three brothers, I mean, my sister Shirley came along later. She had an interesting art. But the two brothers were not at all. I was the artistic one. amongst those three. And so I certainly could relate to my father. He was a very good artist. But he came from an artistic family.

His father was a professional painter, extraordinarily skilled, yes. I mean, very traditional in what he did, but they were extremely skilled artistic works. James Doyle Penrose. Oh, okay, I didn't know that. Okay, so that's interesting. This background you have, it's fascinating.

And all three, brothers of him. So he was one of four brothers. They were all good artists. The one who became most distinguished in artists was his younger brother, Roland, who became part of the surrealist movement. He was a great friend, Picasso, and... Oh, wow. ...dance and the artistic club. And he became a big figure in the surrealist movement in Britain. Wow, that's a whole other subject. I wrote a book about once about... Impressionism and extra dimensions and and and and and and and and and and and and and and and and and and and you know those his seeing many faces a face from many

different perspectives is the way it would look if you were four dimensional looking down at a three dimensional object and and there was a lot of fascination at that time with mathematics in that in that particular art world but that's a separate thing but so you were the artist can you do I mean can you draw well as well or no not because my vision is God's pieces. But no, I used to do that. In fact, if you look at most of my books, you will see the drawings are done by me. Okay. Oh, okay. I didn't realize. On books, you have to look. The earlier ones were not. I got browbeaten into letting the artist. Yeah, but eventually you remember it. It was like this,

and I would sketch it out for the professional artist and that would be drawn, look, that's wrong. This line should be even fine that one. I'd correct him. It'd come back and it'd still be wrong. And I get, look, this is ridiculous. Why did I just do it myself? So in the new book, for example, I want to focus because I thought I should focus on one thing. The new book, which is largely on your new ideas

in cosmology, there are lots of pictures. You did all those pictures? All the ones which were not directly taken from a graph, something like that. Wow, okay. Interesting. All of the ones, going back to the, certainly the Empress New Mind, they were all mine.

Okay, wow. But road to reality, yes, no, I didn't. Wow. And then, I mean, okay, so there's this wonderful Henro's triangle and which I guess, you know, well, was drawn. I don't know if you hand drew it originally and with the straight lines or not, but. I did it originally, yes. Well, I put a little bit of, almost nobody copies, notices the perspective in the drawing. There is a perspective in the drawing in the paper I had with my father.

Oh. Oh, really? Okay. So the Penrose Triangle was with your father or no? Yes. Oh, I didn't know that. The story was. Well, I wrote, I think, three papers with my father.

Is it three or four? Wow. One, two. I think it's four. I can't, the puzzles for Christmas. Yes, that's very much. Oh, wow. Wonderful.

I'm just trying to have a losing count. But yes, the paper on the impossible objects was by my father and me. You see, I'd been to this Escher exhibition. This was when I was in my second year as a graduate student. And I went with a colleague of mine to Amsterdam to see the, this was the Congress, the International Congress of Manhattan. meticians taking place in abstain. And at one point, I think I was just getting on a tram

and my lecturer in topology, Sean Wiley, was just getting off. And he held this book in his hand, which was a catalogue. He said, one earth is there. And there was this picture of Escher's the night and day and the birds are going back. And I wonder what's that.

And he said, you'd be interested. There's this artist called Escher, who was an exhibition in the Van Gogh Museum. So I went and I saw it, and it absolutely stunned me. and I went away thinking, let me try and do something impossible, not quite of the court I saw in this exhibition, because at that time he didn't have one. And then I drew this with trying with bridges and roads and things going off in different directions,

and I simplified it to the triangle. Then I showed my father, and he then started to draw buildings, which were impossible, and then came up with a staircase. So we decided we'd like to write a paper on that. we couldn't think what subject it was so where did we send it? And then my father said, oh, I happen to know the editor

of the British Journal of Psychology, so we'll decide it's psychology. And so he got him to accept the article for the British Journal of Psychology. Oh, interesting. Oh, wow. And we gave credit to Escher in this way, the exhibition, and we sent a copy to Escher, and it was through that that

Escher and my father had a correspondence. And when I was driving in in the Netherlands for some other reason and I was somewhere near to where Escher lived and I phoned him up and he invited me and my then wife and we had tea and I talked to Escher for a bit

and we sat at the end of a long I was at one end of a long table he was at the other end on two sides at one side he had his pile he said I don't have many of these left but he pushed the other pile towards me He said choose one. Wow.

Wow. This was a real challenge to choose one. Yeah. Holy mackerel. Wow. You still have it, I assume. I have, yes. I don't have it in my own house.

I now have a record. I don't know if it's a record or not, but I have nine ashes. Wow. Wow. It's quite a puzzle how I actually have nine of them. I know how I have two of them. But I know how I have,

why it happened. I know how it happened, but why it happened by don't know. It's strange. But two of them were one that he gave Escher gave to my father, which was the staircase, the ascending and descending. Wow, do you have that? And the other one was a pick one I picked out of this pile, which he was rather pleased that I chose,

because he said people don't normally appreciate that one. It's called Fish and Scales, Fishers and scales. And it's the sort of violation of, theory of types, kind of. Yeah. You have this fish and it's got scales and the scales get bigger and bigger and then they become a fish and then its scales become the original fish. So it has this paradoxical nature.

It's a very striking picture. This is one of my favorites. Well, what a fortunate thing. We're on the Ashmolean Museum. They can be seen. Anyone who wants to see them, I can say. Now you, well, this is, wow. well that's a very fortunate experience but and but you actually as I'm right that you

influenced escher right the ascending staircase was motivated by the impossible triangle or am I wrong about that? I have a staircase in our paper oh you had the staircase of paper but his paint his piece of art was done after that motivated by that am I wrong that's right yes no you see he did in the meantime I have to give him credit there's a picture he drew called belvedere a belvedere does use the similar idea. So he had that independent. But the idea, actually people point out to me that it was done by Oscar Reuters for the Swedish

artists and he had a thing very much similar to my possible trying, which is actually doing with cubes or stacked up. But it's the same thing. I haven't known about, actually I haven't known about it. Well, it's often the case that lots of people come up with good ideas at the same time.

Yeah, well, this is This is somewhat earlier, I have to admit, but it was not known to me or to Escher at that stage. But Asher did know some of the, I mean, there's a boy book picture of Gallows. Yeah. Things that joined up in the impossible. Clearly deliberate. I mean, people make out, oh, he made it a mistake. TV wedding is doing.

Now, again, this was relatively early, right? This was when you were still undergraduate, or was it a graduate student? I was a graduate student. students. When you had this and wow. And it was and that fascination

with that the art I think is just as I say it's just a beautiful way of combining the fascination with some aspects of mathematics and the art and the fact that similar things can attract different people. Yes, but it was curious because I didn't realize

it was colorology until later. See this there was a television crew and I can't remember what it was for I'm not sure if it was BBC or not. It was a television crew making a film

and it was about Twisters, strange enough. Much before anybody was physics was interested in Twisters. We'll get to Twisters. At one point, it was very strange because they were doing this thing with Tristers.

At one point they said, what are they actually for? I'm not doing this whole film. We'll ask me a question now. And I said, well, actually, you can use them to solve. of Maxwell's equations. That's for electromagneticism.

Yes, sure. Wonderful equations. And they said, oh, how does that work? Oh, I say, well, it involves an idea I couldn't possibly explain. What's that idea? It's a thing called co-emology. I couldn't explain why they're just, I'm afraid it's not something to do. But then I went away, and then I remember lying in bed that night.

I think, my God, yes, I can't explain it. It's just this possible triangle. this is a realization of chromology. Yeah. They never use it, of course. Did you ever write that up or anything in that? Yes, it was written up. I have an article because another conference I was at,

this was a conference in Rome or something. It's in Rome because Escher spent a lot of time in Italy. And there was a big thing about Escher conference. And I was supposed to give a talk the next day about I was going to talk about the triangle and cohomology. And I was talking to a mathematician, I wish I could remember his name, the night before, the evening before.

And I was saying that I wanted to talk about this triangle, which is an example of co-omology. And he said, oh, or what group? Well, it's really the, which depends when you put perspective, and it's a multiplicative group. The most plicative group is a positive real, really.

You're looking at with perspective. Otherwise, you're still, anyway. But anyway, he said, what I don't agree.

Do any other group? I don't know. How about Z2? That's well, in mind as possible. Well, yes, you can't do it with Z2.

So I, in the lecture, I gave an example of a Z2 example. And then I produced other ones, better ones, later on.

And I have an article, which it's got all this thing. I should send you the reference to that. Yeah, I'd like to see that. Okay, that's, then years later, by the way, we're, we're almost getting to cosmology, just so you know. Or at least, at least, well, we are. Well, yeah, anyway, but we're on the, we're on the pinnacle there of talking about that. But conformal general is part of the connection. Yes, they're gone, yes.

Yeah, but you came, I want, I can't resist coming back to Penrose Tiles. which in some sense is revisiting once again another impossible. It's not quite the same kind of impossible puzzle, but something that seems impossible on the surface. And you came back to it years later. That was in the 1970s, right? Yes, there was a slightly different train of thought. And there we go back to Steam and company,

because I had been interested in computability. at this sort of parallel interests in computability issues and I think I remembered looking at the mathematical reviews and seeing there was an example of a tiling problem which came from this study of computability

and I think that was Robert Berger, was it? I can't remember I'll get the name straight here. No, that was not... Robert Berger was the one who first, yeah, I don't know which part of the story I should tell you in what order it was. But I had this pattern. It came separately from that.

I had a way of, usually my procrastination was the source of these things because I was supposed to write a letter to an invitation to give a seminar for one of the London colleges. And I hadn't responded for ages. and I was trying to get down to write this letter. The fact that it was so late, it was a sort of blockage against my writing it. And I looked at the logo on the university,

and it was this pentagon, subdivided into six more, one in the middle, and then five going round. It's a simple logo. And so I'm wondering, what happens if you iterate that? You put the big one into the little ones, and you blow it up and put that in and it blows up.

Well, you have lots of gaps and holes and then you fill these. And I had a way of filling. the gaps. And there was a bit of a choice there. Would you do it this way or that way, A or B way? I did it the A way, which was very lucky. Or maybe instinctive, I'm not sure what, because a Japanese person had earlier done it the B way, and it didn't need anywhere. Oh, I see. You do it in a way, you get this iteration and it produces these lots of pictures. So I did it that way, and I produced a pattern. I rather like the pattern. And I have a way. And I have a

A friend of mine was ill in hospital, and I sent her a copy of this. She was interested in the medical things, and I thought this would cheer her up, perhaps. So that was just that pattern, that's what it was. Later on, I remember looking at this pattern and just having this, I suppose it's what people call inspiration. I'm not quite sure what. I wonder whether you could force that pattern as a jigsaw puzzle. And I thought probably you could. and this is one of these things

some people say oh they have this idea and it's 100% they believe it's true what percentage did I get 50 probably I think it's always about 50% it could easily be wrong but it has a good chance of being right so I played around with it and I realized you needed five versions

you needed three different versions of the pentagon because they occurred in a slightly different arrangement either they had five others around it three others or two others and this meant that you had a different dealing with them. And so you had six different shapes which will tile the plane

only on non-periodically. Yeah, I was going to, for listeners who don't know about the tiling, the whole point is that you can tie this plane non-periodically in a way that seemed to defy many, much intuition about how you could build things. I knew you could tie periodically

because I think I had been playing around with certain shapes which you could tie with smaller versions of the same shape and then reiterate that. And that gives you a non-periodic. But you take the shape and you could tie them with a period. It's not, there's no way of forcing it to be non-periodic. So the key point here is that it forces the non-periodicity.

The only way of tiling with using these matching rules. And the matching rules can be forced by jigsaw arrangements. And I was visiting Cambridge, Oxford, Oxford, sorry. I was visiting Oxford for a conference. It was in honour of Coulson, who I think had just died. I was going to be his replacement as Rice Ball professor, although he'd moved previously into a professor. He'd become a professor of chemistry.

I hadn't taken up my position as yet, but I think it was the year before, or during the academic year prior to my time. taking up my position there. But I did visit the Institute, Mass Institute, and I talked to Simon Cochin, who was a Princeton mathematics professor,

a good friend of John Conway's. And Simon Cochin was telling me about these six tiles of, now the name's confused. That wasn't Robert Berger. Was it, Bob Berger was the student of how long? who had found the first non-periodic, which used several thousand different shape. You need seven.

These are squares, I think, with coloured edges or something. And you needed, in his version, about, get confused by who the other chap was now, somebody who had got the number down to six. This was right from the number that Robert Berger had originally of thousands. And then I think he had got it down to about 109 or something. thing and the number I got worked its way down to six and that was the smallest one that had been found at that level and I was told by Simon Coaching that this mathematician whose name has slipped my mind now um like to get the numbers down to their minimum you see and that here he'd done it with six and I said well I know I can do it in five because I had my six styles you see and one of the ways I could be blew two of them together.

And you'd only five. This wasn't quite so elegant with the five that I knew you could do it with five. So I said, I know I can do it with five. So I went home and fiddled around for a bit. I think this must have been when I was visiting Compton. You said, my mother lived with Max Newman. She married Max Newman, who had a house in Compton near Cambridge. But during the week, he tended to live still in Manchester.

the way he was you do this research there and then the weekends he came down to Compton. I really can't remember very much clearly, but I think I must have been in Comberton when I

realized that you could get the number down from the five I had to four. I'm quite proud of that. Yeah. And I thought,

after a little while, I thought, why wonder if I can do it better? And I filled around and they got it down to two. And people asked me what my reaction was. I got down to two. And when I say my reaction,

they get a little puzzle by this. Disappointment. Why was I disappointed? I don't know. You see, I think it's just too easy. Surely this is known. This must be, you look at the old and mosaics

of the old people with them. Surely you'll see this thing here. I don't know if that was the reason I thought. I just thought it was too simple. You saw you solved a really hard problem and it must have been an easy problem, but it turned out to be an even harder problem. Yes. I just thought it was too easy.

That's why I was disappointed. It's just too easy. It's stupid. Fights and darts. And then I realized with the rhombuses a little later, the rombuses came second afterwards. Well, were you,

what was your reaction when you kind of learned that nature, nature incorporated some of these ideas? is. Was that a shock, a complete shock, or did you expect that? Well, yes. Well, there is a curious story, which is still a curious story, I think. People often ask me, I would give a lecture on these things, and somebody would ask me, you put up my hand, say, please, doesn't this mean there's a whole area of crystallography? This is way before Shepham, I should say. Okay. Isn't there a whole new area of crystallography opening? And my response would be, yes. Yes, in principle, you're absolutely right.

But how on earth would nature do it? Because you need to have a non-local knowledge. You can't do it simply locally. Yeah. Now, I give an example where you have this correct tiling, and then there are two alternatives of each year, neither a kite or a d'at. You can put a kite here, and then you can put a kite here,

or a dart here. Oh, no, you can only do it with a dart here and a kite here, not to whatever it is, I can't remember. And you can't tell. It only goes well way over here, you see. So how would nature, if Crystal Assembly, as I was mistakenly believing at the time, it's like you've got this little ridge and the Athens join up in the ridden, and then the next ridge and they build up.

You can't do it that way. So how would nature do it? And then Paul Steinhart and I were both at a conference in Israel on something completely different on cosmology, I think, harmonically it was. And we were both giving talks on something different.

I was talking about energy and relativity or something. And he was told you about something about cosmology, inflation probably. And he said, I want to talk about you something else. He showed me these pictures that Shetland has shown. And my reaction was,

okay, nature has found some way to do it. It wasn't a complete shock. It was a pleasant surprise. I would say. I would say, yes, nature has found some non-local way of assembling these things, or else maybe it's not quite as accurate as I think. You could see these pictures were pretty good. And the destruction patterns are amazing.

Yeah, I wondered whether, you know, nature could build up locally, find an obstruction, but then due to some fluctuation, overcome that obstruction, and it just came, and, and, and, and, With enough random trials, you'd appear to have something that's non-local. But I don't know. See, I think when I say it's a mystery, I think it's a mystery still not resolved because I think it has to do with the collapse of the wave function. Okay, well, that's, okay.

When you go from a fluid. My dog didn't like that. Go on. A fluid or a gas to a rigid thing like a crystal, it's got to have collapsed because the crystal really does know where its atoms are. Whereas the fluid or the gas, these states is going to be something where the atoms are not localized. And so there is a reduction of the state involved in making the postal. Okay. Well, that's an interesting idea. I was going to, I've tried to think of the

subjects I wanted to avoid and collapse the wave function was one that in our discussion today. So we can avoid it from now on. No, no, no, no, because we could go on about it. But I wanted to, you think about things I guess that I think are a little more concrete or at least well maybe we'll get there in a different context because it may be relevant when we come to the cosmology aspects coming back let let's get to I you know as I say I find this fascinating and I kind of wanted to divide this two hours or so into into two parts and so I want to move now generally from this fascination with puzzles and mathematics and and I knew of your sort of emerging interest in in cosmology although I didn't

realize it had begun so early. I thought maybe it began when you're, you know, later and when Shama had begun and I didn't realize it was so early. But what, but what brought you into, and I was going to ask about Twisters, but I think I'm going to leave it there. I'm going to, because we're going on. Maybe we'll come back to it, but I was going to ask where Twisters fit. Because I was, I think the first lecture, by the way, I ever heard from you as a student when I was in Boston at MIT or maybe when I was at Harvard was on Twisters. And I admit I didn't understand most of it at the time. But any, I do remember vividly wondering whether it, uh, I was very interested in mathematical physics at that time. I, I, I, I, I moved out of that later on. But always I was fascinated

about, well, what new mathematics, when every time you discover some new mathematics, what can it relate to physics? And I think that's why I was fascinated by Twisters. But, but, um, when you got involved in physics, your focus went to general relativity. And I'm wondering, you know, you obviously had the quantum mechanics experience with Dirac, but whether there was the peculiar aspect of the sort of geometrics and ultimately topology of general relativity that attracted you your interest right off the bat. Was that it? Or was it physics problems that attracted your interest? Well, it was the easiest route into physics in the sense that the geometry was directly there.

Yeah, okay. But let me give you, you see, unfortunately, all these things are little stories which are quite common. Well, let me give you this story, because it's fine. Look, believe me, I want to hear the stories. No one, no apologies. It ties up with me interested in algebraic geometry and all that stuff. And Hodges lectures and why they were all over the place.

And could I make sense of them? And I developed this notation, which was this geometrical notation for tensets, basically. So I draw rather than trying to find where this little A was the same as the little A down there and you need a microscope to see them. You just draw a line joining them, you see. So I said, no, these are just pictures. These are where you have diagrams and pictures and I had this way of representing symmetries

and skew symmetries and I learned a lot about that. And the problem that Hodges suggested, which incidentally I never solved except showing that no solution. Well, that's pretty good. They hardly believed me when I told him at first. There was no solution in terms of polynomials. You have to take rational functions or something. No, that was a big, he didn't believe me for one time.

It was quite striking. But anyway, no, that's probably why he moved me over to Todd after the first year. Ah. Because he didn't, I think he didn't believe me. And I only, I learned he didn't believe me only in my third years. Third year. But did he eventually come around? Yes.

because he repeated a calculation. I remember the expression on his face and he said, you were right all the time. This is why he moved me on to Todd. I don't know if it made much difference to me because I didn't click with Todd any more than I did with Hodge, really. But it was important to me

because in order to cope with this problem, which was very complicated. When you translate, it had to be tensors. That's the way you look at it. And the way you do to test it had been very complicated. And so you had to have this complicated. did notation and senses and so a lot of what I did in that thesis of mine which is really not so much to do with that it was a horrible notation I learned the right notation later on I should

have done it that way it was a horrible way of doing it so my thesis is not to be recommended but but it I did this problem of Hodges where you could solve it in a certain way but I showed there was no polynomial solution which is a bit of a shame because it looks at the is playing with the indices and joining them up, so on. But in order to play with these things, I developed this graphical notation. And I realized this was sort of an abstract idea. You could develop tensor ideas which were not realizable in terms of components. So I had these abstract tensors.

And the one I like the best with the minus two dimensional tenses. They had the nice symmetry and beautiful. And you could relate them to the four color problem and things like that. But anyway, it wasn't so much about the minus two dimensions, but the idea that you could have these abstract things. And then I learned about physics. I was interested in physics and I talked to Dennis about them and the Dirac equation, this wonderful equation for the electron.

How do these things work? Well, they involve spinners. One of the spinners. I mean, how can you have a spinner which seems to be a square root of a vector? That means you take one of these lines and you take your razor blade and split it down. And there is a curious story here, which I don't know the answer to me. The Iraq's lectures had two parts. There was this quantum mechanics one, quantum mechanics two.

I went to quantum mechanics one when I was an undergraduate. And by trying to fit things together later on, I think it must have been in my first year as a research fellow. Did I say undergrad? When I was a graduate. Yeah, you did say graduate. when I was a research fellow and that must have been when I went to Dirac's quantum mechanics too.

In his course, he gave, he deviated from his normal course and he gave a week's lecture on two component spiners. I had struggling, been struggling with the book that Dennis had recommended to me, which was Corson's book, totally unreadable, full of information, absolutely full of information,

but utterly unreadable. I couldn't make sense of it at all. I couldn't understand what spinners were at all from that. The Rack's course, beautiful, made it absolutely clear to me. I could see what they were doing and what they were, the two component spinners. And the Rack had a beautiful paper on two spinners where I looked at all the different spins, rather than going to all the different cases while after the other, you do the whole thing all at once.

It was a beautiful paper which influenced me very much. And so I thought two components spinners, my gosh, that's something I think I understand that. Then there was the lecture given by David Finkelstein in London when we were both in Cambridge. I was my first second year, I think, as a research fellow at Cambridge. And Dennis said, there's this lecture given by David Finkelstein in London. I think it would be interesting to go to it. So he went to this lecture. This was on

how you could go through the short short so-called singularity. And using these coordinates that Finkelstein, we now call them Eddington-Sinkleston coordinates because Eddington used them unknowingly at some early time. But I've learned you could go through

this so-called horizon, I mean, so-called singularity and it was really only horizon. So I learned about that. And I was amazed by this, and I remember having discussion with David Finkelson afterwards, where he pointed out, we swapped subjects. I went into general relativity, and he went into computational physics. I got the better deal out of that, I think. Yeah, well, it turned out to be good for you.

Let's put it that way. Anyway, I talked him about spin networks, you see, which would be used to use. I see. And then he taught me about the singularities being not R equals 2M at all. So I came away from this and seeing there's still a singularity at the middle. And I had wondered, so, look, you got rid of a singularity seeming at one place, but you've got it pushed into the middle now. Is there a general theorem, which would tell you can't rid of the singularities?

I had no idea how you, I said, how on earth would I prove it in? having the foggiest idea. What would I know that most people don't know about general relativity? I've got an idea. How about two-component spinners? I try and see

whether two-component spinners any use in general relativity. So I did. I looked at that. And I think it's amazing. This very complicated conformal tensor, which is the viral tensor, becomes this very beautiful

totally symmetrical object, which I understood perfectly because it was only in two dimensions, and it was complex dimensions. You can factorize every polynomial and homogeneous monomery. And this is a wonderful subject. And it was that that took me into general relativity in a serious way. Oh, okay. Now, okay, I actually hadn't heard of that before. I want to put in perspective, especially for younger people, don't realize it. I mean, the Fickleston result was part of an emerging, people don't understand how misunderstood black holes were. At the time, I mean, people thought indeed that what was now we think of as inventorizing, which is if you pass through it, you wouldn't know you pass through it to some

extent. And but it was something singular and represented some real issue. Wasn't there. But people also, of course, partly what amazed me, partly until you were there, before me because I was alive then, but not a physicist, but didn't really appreciate that black holes were inevitable at all. And I had heard that Wheeler sort of got you interested. And I think Wheeler's, who I happened to meet when I was young and had influence on me, but he had a remarkable influence on a lot of people. But it was almost ironic. I had heard that Wheeler got you interested in this question. And again, for historical perspective, as I've heard you point out, but people should know, this question of whether

black holes were inevitable, not mathematically, but physically, was an open question that had been dealt with. And people had constantly, especially Einstein, had constantly felt it couldn't be, because there was something pathological about them. And even when Einstein constantly didn't believe the results that were showing the opposite for right sort of beginning with Chanders-Sakar, but then with Oppenheimer and Snyder in 1939, which in some sense should have convinced people. It was, and that was 1939, but my understanding was Wheeler was a holdout right through till,

perhaps it was your work that trained him around, but he was a holdout right till the mid-60s, although ironically he was the person who is often credited with giving the name Black Hole to Black Hole. He came around the opposite way and became a, a cheerleader for black holes. And so I wonder if you could talk about a little bit about Whaler's influence on your thinking at the time.

Maybe you'd already, well, there's two things I want to address. One was his influence versus sort of what you just talked about, Finkelstein. And then the other one, which is so important for people to realize, not just that our picture of black holes as being inevitable, was not at all the conventional wisdom in the 50s and right up until the 60s. but then also to do you justice, the significance of Penrose diagrams, which in general relativity, at least, are as ubiquitous as Feynman diagrams are, in my opinion, in quantum field theory. Namely, they just change the way people pictured things, allowing you to picture things in a way you couldn't before. And I wanted to ask you, you said that they were there, but, you know, these conformal diagrams were always in your head.

So those are two questions. I've convoluted them. But what was Wheeler's influence on you in terms of thinking about what would eventually lead to the singularity theorems? And were the pictures that ultimately gave you, you thought about things globally in a way that people hadn't been thinking about general relativity before you in terms of these conformal diagrams or Penrose diagrams. And had you been thinking about them a long time before as well? So if we can go to those two questions, I'd love to follow up on that. Okay. Let's talk about the conformal diagrams.

Okay. You see, takes us back to Syracuse. You see, I was in Princeton. You talked about Wheeler, and he also influenced me distinctly. I went to, I think I was, I gave up my third year of a fellowship in Cambridge. to go to the US, primarily Princeton, to work with Wheeler on a NATO fellowship. The NATO fellowship was a two-year fellowship,

and I went, well, you see, it was partly, I guess there was some complication about my wife being, my wife to be being American and all that. Oh, okay. Which I think, I won't go into that all that, but it was a big mistake. too, but never mind. You can't say it to a mistake because they have too many implications. And if you change one of them, it changes the whole life. Everything. Yeah. It doesn't make any sense.

Yeah. But anyway, one of the reasons for going there was because my wife to be at that point was America. But that, I don't know how important that was. I also was interested in working with Wheeler because he was interested in crazy ideas. Yes, that Wheeler was definitely interested in crazy ideas. And I wrote to him a letter full of my crazy. ideas. Probably very stupid to think for Wheeler it was all right. But he apparently was, as I learned later, he received this letter and he couldn't make his tale of it.

And he gave it to Charles Mizner, Charlie Mizner, to see, is this chap a complete not or does he make any sense? And I think Charlie Mizzner said, look, this makes a lot of sense. I can't, I don't know, fact fabrication of the story was correct or not, but there was something of that.

I think it must have Charlie. I think it must have Charlie. was an influence on me in interesting ways but yeah there were crazy things in that paper which some of the day. It's still crazy. Well, you still like crazy ideas and we'll get to some of them that I think are kind of crazy but we'll get there. That's true. Now I have to give up on something.

But some of them turned out to be right, which is curious. Yeah, yeah. But anyway, the wheeler part of it was to get interested is a gravitational collapse and the states of matter which you could have which were very concentrated and there was a limit to what you could do and Chandras Sekehle and all these things

and the Oppenheimer-Snyder collapsed. Did you know about Oppenheimer-Snyder? I think I must have learned it during that period in Princeton. Exactly when I picked up on it, I'm not totally sure. But I think again let me let me just step back for listeners the point was that you know

people had wondered whether these this ultimate you know stars can collapse to white dwarfs but then after a certain level they can't they appear nothing appears to be able to stop them and then some sense that's what chendres say car had shown and but there were big quag but everyone felt something had to stop them physics couldn't be that crazy and what oppenheimer and snar showed in 39 just before the war when upenheimer

involved with other things, was that if you took a very special case, spherically symmetric collapse, under reasonable conditions, which they thought were reasonable, if the matter had a certain kind of form, which was called pressureless, and that it would,

that a black, what we would now call a black hole was inevitable. And then the question was, was it only inevitable because of the simplifications they had made? And it took a long time. I mean, that took, I guess, 25 years before anyone, namely you, ultimately resolve that problem. And so that that problem had been around for a while and one people wondered whether that's

nice and that's cute, but maybe there's a way out of it because things aren't really spherical symmetric and there'll be all sorts of complexity. And I'm sure that that led Wheeler to not believe in the Oppenheimer-Snyder thing. And I don't know. And maybe he expressed those concerns to you when you were talking to him. I don't know. Yes. Now, let's just think, you see, the time we're talking about is 1964.

64. I was back in England. I was in Birkbeck College. Now, you wanted to talk about the conformal diagrams, but that didn't have much of a role at this stage, except it did in a certain sense. which I could explain, perhaps. But it's true, what was more important in all this was the discovery of quasars.

There would be signals coming in from the deep universe, radio signals, which seemed to indicate there were objects out there which were extremely energetic, producing enormous amounts of energy, much more than the entire output of a galaxy. You would need to have more than... But yet these objects, the variations in the intensity or whatever it was were of such abruptness. Let's say they varied in such a small time scale that if these were coherent bodies, and since it was the whole thing that was varying somehow, they had to be no larger than the solar system. Because you had to think of how long would like take to propagate from one side to the other.

Exactly. They couldn't be that big and still be coherent to the level of getting these, these variations which were seen. So there was a lot of discussion and people were very excited about this. And Fred Hoyle, I remember. Fred Hoyle and, and what's this? Oh, what was this collaborating? Oh, I should remember his name.

It was a famous paper by the Burbitt, the Burbages. and Horwich. Wasn't Burbage? No. There were two loberges. There was Margarbordich. Jeff Burbage, Merg & Burbage, Hoyle.

Jeff Burbage and the other one. Well, I should know. It's stupid. The one who actually got the Nobel Prize. Oh, yeah, yeah, yeah. Okay, I was going to say was, what's his name? Yeah, yeah, yeah, yeah, yeah.

I would just, to my time, I was going to say the guy who actually won the Nobel Prize and went for some reason the other guys, especially Hoyle, missed out, which it seemed kind of crazy. But, oh, what's his name? Isn't that awful? I know him. But anyway, I know that forgetting somebody's name is infectious. Yeah, yeah, absolutely. Okay, in any case, the unknown Nobel Prize winners. Fowler, Fowler, Fowler. Willie Fowler. Thank you. You got it before me. Okay. Anyway. Yes, that's right. And what was I going to try to say here?

we have we both got distracted. Hoyle and Fowler, they were worrying about what the earth could, could there be structures so big that they were down at less fortunate radius, sort of side. That's what they seem to be. And there was a lot of confusion about what that meant. And there was also a lot of confusion about whether the red shift was real. Was it really the distance? Was this because these bodies were taking part in the expansion of the universe and therefore

extraordinarily distant and therefore these signals really were as strong as people thought or were they a lot closer and it was really a gravitational redshift instead or something else some other feature and there was a lot of discussion about that but anyway it was sort of in the air that bodies could be out there of this sort of size getting down in their short radius scale which was I suppose what got me interested what got what got wheeler interested he was very excited about this and what would happen. And I think, as you say, there was this belief that the Oppenheimer-Snyder model was unrealistic for the two reasons you mentioned.

One is everything was falling exactly focused at the centre. Secondly, they were what was called dust. There was no pressure. And therefore, there's nothing to stop them. So why, if there's nothing to stop them, focused at the centre, obviously you were going to get an infinite density. and therefore a singularity. But it's clearly artificial

because the closer they got to the middle and more of the slight deviations would mean they weren't all focused towards each other. They would swish around and maybe pressure would do make them swish more

and they would swish around and come back and swirling out again. This point of view, picture was confirmed, in quotes, by the paper by Lishitsch and the Kalaknikov, these two Russians, who had apparently shown that in the generic case, you would not get singularities.

So this was the background I had to think about. Now, for some reason, I wasn't very convinced by Oppenheimer Schneider. I looked at the paper. I did not notice that there was a mistake in the paper, which was it was corrected later, I suppose, by Balinski. I hadn't noticed that's a mistake. I didn't look at it. Oh, no, you're not talking about Oppenheimer-Sni. You mean, you mean,

you mean, uh, Klitschitzkoyev. I may have said the wrong name there. Yeah, yeah. Lipchip. Kalatnikov paper. Now, I'm not talking about up in my own side. Yeah.

There's no mistake in their paper. Yeah, it was. And the Oppenheimer Snyder paper, yes. In the Lifshitzkial paper, yeah. Which I did not find convincing. I thought the techniques they were using

were taking too much, making too many assumptions, which might not be right. There was something that was not right, but that was different from what I was worrying about. It wasn't that they were, let me just ask, it wasn't that they were thinking locally

and you were thinking globally in any way. I mean, it wasn't they were focusing on. But the question is, the one question is whether you're allowed to think locally in this problem. Oh, okay. And I think that one of the things that worried me, whether locally thinking was, and I certainly was,

I went around and said walking in the woods, so we had a nice woods lived where I lived. And I used to walk in the woods to try and get inspiration. I remember trying to think what it was like falling inside this entity and could a local infinite divergence produce a problem? If there was going to be a problem, it had to be a non-local problem. That was the sort of view I'd formulate what it was. But then I'd had this paper.

You see, there is a relevance to the conformal boundaries which was sort of incidental because I had been writing paper which involved that idea, which I'd put into the Royal Society, more or less simultaneously. I think I put it a little earlier than the other paper. But in this paper, I had to use the fact that infinity had to have a spherical structure. It had to be like a sphere. It was a sphere you see when you look out to the world. Or could it be something more complicated? And part of the argument depended on it being spherical.

So I thought, well, any sensible person would assume this and who cares? write the paper and send it in. I worried about it. I thought, can one show that it had to be spherical in some reason? And so I worked out, what do I know about general structures? I don't know much. So I looked at the boundary of the future of a point. I think that was what I was looking at.

And so I began to go a little bit used to what the boundaries of futures looked like. And they had certain properties. And so I had this at the background of my mind. I knew certain properties that boundaries of futures have been able to work. But I say a future, I mean, you look at the, take some region in space time, look at all the points that can be reached, not going faster than light from that initial region. And look at the boundary of that region. What is its structure?

What curious features does it have? So I got a bit of an understanding of that for this separate reason, which was purely incidental. accidental too okay now at one time this was a little bit later I was walking with Ivo Robinson

I told this story to many people before but let me tell you it again he was visiting he was an Englishman very English but the Americans loved him because he had this wonderful English way of speaking which is so different from the way they spoke and it was poetic and musical

and he really did have a way with words that nobody else that I knew did have. We had a way with words. And we were walking along, like in Mallet Street or something, near where I worked in college. And he was talking to me, in fact, he had a way with words, as I say, and also didn't want to be interrupted normally. Okay, so he was talking to me. We come to this side road, we have to cross. as we cross the road, the conversation stops. We get to the other side, the conversation resumes. After a while, he has to go off somewhere, and I go to my office and work back college.

And I have this strange feeling of elation. Why on earth do I have this feeling of relation? So I go through all the things that happened to me during the day. What about for breakfast when I go walking through the woods? How did I work at him? The bus? and I get on the right bus and then I get to crossing the street

and the idea comes back to me which was evidently the idea of a trapped surface this was how you would use the knowledge I had of boundaries of futures and see that there was something odd about the boundary of this notion

of what I call a trapped surface the boundary of this trapped surface would have to be compact because of the things I knew about. I'm not quite sure how many of them I did know about at that time, but I realized that this was something I should follow up on. When I got back into my office, I sketched out the argument,

which became the argument in the paper, which got the Nobel Prize. Yeah, yeah, yeah, yeah, the trap surfaces, which is a global way of thinking about what's, inevitable. But it was the idea, don't write down equations. You see,

what did people do about general in those days? Either they would look at exact solutions and Ivo was a real expert. You know, you had the little tricks to show you how exact and Roy Kerr. Yeah, sure.

In the Kerr solution is the, and Ken New and looking at various tricks like this, you know, experts at finding exact solutions. Now, I wasn't. well I did a little bit

in that route but I wasn't a good particular expert at that I was certainly not as an expert and computers and that's the

other thing people but they put it on a computer in those days there's no hope in any case you might say

there's no hope because when things parameters start to get very large you don't know why they're diverging maybe it's a

computer problem and something to do the code or what knows and who knows if it's really singular

yeah anyway I don't believe anybody has computing very far into a black hole that would be an interesting question well i'm dealing with those divergence i mean that's been a large part of the work and trying to understand gravitational waves is how to deal with those divergences near event horizons a lot of progress has been made of course yeah of course the gravitation waves you're looking at retreats on the hill's yeah yeah yeah

worry about the but the exact nature of the signal and the ringing you have to worry about taking your computer you have to go over many scales and that and and and and and that's been a Without that, I think that progress couldn't be made without those. No, that's true. The computers have come extremely important. No, I completely agree with that. That's right. But for the actual singularity situation, it's not so clear.

Yeah, okay. But what you could show with these global arguments, yes, it had to be singular. Although I've always kicked myself for not using in my paper what Charlie Mizner pointed out to me later. There's a much, the most complicated part of the argument, which I sort of skirted over in the paper, can be replaced by a much simpler argument, which was, I mean, I knew it. I should have used this already, but Charlie pointed out to me later. Well, did you, did, but the, the, the traps, what, but already thinking of these cones of the, of the sort of, of, critical, yes. Yeah, were critical for trap surfaces, but you had been thinking about them for a while or did that, or, or, or did that just.

in the context of the trap surfaces. Now we have to back out a bit to the conformal diagrams. Yeah, yeah, yeah. You see, in my two-year NATO Fellowship, I decided that, okay, there was a lot going on in Princeton, and I learned a lot of GER and stuff, but it was one particular perspective, and there was also a lot going on in Syracuse,

and I felt that I really needed to be present to what was going on in Syracuse. And so for half my last year I went actually to Syracuse. Actually spent a little bit on the Cornell as well, but first Syracuse. And there, I got to know Ted Newman much better. I had known him a bit before, but that's we collaborated together and started working on the spin coefficient notation and things like that. But also as an important, Arj. Troutman visited there from Poland, Another well-known. And he gave a talk on the asymptotic properties of gravitational fields.

And I think in particular the fact that the leading term had to be null, I think he was the first, I think, to show that. And he gave a lecture, which was an interesting lecture, but it was full of complicated calculations. And I thought, oh, I can't cope with this. Maybe there's another way of doing all this stuff. And I thought, how about inverse? I don't quite know what made me think of that, and I knew that you could turn the, well, the Riemann sphere, you get out of the complex plane and things like that.

Can you make infinity into finite by inverting? And I started talking to Engelbert Shooking, who was my roommate in Syracuse. He was a big influence on me in two distinct factors. one was I started talking about conformal transformation. I did think about you know inversions for short-shot solution and I got put off because you invert and the point of infinity is singular. Mm-hmm. Doesn't work. Oh dear, what a pity. But I did in the meantime talk to Engelbert about conformal transformations and he told me that Max was equations who conform the invariant. I think he referred me to a

paper which did it only in the special case where you were taking versions and things like that. I did it a different way and I realized that conformity in a strong way that you can have a conformal factor which is variable. Yeah. Again, for the listeners, conformal and variances, some sense allows you to scale lengths arbitrarily at different ways over space and things look the same. I mean, to be very crude about it. To be more precise, have a look at Escher's circle limits.

Okay, yeah. Very beautiful examples of conformal max. Yeah, yeah. He's got a lot of other ones which you use conformal mass. But the circle limits are the most clear. You just look at the age. And there you can see infinity has made into a finite boundary. I was trying to do that in the space-like sense,

looking at spatial sections. One of the visitors at Syracuse, if I have it right, was Ray Sacks. At the time he was in the army, I think. He had to join the army, the US Army, I suppose. I can't remember. I think he learned how to play Goa there. He must have been pretty good.

He was able to beat me at Go, which impressed me. What was the other thing he did was he had this wonderful result, which you didn't just have the lead. term was null according to Troutman but if you look at not the one over R but the one over R squared then you have three principles you see this is something I'd learnt from my understanding the spinners and that you could look at the vial curvature that's that part of a curvature which describes gravity you remove the witchie part which is the mass part and pure part is represented by the vial and formal curvature and

it's got the four principal null directions they They're pointed along the right curve. So you can classify them by how they coincide. In general, they're separate. In the now part, when what Troutman had shown was the leading term out of infinity, they all come together. What Ray Sachs had shown is if you come in from infinity, they peel off one after the other. That's to say, one over R, one over R squared, one over R cube, one over R to the fourth,

one of the last and it was a very beautiful result yeah very very very very striking and beautiful result that that's race acts his work with Bondi you see Bondi had

Bondi had looked at the axisymmetric case of radiating spaces had an inkling as to how the energy was described and how it could be the radiation could carry energy away.

Troutman had some understanding of this, not in the full way that Bondi described, but it was axi-symetric. You had to assume that there was a symmetry around an axis. Sax generalised it so you could remove the symmetry altogether. And he had this result about the curvature

of peeling off properties, as he was called it. I was very impressed with this. I remember being at home back in England in Stanmore and where I used to live, in the basement where I had my private, used to be a, meant to be a garage, but it was the badly designed. Nobody could get into the garage there,

but my usage is my study. Having drilled through the attic, through the ceiling, which was made of this poisonous substance. Asbestos? That's right. No knowledge that this was very dangerous, and you should nowhere drill.

through a little hacks all through it, which I did. I made a little trapdoor up into the house. This is my way of isolating myself from what was going on there, which was a good thing to do. Anyway, thinking I had my nice big blackboard down there, and the thought came to me, I'd been going the wrong way. I've been going out in a spatial direction.

If you go in a null direction out from a light cone, it doesn't go in Trinity. You see, the thing is that things go as a different power of the radius, one over R and one over R squared and one over R. And I hadn't realized that this different power. And that made everything finite instead of instrument. And if you're in vial curvature's finite as the Trinity, and you look at the different components,

and they peel off, that's exactly the peering property. It's just saying that the curvature is finite on the boundary. And so I began to realize looking at these conformal boundaries was a fruitful thing to do. And it's just a way it's funny how, you know, well, I guess it's the way it is. Yet the right tools randomly from different places just happen to come together at the right time. That's right. And ultimately produced something which changed. And by the way, to be fair, though, wasn't just that.

They did just not just change that paper. As I said before, they changed things. I like the quote from Kip Thorne, who said that, you know, you revolutionize the tools of, and I certainly, you know, thinking in terms of what I call Penrose diagrams and what most people do now, but do change the way you think. I mean, you know, if I'm pointed out, you can think about the same thing many different ways, and sometimes for certain problems, thinking about it one way is more fruitful, and for other problems thinking about it one way is more fruitful,

and in the case of thinking about general principles that don't rely on specific, things like spherical symmetry, thinking in these conformal pictures gives you a, well, certainly either way, both for black holes and we'll now finally get to the other aspect of cosmology, thinking about far future and far past, conformal tools are very useful. And obviously, they drive your thinking right now. Before I do get, I want to get to your, the modern thinking of the far future and far past that you're thinking about, which I will say in advance, I find, I don't think are right, but, but, but, but, but, but, but, but, but, but, but, but, but, but, but, but, but, but, but, but, I, I, I, I, I, I, I want to leave that to the end, because I, I'm fascinated by these things, and I didn't want this to be sort of, sort of, back and forth about what, whether we agree or disagree about certain things, but, but, but, the, the, the, the, the penro singularity theorem later, later, and I don't want to spend a lot of time, because people focus on Stephen Hawking a lot.

But, you know, it's sort of almost obvious that there's another important singularity in the world. And it's not just in black holes. It's in principle at the beginning of the universe. And I was surprised in a way that you didn't think, or at least incorporate that in the original paper. Unless maybe there was an offhand remark about it. But I'm wondering why you didn't. And it was just you were so focused on that particular problem or hadn't started to think about the other aspects of cosmology yet at that point. I think there was the feeling I had that once having shown that the similarities were generic in collapse,

but they would clearly be generic in a Big Bang universe. So you just saw it was so obvious it wasn't worth mentioning. Is that, maybe I'm a... That's a way of putting it. I'm not quite sure. I thought my thought processes were quite like that. It is sort of like that, but you see, Stephen Hawking picked up on this in a serious way. I had the story, of course, the movie is claims that I gave this talk.

Movies are movies. He was present at this talk, which he wasn't. The lecture I gave in London, I did give a lecture at King's College. This was in late in 1964. When I had the argument, I hadn't got the publication. I don't know whether I've written the paper at that point yet. I'm not sure. I would remember being very pleased.

Not that Stephen Hawking was there because he wasn't. I didn't know anything about Stephen Hawking. But J.L. Singh was there. John Litt. Yeah, the general relativists, which were a book I first learned general relativity from. I was so pleased he was there because he looked at general relativity in this geometrical way. I loved it. So he was the person from whom I learned a lot from GR.

Absolutely. Anyway, that's not very relevant. But Stephen had picked up on this and eventually pushed it. Dennis persuaded me to give a repeat. So I did give a repeat early in 1965. And Stephen Hawking was present at that lecture. And more importantly, I had a private session with him and George Ellis. see Stephen and George were trying to do something

much less general in thinking that he's a good guy and I'm not sure whether Brandon Carter was there he certainly was part of the story but Stephen picked up on it very quickly and applied actually my actual theorem to cosmological situations so his first paper was a I think he's Rev Letters paper

which reversed at the time And you had to see the point was that I needed an assumption that the initial surface was non-compact. There was this conflict between the non-compact initial surface and the compactness of the boundary of the future of the track surface. And that's where the singularity theorem comes in. You need that conflict. And if you don't have the compactness, the non-compactness of the initial state, then you can't prove the theorem. So if you had a universe that was closed, then how do you do it? but Stephen used it in a way in reverse time direction

in a way I hadn't thought of this was looking at the microwave background, early stages of the universe. It did become the basis of our much, much later joint paper that we wrote, where he then developed the ideas, with discussions with me from time to time, but they were primarily with people in Cambridge.

Brandon, I think, was a big factor, correcting mistakes and things like that. Even was a little bit sloppy in his arguments. But these were mistakes of the first kind rather than mistakes of the second kind. By the first kind, I mean those that you just changed the argument a little bit and it comes correct. Those are the second kind of the ones that completely wrecked the whole thing. Fortunately, they were mistakes of the first kind. But they were corrected.

And this story sort of went on, even when I was up to his thesis, which had mistakes. and I think I found about five of them in the thesis and I was going to point them out and he'd found them all by the time of that presentation examination yeah okay he's not a fun I mean he certainly developed these things very much I just didn't bother I thought I was probably working on twister theory so I want to I want to work these ideas on twist of theory and okay singularity is a generic we know that okay it would be nice to have a problem theorem for big bang but um which eventually this paper we had. Yeah, so when Stephen pushed it, but your interest was, yeah, as you say,

a little bit elsewhere. In fact, it's interesting because right after this, I have the question about twisters, but that's the question I'm not going to talk about because I want to get, I want to get, because it was clear that you were interested in them at the time. But any case, but, but I want to, so Stephen had taken it and pushed it back to the,

to the key question of, of, of, of the existence of a singularity. Yes. And the big bang and the non-aboidance of such. The fact that that classically, there is no way of avoiding a singularity classically in a big bang. And of course the question many of us have, in some sense the same question people might have had about a black hole was, well, you know, can quantum mechanics get around that? And I think there are different viewpoints on that.

I'm of the type that I suspect that the answer is yes and that quantum gravity will allow us to get around it. But this leads to your fascination with cosmology, both in the far future and the far past, which brings us more to the present. And you have been one of the most well, most of the most well known and to some extent vocal holdouts against what has been. been become for most people the standard picture of cosmology which involves this thing called inflation which which um which says which you know again i'm not going to we don't have neither the time nor the probably inclination to to do a whole show on inflation right now but but which basically says that the standard big bang model has a bunch of paradoxes and there are and what is fascinating for me about inflation it always has been um

is that it involves physics well below the plank scale, involves the kind of physics that you don't have to speculate about, oh, well, maybe this miracle happens or that miracle happens. In particle physics, it's a natural phenomenon that there are phase transitions, as we would call them now, in the universe, and under certain fairly general conditions, a phase transition will inevitably happen that will cause the universe to expand dramatically

and exponentially in general. And if that happens for some short period, it will resolve a number of the paradoxes, in fact, of the standard monocosmology. And moreover, it was later understood after Alan Gooth had first recognized that were then the three miracles of inflation, but people don't often talk about monopoles anymore.

But there were a bunch of paradoxes why the universe appeared to be so flat, why in some sense there was much entropy and also why these objects called magnetic monopoles didn't exist. But later on, there was another result, which in some ways has almost become more important, is that it allowed you a calculational mechanism to say that the fluctuations we see in the university, which are very small back in, could work calculable and could be due to nothing other than quantum mechanics.

So really, in my opinion, a beautiful result. not in your opinion, I think. But and so, but the great thing is it doesn't rely on going all the way back to T-equal-0. In some sense, and I don't want to play up the analogy too greatly, but I remember actually when Alan was talking to you in the program I was watching, he pointed out that inflation isn't a theory for the origin of the universe. It's a theory for what happened after the universe origin. It reminded me of the statement that Darwin once made, you know,

or that evolution is not a theory of the origin of life. It's the theory of what happens after life. The hard part is what gets life going. And the easy part is natural selection in a sense. And I kind of think of that way, too. Inflation happily obviates that burning question about what happens at T-E-E-E-Gal-Zero, which is a question that obviously has intrigued you more. And your argument against inflation, which is really what I want to get to,

there are a few of them, is that somehow it requires very special conditions in the early universe, that it's not as generic as it seems, I think you would say, to be fair. And that it requires, and you focus on this, on what's, on entropy, which is a subtle and beautiful concept, so subtle that the person who developed entropy killed himself because we wouldn't believe it in some sense, Boltzman. But but but but and then later on Paul Ernfest killed himself also who was a

who was a who is a disciple of Boltzman so it's had a long history yeah in fact one of my favorite lines in a book I think by Goldstein is a book and I forget who but it who it's a book on condensed matter physics and it talks about entropy and it says to noble history. Bowlesman did this. He killed himself. Aaron Fess thought about this. He killed himself. Now it's our turn to think about it. I love that line. But, you know, your point is that somehow it requires extremely low entropy, low, low, an entropy in someone since one can think of as disorder. It requires a very low disorder.

order in the gravitational field early on. Or another way of saying it, it's to require some smoothness in the universe that everything that you think about when you think about collapse defies your understanding of what collapse of what the early universe should look like, which you think should be incredibly messy because if you think of the final stage of collapse, it's incredibly messy. There's curvature. There's all sorts of garbage. And how can an early universe be smooth enough to have inflation happen?

So have I capitalized your concern accurately? That's accurate. It's not put as quite as forcefully, well, I wouldn't expect as I would put it. Yeah. You see, it's been a conundrum, which has worried me for a long time. And for some reason, I look around and nobody else seems to be worried by it. But yet to me, it's been the huge conundrum. I remember this is, I don't know, I shouldn't tell that story.

Okay, well, let's, okay, let's skip that one then. Unless you really want to, it's your, it's your, it's, it's one of my Feynman stories. Oh, well then, since I wrote a book on Feynman, I'm always happy to hear about Feynman stories. So send you my book on Feynman sometime. I'm very happy with that. Okay, now I have about four Feynman, sorry, I won't tell you all of them. But this one, I have to tell backwards, because I learned later. I was giving a talk in Caltech about the second law of thermodynamics and cosmology. and I can't remember what the title was or something,

was bringing those topics together. And I learned later that Feynman had seen the notice about this lecture. And he had told some colleague of his, oh, I'm going to go into this lecture and I'm going to heckle. I'm going to heckle this guy. Okay. If you like to do. Absolutely.

So this is the beginning of the story. Okay, I start giving my talk. And I come to what the talk is about in the minute. Start giving my talk. And I come to a certain point, Whereas somebody, the room is not all that full, but there was fireman over here and someone way behind him with somebody else.

This person behind Feynman, I assume, was some Nobel Prize winner because Calvertaker's full of him. And he started heckled, not Feynman, he started heffleman. Fireman turned around and he said, you shut up, listen to what the guy's saying. Perfect. Anyway, I should tell you what it was saying, you see.

The point I was made. which I haven't really appreciated up to that point. So people talk about the microwave background curve and there's a beautiful curve and they put the error bars for the temperature. And they're magnified by a factor of 500. They're really hugging the curve to within the incline. Let me point out. I think it's still true that the best black body curve in nature

has never been reproduced on earth as faithfully as the universe does. I don't think we've ever produced a black body, which is the canonical picture of an object at a finite temperature in quantum mechanics. I don't think it's ever been reproduced in a laboratory on Earth as effectively as the universe did it. That's interesting, yes. I see, I haven't quite realized that. But anyway, you see this absolutely beautiful plank curve. What does that tell you?

It tells you you're looking at thermal equilibrium. Yes. Thermal equilibrium. You go back and back and back in time and back and back and back. and back until the earliest thing you actually see, maximum entropy? Surely the second law firm in the anemic says it should be small. I mean, it's such an obvious, obvious, obvious point. Why don't people talk about it and stress it?

Well, you know, let me give you the counter. Well, okay, let me give you my counter argument coming at it relatively later. First of all, why would one, expect otherwise. It's 10 of a sense. If I come thinking about it as a particle physicist, which is originally my training, although my thesis, well, the idea of the problem, although my thesis relates to something that I want to get to you in a second, which I think is another argument about why the early universe, it's not a problem at all about generating entropy. But, I mean, reaction rates are fast compared to the expansion rate. You would expect to be in

thermal equilibrium. It's the natural, it's the rare violations from thermal equilibrium that have caused interesting things to happen in the universe, which is why you and I are here having this conversation is those rare violations that have allowed us to happen. But thermal equilibrium should be the norm in a sense, as long as interactions are fast compared to expansion. Yes, but our universe is not the norm. We've got an entry which is not as its maximum. Well, so where does it go? Starts from the top. I've reached the top and Oh, there's a line, yes. Well, it's, but, you know, we're just going to go to another maximum that's larger.

Ah, you see, there's a mistake in thinking that your expansion of the universe is going to make it bigger. There's more entropy, room for entropy as the universe gets bigger. That's the theory. No, as gravity begins to be partly because of negative specific heat, as gravity begins to operate effectively, I mean, and become black holes. I mean, we're already both on the same way. Okay, go on. I want to interrupt. No, it's gravity.

That's right. I mean, gravity was not thermalized. Yeah, gravity wasn't thermalized. But again, okay, but why would you expect it to be? Gravity is the weakest force in nature. Why should it be thermalized until late in the universe? Why should you expect it? It's irrelevant.

It has to start off low. Yeah, it has to start off low. But there would be a universe in which the degrees of freedom and gravity were not excited. Yeah, but, but okay, look, but let's say, let's get to inflation. I mean, the point is that you don't need, it can be, you can have a crazy universe, but as long as there's some small enough region where it isn't that crazy, which is kind of inevitable, ultimately, you're going to get inflation. And one point that I didn't see you emphasize in when I saw you talk with Alan, which I think is really important

when it comes to calculating probabilities, because I know you've calculated how improbable it is to get such a small reason. But exponentials are wonderful. And the point about inflation is not that it'll just inflate long enough to create a universe that we see and why isn't it half as big and a quarter of a big, but it doesn't go away. The hard part of an inflation is getting it to stop. And therefore, if you have a small region that's going to inflate, inevitably, because of that exponential expansion, which is in general eternal because it can't percolate, if you find yourself no matter how small it is, because exponentials are exponentials, you're inevitably, if you look at space, space is going to be dominated by regions that have inflated because of the fact that event,

that's the argument I don't understand why Alan didn't bring up with you. Inevitably, it doesn't work. Why? Well, I mean, there's my opinion it doesn't work. I mean, I don't know why. I think I, I, the strongest argument is probably in fashion, faith, and fantasy. not reality. And I do talk about this, and I can't see why you don't have an inflation which

maybe, okay, give us our galaxy, if you like. Why do we need all those other ones way over there? I mean, we don't need them, do we? I mean, maybe they... What's the use of the Andromeda Galaxy to us? Well, it could be many things, I suppose. It could be that we might be an outlier, and therefore you need lots of them in order to get, in order to get one that that, that, that, that, that, that, that, that, that, that, it could be, it, it could be, it, it,

that varies enough to be us. I mean, you know, there's a hundred billion of them, and that allows for... But that's the trouble, you see. This God has made all these useless universes out there not doing anything for the natural selection which evolved on the earth. Okay, give the whole galaxy, if you like,

I don't really think we need most of it. It has to be fairly calm. Probably you need most of it in order to get the stars initially, and in order to get the iron up, in order to get the heavy elements up enough. to have enough supernovae to get past, to get, to get enough stuff for you and me. Inflation is terribly wasteful, you see. It's trying to produce all this entire universe.

It's really an anti-anthropic argument. So maybe I shouldn't go into an anthropic. Well, I mean, but the point is that wasteful is in the eye of the beholder in some sense, because you might say that about the human genome, too. there's a lot of events, but, but the point is that it does, universe doesn't care whether it's wasteful or not. I mean, it's not trying, the purpose of the universe isn't to have life. There's no purpose.

And so it's, so if, if, if, if it's wasteful related to the things that you care about, who cares? That's what you care about, but the universe doesn't give a damn. That's misrepresenting what I'm trying to say. Oh, okay, sorry, good. Probably because I misrepresented this. Oh, okay, good. Because I purposely don't want to misrepresent you.

Okay. I think it's somehow using an argument of this sort to, I mean, you say that the reason, I forgot where we started now, the reason that the entropy was low, or the entropy is low in gravity was because it needed to be in a place where for us to be around, you needed to have a part of the universe of that nature. Well, I guess, I guess I don't think of it. I think that's too teleological. I guess I'm thinking the point is,

anything that can happen that can happen will happen. That's a really important property in physics, right? Anything that can, especially in a universe that's old enough, but in general, anything that can happen that isn't it possible, is going to happen. Okay? And so there will be a region that will inflate because inflation is kind of generic when it comes to thinking about the physics of the early universe.

And once it does, space, and I mean space, well beyond our universe, the multiverse, if you want to call that, if you ask, where is it likely to put your finger down, it's going to be in a place that's inflated and maybe still inflating, because once it happens, everything else goes by the wayside. It just becomes this cancer, that, if you want to think about it, that goes on forever, exponentially increasing regions of the universe in this false vacuum state. And no matter what you do, you can't get rid of it. but why does it do it globally in the whole universe rather than just locally? Because the uniform way, it has to know exactly when to turn off.

Well, no, but that's the point. It doesn't have to know exactly when turn off. In principle, it never turns off. Locally, it turns off. Locally it turns off, but inflation's already done its business by that point. And locally, you get this hot big bang after inflation, but inflation is still happening in most of what you would call the multiverse. and it's kind of, you can't get rid of it.

It's not a matter of, of why is it there? In some sense, it's, once it happens, it's like a cancer in a sense. If you, maybe, maybe that's a good analogy for you because you probably think it's a cancerous idea. But once it happens, you're stuck. But it shouldn't happen so uniformly globally. I think, you see, let's not, I don't know, perhaps I shouldn't go into all this. You see, I'm worrying about the dissimilarity between this picture and what happens in collapse. Yes, I understand.

Gravitationality is absolutely different. Yeah, and I've read, I should say, in your new book, I mean, I've read your new book in anticipation of this. So, and you talk about that in great detail. And so I worked through your new book, so if people are interested, they can look at that. Anyway, go on. So when you say my new book, you mean the fashion, faith, and fantasy. Well, I don't know. with the new book. I forget the name of it now. Is that what it is? No, I thought it was the one where you

some way you describe your new picture. The real, you know, cycles of time, yeah. Cycles of time. Isn't that the newest? Is there another one? Isn't that the newest? I think you could be right. Yeah, yeah, yeah. And that's, I mean, I wanted to look at the way you, because I've always is, I try to do people justice, especially when I'm going to talk to them on this. And so I'd kind of dismissed CCC for some time because it just didn't smell right to me. And I thought it's not fair. So I wanted to read your book to learn about it. I went through in detail.

Anyway, good. No, no. I'm glad to hear that because most people have never looked at the book. Well, I think you can't criticize, well, I mean, I can criticize ideas offhand in my office without knowing what I'm talking about. But generally, I like to think that if I'm going to do it in a form like this, I should at least have you. No, I respect that point of view very much.

And I appreciate that. No, I think, I mean, the book needs rewriting. Yeah, I think so. But that's one of the three books I have to be writing now. How am I going to write three books or at once? I kind of sense that it was core dump for you. You wanted to get the ideas out. And also, because you were you, the editors were afraid to say, no, no, you really need to, you really need to do say another way.

That's what my assumption was. But I was, it was not. I don't think even. observations of the circles was present there, was it? No, because that's right. No, there must have been something because there were in a little story. There's the boy looking at the wings. Yeah, yeah, yeah. There's discussion of the circles.

There must be some indication, but the fact about them, no, nobody was believing a word of it at that time. Yeah. And I think with some reason, because I don't think Bahay had, you couldn't trust. Well, it's not quite clear what you could trust and you couldn't. A lot of stuff you can't. that's still true i think yes that's absolutely true and and have been ignored and still being ignored but then you see the polish group got in and they found completely independently and doing different

methods and all that and they see these things yeah and the question whether you see them and i i don't want to get partly i don't want to get broiled in that debate whether you see these things you may think are remnants which i'm still not are i'm still not convinced or generic for maybe what reasons we'll get to or and but even if they're there, whether they're significant and they really differ from inflation, there's debates about that. And I'd rather avoid it right now. I want to go to the heart of the argument, which is why one is driven to this. But the heart of the argument is not addressed by inflation. And the heart of the argument is that the singularities in collapse are utterly different from the

big bear. Okay, well, let's go back and look at another argument. I gave one argument for why I think inflation is so, not only so generic, but so overwhelming that you can't get away from it. And it does what you need to do in a capital way. But let's go back to another one, which is, you know, classical singularities are nice, but many of us, well, I'll speak for myself, but I think it's fairly common. Think that quantum effects, you know, you can't go all the way back to the singularity. And I'm actually, I actually, I don't know if I said this in public, but I remember when I was a graduates when I would just had got moved to Harvard after being graduate student I actually

did a calculation which I found out my Alex Valenkin was doing at the same time um and I never published it at the time I was working with a friend in Affleck and I thought okay well it's not what publishing but but the idea that quantum mechanics can allow creation of universes in principle um is something of course I've written about I've written a whole book the universe from nothing about this and I find it I find it inevitable and fascinating but it's a way to avoid that question and obviate that question and say we don't have to go back to singularity. Quantum mechanics can create a universe with properties that are not, that are not surprisingly perhaps appropriate for the initial, what you might call the initial state of our universe.

And, and you think you've gone back to a state, you say that you haven't really quite gone back to the Big Bang. You've gone back to some early stage before inflation is even starting. Yeah, I've gone back from literally what I would call nothing, and the philosophers have debated whether it's really nothing. I think that's just semantics. But no universe, no space time to suddenly creating a space time. And if gravity is a quantum theory, you will have space times that come spontaneously into existence. That should be, since the variable, the quantum variables are space and time.

If you're going to have fluctuations, you should have a fluctuation that creates a space time. It's an unlikely one. What was that? Why is it such an unlikely one? Because you see, in the collapse, you have these singularities, and they seem to represent some kind of end. Sure, quantum gravity, and I used to think like everybody else, if quantum gravity comes in, where it probably does.

What good does it do you? I mean, it doesn't. Let me tell you what good it does you. And I will allow you, this is a chance for me to talk about my thesis and the physical review of letters that I've written on, which may have a citation. I'm not sure. But I asked the same question.

And here's an example. I thought, well, look, if you're going to spontaneously create stuff, then it seems to me what you're going to spontaneously create is a system that's much more likely. And if I have small regions, and I'm going to spontaneously pop into that, I'm not going to create something that's uniform. I'm going to create a black hole surrounded by radiation because, in fact, the entropy is much larger. Right. And so therefore, I suggested that if you created all these regions, you'd have all these primordid black holes and they'd evaporate.

It was actually just before inflation. It was my way of creating a lot of entropy in the universe. Black holes or white holes? Well, no, they can be black holes which will evaporate. Because it turns out, interestingly enough, you know this, if the region is small enough, then a black hole will be in thermal equilibrium with the region. Once it expands beyond a certain size, the black hole will suddenly become a. unstable because if the volume is less, I think, if the black hole is more than two-thirds the size of the volume, I forget the number, it turns out that specific heat being what it is,

the black hole more, as the black hole radiates, more energy will go back in than out. And so as the region expands, only after it's a certain size, will the black hole become unstable. But anyway, my point was it was a way to generate entropy. And inflation generates entropy beautifully. So I don't see that. You want to get rid of it. The point is the entropy is so low.

No, you want to create entropy and huge amounts of entropy and matter, so whatever's there in gravity seems irrelevant. I mean, the whole point about our universe is it's hot, right? And why is it hot and not cold? That was the problem that particle physicists asked. Why do we live in the universe with a billion photons for every proton? That seemed like a strange and crazy. Mimi to you wasn't strange and crazy,

but it was a strange and crazy question, I think that led most particle physicists to start thinking about cosmology. Why are we in a hot universe? Which from your point of view is saying, so the puzzle for us is why is the entropy of matter so great? Not why is the entropy of gravity so low? That's a different way of... That's a different argument. Yeah, but quantum mechanics seems to do that very well.

And it automatically in some sense does it in a way that ensures that curvature is small. Where's the time asymmetry in any of this? I don't see it. I mean, you've got these horrible things which come up in black holes, and we don't, of course, know in detail what happens. But it's so different from what our universe is like. I mean, to me, it's just that we haven't got the right theory. We're talking about the early universe in ways that we could talk about the remote universe

when we get the wrong answer, because the remote universe in the remote future is completely different. It isn't like this at all. There you do have the gravitational waves, gravitational degrees of freedom dominating. They run right ahead of everything else. They dominate completely. Well, it's interesting to hear you say that because, oh, sorry, I don't want to, because, because in some sense, the whole point of conformal cyclical cosmology, I think I got to write CCC. Is it ultimately the late universe does look like the early universe. in your picture. They're one in the same, in a sense. And so in a sense, it seems to me you're trying to do

with a picture which relies on physics we don't yet know, in some sense. Only in the tiny little spots, only in the hawking points. Yeah, well, I don't know. There's a whole, if I list, you know, my old friend, Mike Turner, Mike Turner, I think, said, you're allowed to have one tooth fairy in your cosmological model. And I tried to write down what I thought were the tooth fairies, which I counted five in CCC. One was, in some sense, that quantum gravity is not relevant at the beginning. But also, the black holes destroy all that entropy by, you know, that's another, I mean, that's a supposition, but it's a tooth fairy.

I mean, it's your require, in order for your late universe to look like, you know, you get rid of all that gravitational entropy. in the final stages of a black hole singularity. So you require that. It seems to me also that particle masses might decay without any evidence of that. In some sense, you require that Lambda be fine-tuned for a reason. So you require a large number and, you know, a large number that allows Lambda to be a small number today. You know, this end to 10 to the 20th, which you say Lambda can be that to the fourth sixth power or something like that. And you require, don't you require a massive scale or field at some, a very massive, which you later on you put to be dark matter.

So you kind of require, and you require. There's no tooth fairy there. That's necessary. But it's necessary. What I'm saying is, you have, what I mean, it's not, it's not, it's not, that's not a tooth fairy, okay, okay, okay, I'll give you that one. But in some sense, you acquire avoiding, it's, I guess what I'm thinking is, You kind of say quantum gravity solves the problems in the late universe of gravitation entropy,

and it can do it because of black holes can do strange things. But if you say that, why don't you just say quantum gravity solves the problems in our universe? And quantum gravity, for reasons we don't know, produces a beginning a universe that has low entropy. I mean, it's almost the same thing. You're just pushing the problem to the end of one universe instead of saying it happens at the beginning of another. I don't think that's at all fair. Okay, maybe. And I'm glad, and I'd like to hear why. Almost the entire crossover from one to the next is not.

Okay, you do need a mass fade-out, which is a big assumption. I always said that. However, it is based on something which is part of mathematics, namely that the first thing that you do in particle physics, more or less, is look for the Kazimir operators of the Boncary Group. Yeah. Now, these are mass and spin. So you say the absolutely conserve quantities.

Now, what I'm saying is that this is only approximately correct because the right group is not the Pochorei group, the city group. Because the cosmological constants, the one that we normally refer to, not one in inflation or something. Yeah, the real one. The real one.

The one that Einstein mistakenly introduced into it. The one that, I'd say the one that comes automatically from quantum fuel theory, but again, it's my thinking that, you know, you can't get away from, you can't get away from the vacuum having energy. Maybe it has to be there for some other reason. But it's certainly observed to be there. So it's not a true theory. Yeah.

Oh, absolutely. It's there. It's a big. So I'm trying to say that there is that term. And if you take the view that the group actually at which could be relevant in cosmological scales is the decider group rather than the Funker A group, it's not so surprised. that mass is not absolutely conserved. It's not saying it is, it K's in exactly this way or that way.

I agree that's missing. I've always said that's missing. But on the other hand, it's not such a tooth theory because it's already said that you've got to have something if you're going to accommodate the cosmological constant into your particle physics. It's just not shown up in most... Yeah, okay.

I mean, it's well motivated in the context of body, you want to do. I'm not arguing it isn't. I'm just saying it's something you kind of have to introduce it. Well, I think the one tooth fairy that bothers me the most, I think, well, I don't, I mean, it may be true. It's this insistence that all of that extra entropy that's generated, the gravitational entropy that's generated in the late universe disappears because it goes, it falls into black holes. And then black holes destroy it and they don't admit it. It doesn't come out of the black hole. And that's required, right? That's really required. Otherwise, the late universe, your late universe doesn't look like the low entropy universe you really need to be the beginning of

the next universe. Well, does, yes. No, you see, most, look at the conformal picture. It's almost entirely, the junction to the next neon is almost entirely smooth. That is the, all the effect of a, of a, take a galactic cluster, what happens? It gets swallowed, probably mostly anyway, by a supermassive black hole. that thing stays around for maybe 10 to 100 years, it depends how big it is,

finally evaporates your way by hawking evaporation. Now, you look at the conformal picture. That's tiny, it's less than a plank scale on the other side. Yeah, which it's less than a plank scale. So you were automatically driven to transplankan physics, which means you're already, in some sense, you're already making assumptions about a theory we don't kind of know. Yes, but you know a lot about it.

Was that? You know a lot about it. You know how much mass that I shouldn't go into this because I'm still in the middle of trying to write this paper. Okay. I mean, two papers with Christoph. And it's really interesting because it does use Twister theory, so be the boy that. It uses a bit of Twister theory to show how you can work out what the mass, how much energy comes out of the spot.

So the Hawking Point. and you can work out there should be a certain amount of energy which will spread out to a certain size by the time you see last scattering. There is an interesting thing from the discussion with Alan Goose which is developed in a certain very interesting direction which I think I certainly should talk about here. Okay, well no, no, no, yeah, we'll wait until you publish that. But I mean, I still don't quite understand why these high energy

stuff that's transplanckian comes and just manifests itself the causal microwave background, when in fact, I would have thought that would mean you'd have antisotropies in the energy early on in the history of the universe, which would then, I mean, one of the things that inflation overcomes is the fact that any small fluctuations in the early history of the universe will magnify due to gravity. And therefore, we've got an inflation given for free, which is the cosmological inflation. And that is the universe. Yeah, I guess it seems to me what you're saying is I don't like this inflation in the early universe, even though it happens naturally in every particle physics model. So I'm going to invent some aspects of general

relativity and quantum gravity in the late universe that allow me to produce exactly the same thing without having the natural consequence of the evolution of a general universe. Well, let me ask you. Let me, and you know, I'm bringing these up as questions, not to attack because I'm trying to understand it. I mean, I have problems with it, but I'm also realizing I probably don't understand things. Here's another question I have. Obviously, conformal transformations have been very good to you.

And it's something that's focused a lot of your thinking about. And that drives your thinking about this conformal cyclic cosmology. But conformal, but quantum mechanics breaks conformal invariance. and masses break conformal invariants and both in the early history of the universe I mean there's dimensional transmutation there's always scales put in there's a scale of QCD

what do you mean by those well it introduces quantum quantum mechanics and relativity automatically introduce scales that are like QCD scale the scale at which and so and when you when you do

yeah renormalization group automatically produces dimensional parameters which which which which which which which which which which which variance, unless you have string theory, but I know you're not depending on string theory either, so we'll avoid that. Okay, I see what you're talking about, but I think one has to be careful about these things. And also it plays a role in what I'm trying to say, too, but I can't talk

about it because of... Okay, okay, no worries, but that does bother me. But here's another, here's another, I'll just throw out some of the things I've been thinking about, because as I say, I don't want to just have a back and forth. I think I made it clear that I find inflation kind of inevitable and natural and automatically overwhelming. But aside from that bias, here's another thing. The late universe, I've thought a lot about the late universe. I didn't even know that was the word until Freeman Dyson told me that's what I was doing. And because we and I had a lot of fun. Eschatology, eschatology, the far future of the universe. It's what you're doing too. But now you know. And Freeman and I had a bunch of debates.

partly be and it comes back to the beginning it was actually hardly due to good old Fred Hoyle again who was not only just a wonderful scientist but a wonderful science fiction writer who wrote the black cloud which I'm sure is a oh yes no I completely agree and and Freeman when I were thinking about life in the future history of the universe and what fluctuations could do and other things and if you're going to wait 10 to the 100 years

for the black holes forever then you might expect other then other extremely rare fluctuation can produce things like maybe even galaxies. And so why are you so certain that the universe is just pure radiation? And not only that, but more largely low frequency radiation. There's a bit of hydrogen running around in this. Well, it could be more than hydrogen. It could be, I mean, if you have 10 to 100 years, quantum fluctuations are wonderful things.

And you could imagine a very improbable fluctuate, not even a bolshemin brain, but a improbable fluctuations. on, but I don't believe it. Okay. I think these arguments, a lot of arguments which are, well, they're all sort of anthropic too, some of them, where you somehow, if the universe lives long enough, then anything can happen, sort of the arguments. I think that's not right.

Now, you see, when I'm saying that, it's probably more a kind of feeling that has grown up since coming across CCC. and the argument is when it's from a conformal perspective, it's not that long. I mean, the end of the universe, what I mean is infinity. But that's not such a long time. If you've got a mass fade-up, it depends on how quickly it happens. Then you can't think of that as enough time. There's a huge difference between infinity and long time,

and my favorite quote of that is Woody Allen, who says eternity is a long time, especially near the end. Yes, the argument, I know. And you're going to say in some sense it's not too long because... I'm trying to say it is not that long. Yes. Yeah. It's a long time, of course.

10 to the 100 years is a long time. But in a certain sense, compared with any kind of infinity, any mathematician who plays with infinities knows, that's a trivial time. And mathematicians love infinities. Physicists tend to not like them. And that sounds... The question of... of probabilities of things happening?

Do those probabilities stay the same, or do they start going down when the universe becomes more rarefied? And that's the problem, I should say, about not just the anthropic principle, but to some extent, any time we start imagining probabilities, when we don't have a fundamental theory, when you don't have the face-face of probabilities, then you can almost prove anything, right? And I think it's a problem that's often you...

The CCC picture gives you a perspective on the world, which makes you not scare the infinity. Okay, okay. And, okay, and I, well, then, yeah, I agree in principle. Inflation does too, because it gives me a potentially eternally future universe of inflating. See, that's an interesting thing. I mean, the way that Christoph has been playing with it, and I'm sure I may be revealing too much.

The interest, the question about inflation has come up in this. You see, I've always dismissed the whole thing. I say, well, it doesn't play a role. But he's taking it more seriously, being a particle physicist, and he knows the reasons that people put these things in. And there is a role for some of these things. It's not quite what I had. The picture we have at the moment is not quite.

Well, any good theory evolves, hopefully, as especially, you know, and that's the whole point. I think for people who may view the discussion you are having as me being a contrarian, physics evolves by discussions like this, and I think it's really important for people to realize that. And I think the other, and I guess I want to sound about, because it's been fascinating, and I hope it's equally fascinating for others. And as I say, the purposes wasn't to say, hey, I don't, you know,

I have problems with CCC, was to explore your ideas because they're so fascinating and your history of ideas is fascinating to me. But I think what I wanted, what it does also illustrate is that when you're at the edge of physics, when you're at the region where we really don't know what's happening, There can be these vastly different views, and that's a good thing. And ultimately, ultimately nature is going to determine what works and what doesn't. And it's important for people to try and poke holes in other people's work,

and as well as in their own. Now, the hardest part is to poke it in your own. That's why having discussions with others is often useful because you realize that. And so therefore, you know, I think it's, you know, we have different views of what's, likely and what's not likely. And that's because at this point, we're at the edge of knowledge. And I think, and that's fine. And right now, opinions and views and biases come in. Eventually, that'll all wash away like yesterday's newspaper, because nature will tell us which

way it works and doesn't. I certainly hope anyway. And whether it'll be in our lifetime or or in a thousand years, I don't know. But, but let me just get to the end of this and say, What do you think remains to be done? What are the key challenges without revealing your papers? Where do you think the future of cosmology lies? And I'm not talking about the future of the universe. I'm talking about the future of the field. Well, I'm hoping that people will start to take us seriously.

I haven't seen it happening. It happens much more likely with people who aren't cosmologists and people who aren't wedded to inflation, for example, and all these ideas which has become part of their thinking. And certainly I remember this conference I was at, one of the most awful experiences I remember having in a lecture, which I had given it. It was an invitation to go to the 50th anniversary event in Princeton.

15th anniversary of the discovery of the microwave background. And Jim Peebles, whom I have a lot of respect for and liking for, asked me to. Absolutely, absolutely, completely. And he asked me, would I take part in? one of the discussion sessions that they have. And they had several of them. And each one of them, before the discussion session,

each one would present a paper, they give a own point of view, and then they have the discussion. Each one, now our one was the last one. This one, which is the name, Green, Michael. Michael Green, or Michael Green, the string theorist? No, not Michael. Brian Green. Brian Green. Okay. Yeah, he was also string theorist, but anyway, a different one. Yeah.

I know. He was more of a popular. Yeah. Yeah. And he was going to be the chairman. And he said, we're going to do this differently. I'm going to ask all the questions. We won't have the initials giving your official point of view and so on. I said, look, I went to see one of the organizers. Look, everybody else up to this point, you had a chance to giving, presenting their own point of view. Why am I not allowed to do that? And then I said, well, look, I have a few transparencies I really wanted to show. And he said, how many would you like to show? And I thought, how about three? He said, how about two? So the moment came. I said, well, look, none of the questions that Ryan Green was asking had anything to do with what I was going to say. Except the one was slightly close to it.

I thought, here's my chance, you see. I said, I've been given the opportunity. to show a few slides, two actually, didn't grumble the same way. I was hoping it was going to be three or four. So I started showing these things. And it was basically one of them was on the circles. And when you twist the sky, they just get less and less and less. So it is a circular feature.

And that was the thing that Bahad had done on my suggestion. because there was another way of doing it, which I won't go into that complicated story because it needs to be resolved sometime, but never mind. I think it was, I can't remember what the other one was, but it was mostly about that. And then at the end, somebody, and I made the point about the fact that, oh, gosh, I'm going to remember, forget people's names again. It doesn't matter. Most of the public won't know the names anyway.

Anyway, he's been Princeton, very distinguished Princeton cosmologists who got to look and repeat by his things. Do they see these things? And I was going to say, and they never, we never found anything, this was a voice shouting out from the audience. And I said, they never found anything because they were looking at the last. I bet it's David Spargel you're talking about. David Spargo. You've got to say, there's David Spirgel. You're absolutely right.

It was David Spargo. But then other people from the audience started catcalling. say, we thought Penrose had done good work about all the singularities and black holes and all this stuff. And what's he talking about before the Big Bang now? All this nonsense. And I thought, this was not a very improper way of dealing with the speaker. And, you know, they were just catcalls. Yeah, sure. It was very strange. And I said it was the most unpleasant experience. I had an lecture, I think it was. Well, I hope that you haven't felt that way over our talk, because I have great respect for it. No, no, no. I don't know. I.

I mean, I think, you know, we've, the last part of this has been contentious and it should be because. I think it's just somehow being disregarded. Yeah, yeah. It's better to be, oh, yeah, it's better to be argued with than disregarded. I think that's always. It's just being disregarded. And nobody's being, nobody looking at it. Well, look, I, I hope we've now gone on a little over two and a half hours.

And I hope, and I hope it didn't seem like that for you. It didn't seem like that for me. And I think it's, you know, it's been more than worth every second. And I have really enjoyed learning. Try to finish answering your question. Where's cosmology going? So I hope people will take me seriously. And they realize that the evidence that we have for the hawking points,

which the confidence level is 99.98%, you can't throw that away. It means something. Curiously, it doesn't quite. mean what we say in the paper because there was something slightly true, I would have to say, which came out of Alan Goof's discussion. And it's interesting, but I'm not going to go into that. I presume that is that, you know, that the correlations introduced by adiabatic random Gaussian fluctuations also produce something that doesn't look that different. Well, there is something else, which... Oh, okay. Well, wait. It'll be fun to learn.

It might be important, which is very intriguing. And I think it gives a different angle on that. So when I say, where is Kelsomel's going, I'm hoping that some of these things will be picked up because it's much more exciting to me than playing around the things that we don't know much about. These are observational facts. Yeah, sure. Well, that's what I mean. The universe is also going to be the arbiter of this. It isn't going to be a gang in Princeton or me or you. It's going to be the universe.

And that's what makes it so exciting. We will ultimately, hopefully, if we're lucky, the universe will give us a significant. that will allow us to adjudicate debates between prejudices or beauty or other things that may or may not be relevant. And also, the wonderful thing about science, one of the wonderful things is finding out you're wrong and learning. And I think I like to think, I hope both in you and I feel that way. I would love to be wrong about my bias. I think it makes it much more interesting. And there's a lot of irony here.

Let me tell you a story about somebody saying, you see, I learned my cosmology a lot from Dennis Shelma. Sure. And he was very dedicated to steady state model. Yeah. Comes the micro background observations. First of all, he struggles a bit and says it could be some effect and so forth. Then he gives up.

He goes around giving talks saying, I was wrong. The steady state model is wrong. and I have always had a tremendous respect for him. I don't know many scientists who go so emphatically to say that something they had been arguing for such strength and simply saying it was wrong. It's a mark of a great scientist. And Feynman said that too.

But the hardest person, the easiest person to fool is yourself. And the hardest thing to do if you're a scientist, especially if you love something dearly, is to look at it and say, what's wrong with it? And it's a great, it's a great. And look, I think this has been, has many lessons for young scientists and members of the public. I give you another little coda to this too. Absolutely.

I'm enjoying it. Go on. So Dennis Sharma said he was wrong. He then built up a group of people studying quantum gravity. He says, what we need to learn is quantum gravity. That's the important part of, of course, Big Bang. That's how we understand the alien universe. I get along with all this.

I agree with all that stuff. Now, I'm saying he was wrong dead. Because it's not quantum gravity. It's the CCC model because quantum gravity is, I don't think we've kind of resolution to this because I'm saying that quantum gravity, yes, you seem to be led to something like that in the Big Bang singularities. They're a mess. They're probably Belinda Kalatnikov, BKL model, Misman, BKLM, Mold.

sure they probably are. But that is not going to answer the problem for Big Bang. It's completely different. Well, let me add, let me, oh, sorry. So let me, let me put a different code on this then. What would it take for you to say, to go around giving lectures saying I was wrong? Well, the CCC model is shown to be wrong. But how?

What would it, what would do it for you? It wouldn't be hard. Look, I mean, if one could, could see that, well, I mean, nobody's accepted, apart from them. I haven't seen anybody outside our group. When I say our group, I mean people who become into our group through not having been in it before. I mean, the Polish people, for example, you see. I mean, Alan Gu keeps saying to your group, and I said, my group, these are people who came completely outside. Yeah, yeah, sure. The group expands and people look at these things. So I'm hoping.

that people will take these things which have a strong evidence for them, not just the walking points. There, these signals are stronger, but the rings, and the rings are consistent. There's also the thing which we... Well, that's not the answer to my question. That's, you're saying you're hoping the be proved right. I want the answer. The question I want to know is what...

They can prove wrong. Well, if they're not seen, that would be significant, evidence against it. They are seen. That's the trouble. we see. So, probably wrong would have to be something else. Okay. And we don't, but is there any smoking gun that would, just out of interest that we'd say, look, this convinces me it's the wrong, that I'm barking up the wrong tree? There are places where the numbers could come out wrong. Okay. You've got to have, for example, as far as I can see it, you've got to have the decay,

yes, the decay of dark matter particles. You see, this is, we haven't stressed this particularly. Yeah. I mean, I have written it in the paper. Yeah, well, I was going to, it was one of my tooth fairies. You've got to have the decay of dark matter particles, which involved in. The half-life has to be about 10 to the 11 years. Yeah. This has to give you the, in the, it has to give you the, what are they called it, spectral index. The spectral index doesn't come from some fancy quantum oil in the bottom.

It comes just from the fact that you're thinning out in the dark matter particles. That could be wrong. Yeah, and that's another, and my, that was. on my tooth fairy list, I think. And so you require it. Some of you add to the theory didn't come out naturally, but you require it to be there.

On the one hand, it's a tooth fairy, which is regarded as bad, and now you're putting it in the good side. But it's, yeah, but, you know, yeah, but if it makes a prediction that can be ruled out, then it's good. So, so, so let's, bottom line is let's wait and see.

And I hope, I hope. And this is not theoretical. You want to see, does the implication of introducing the, the cosmological constant into the particle physics picture give you a decay of dark matter. We don't know that. That could be shown to be completely wrong. Does it give you a decay rate, which would agree with the spectral index?

That could be wrong. I mean, that could be, these are observational things. I don't know how much decay of the dark matter of particles is observation at this stage. Well, I hope we don't have to wait 10 to the 11th years. before we resolve this question. No, I can't see why there's any real problem about proving it wrong. There are a lot of places you can prove it wrong. Well, I don't, you know, I have, I'm going to be in this way agnostic to some extent.

I have my prejudices, but it's fascinating to learn. The story of how we got here, which I think has been for me fascinating. It's just, I'm glad we got to focus on so much interesting science. and the way of thinking about the world. So I think some people with regard C.C. is actually having been proved wrong. Oh, yeah. I realize that. And that's why I wanted to read what you said, because I kind of felt like if it had been, you might have agreed. And obviously, you don't think so. And I'll bet against it. You bet for it.

And one of us can have a nice bottle of wine if we find out that. I might have regarded this proved wrong. You see, but now we skip side. waste, which is the size of the hopping points. You see, Alan Goof told me from standard calculations of when the, if you put in all this particle stuff and you try to work out in conformal time, when would the last scattering surface be? And according to his calculation, it would be half a conformal time than we actually see it. So that could be regarded as proving it's wrong.

So it is like it is proving that version. very wrong. I think that's true. Well, you know, I'm glad there's that back and forth discussion. And I'm glad we're having one. And I hope to have another one if we have an opportunity. But I'm really glad we had this chance to have this one. I hope you enjoyed it. And I hope we got to talk. I mean, you know, you've done a lot. Obviously, anytime one wins a Nobel Prize, it's lots of inevitable interviews and discussions. But I hope that this is, I tried to wanted to make this a little bit different. It has been a bit different and it's been much more

interesting for me. Thank you very much. Well, thank you so very much. Also, your point about inflation, which, as I say, these are very relevant to what Christoph has been doing. I've never taken it seriously, probably for a bad reason, not partly because I haven't known enough about quantum fuel theory in particle physics and knowing where all these condensates and whatever they are that seem to produce inflationary phases and things like that. I've never taken it seriously because mainly because it doesn't smooth the universe out. It may do things, certain things are importance, and that could be looked at in the right way,

which is, in a sense, proving me wrong to a certain degree, because I've never taken any of it seriously. I'm glad that my notion, at least the discussion, not mine, but the ones I emphasize that matter to me about the inevitability of these face transitions is an issue that you're thinking about now. it's something that I have swept to one side without looking at. And it really, I have become persuaded that they are important in this picture. And that is, in a certain sense, showing me wrong.

Well, that's a good thing. And let me put it conversely, one of the reasons I wanted to have the discussion besides the fact that I wanted to have a chance to chat with you again was that I knew unless I did have had it, I probably wouldn't have the patience to work through your book and your ideas because I would tend to just dismiss them. And so for me, it's been a learning experience and caused a lot of thinking, which I particularly appreciate as well. So I hope we both benefited and every time I'm with you, I'm sure I do. So thank you again. And I know the public will, I convince the public will benefit from this discussion. So thanks so much. Thank you. Thank you very

much. I think I've missed out on my walk. It's passing that. I hope you enjoyed today's conversation. This podcast is produced by the Origins Project Foundation. a non-profit organization whose goal is to enrich your perspective of your place in the cosmos by providing access to the people who are driving the future of society in the 21st century and to the ideas that are changing our understanding of ourselves and our world. To learn more, please visit Originsproject Foundation.org