Eric Weinstein: Hello, this is Eric with two pieces of housekeeping before we get to today's episode with Sir Roger Penrose. Now, in the first place, we released episode 19 on the biomedical implications of
Eric Weinstein: Bret's, evolutionary prediction from first principles of elongated telomeres in laboratory rodents. I think it's a significant enough episode and we've had so much feedback.
Eric Weinstein: Around
Eric Weinstein: it before we continue any kind of line of thinking surrounding that episode, we'll wait for my brother and his wife, Heather highing, to return from the Amazon where they're currently incommunicado. So thanks for
Eric Weinstein: all the feedback. It's been very interesting to process. The second piece of housekeeping surrounds today's episode with Roger Penrose.
Eric Weinstein: Now I know what I'm supposed to do. I'm supposed to talk about quantum
Eric Weinstein: consciousness and the emperor's new mind. Maybe ask Roger about the many worlds interpretation of quantum mechanics or the weirdness of quantum entanglement. I'm actually not that interested. I also don't want to go
Eric Weinstein: back to his earliest work on singularities and general relativity with Stephen Hawking.
Eric Weinstein: What I instead want to do is to remind you what Roger is in fact famous for. He's
Eric Weinstein: one of the greatest geometric physicists now living. He's perhaps the best, a descendant of Albert Einstein currently still working in theoretical physics in this
Eric Weinstein: particular line of thought. I also think he's a great example of what the UK does well.
Eric Weinstein: He has a very idiosyncratic approach to trying to solve the deepest problems in theoretical physics
Eric Weinstein: called twister theory. I'm not expert in it, and I can't always follow it. So if you're not following everything in today's episode, instead of deciding that the episode has somehow failed, youyou try to remember that.
Eric Weinstein: People who are working in mathematics and theoretical physics spend most of their time listening to colleagues, completely lost as to what their colleagues are saying. So if you start to feel that you are being
Eric Weinstein: left behind by some line of thinking, what we do is in general wait to see if another line of thinking opens up that we can try to catch.
Eric Weinstein: You're not going to get all of the waves. And in
Eric Weinstein: fact, the same thing is happening to me while I'm interviewing Roger. He's not understanding everything I'm saying. I'm not understanding everything he's saying. And in fact, this is normal. So what I would like to do is to instead
Eric Weinstein: present you guys with an idea of what science actually sounds like when people are talking from two slightly different perspectives, we spend an awful lot of time simply trying to
Eric Weinstein: understand each other.
Eric Weinstein: And if that feels a little bit uncomfortable, well then in fact, you're getting a true scientific experience, which is often very different than what you're getting when everything is pre
Eric Weinstein: chewed and spoonfed. Hope you enjoy it. Without further ado, si Roger Penrose.
Eric Weinstein: Hello, you found the portal. I'm your host Eric Weinstein, and I'm here today. With none other than Sir Roger Penrose. Roger, welcome.
Roger Penrose: Hello. It's
Eric Weinstein: good to have you.
Eric Weinstein: Um, I'm extremely excited about having you here. Uh, there are lots of questions that you typically get asked these days, many of them about consciousness, some of
Eric Weinstein: them about, um, art objects that come out of your thinking.
Eric Weinstein: But I know you. In a professional capacity has one of the important,
Eric Weinstein: most important people at the nexus of geometry and physics. In our time. Of course, you can't say that you can make all sorts of faces, but I can assure you that it's true. You know, there's a
Eric Weinstein: Leonard Cohen quote where, uh, from a song called the future where he says, uh, you don't know me from the wind.
Eric Weinstein: You never will. You never did. But I'm the little Jew that wrote the Bible, and I
Eric Weinstein: have what I considered to be the Bible right here, which is a book you wrote called the road to reality. Which there's no getting away from maybe, in my
Eric Weinstein: opinion, the most important modern book of our time. Because what it tries to do is to summarize what we know about the nature of all of this at the deepest level.
Eric Weinstein: And
Eric Weinstein: I think what I want to do is to introduce you to our audience, which has been habituated, uh, over perhaps 16 or so, uh, interviews. Not to expect to
Eric Weinstein: understand everything. Um, they want to work. They want to hear conversations unlike any they've heard. And so we'll do some combination of explaining things, but some
Eric Weinstein: combination of allowing them to look up things, uh, in their own free time.
Eric Weinstein: If you're game, should we talk about the road to
Roger Penrose: reality? You can talk about that. It'd be great.
Eric Weinstein: So we're. Where are we in the history of coming to understand what this place is in which we find ourselves, what
Eric Weinstein: we are made out of, and what we know about our own context.
Roger Penrose: It's a very tough question then. I mean, when I wrote that book, it was
Roger Penrose: no more or less the state of the world at the time.
Roger Penrose: I now feel I should rewrite part of it because things have changed, uh,
Roger Penrose: in one important way in particular as far as I'm concerned whether other people agree with me as another question. But, uh, I don't think I'm going to rewrite it because it was such an effort and I
Roger Penrose: don't think I would be likely to live long enough to do a good job out of it.
Eric Weinstein: Has that much really changed since you wrote the book and a lot of it level
Roger Penrose: a lot has not changed.
Roger Penrose: The thing that has changed in my view, you see. Whether people agree with me on this is another question is to do with cosmology, right? You see, I have a proposal,
Roger Penrose: which I didn't have. I mean, it's new since the book is not all that new, because it's about 15 years old, but it's new.
Roger Penrose: Since I wrote that book.
Eric Weinstein: And in our
Eric Weinstein: timescales. That's quite new now. That's pretty new. Let's just, just to get some context. You were born in the early 1930s.
Roger Penrose: Yes. Okay.
Eric Weinstein: You, um,
Eric Weinstein: you got a chance to live through. Uh, if not the original general relativistic and quantum revolutions, there are consequences. Um,
Eric Weinstein: in particular, you were able to take classes from people like Paul Dirac who scarcely seems like a, a human being sometimes more like a God.
Eric Weinstein: Uh.
Roger Penrose: Oh yeah. That was an experience. Yes. Uh, well, the, I, when I was at Cambridge as a graduate student, you said, I did my
Roger Penrose: undergraduate work at London un iversity, university college, and then I went to Cambridge as a graduate student, and I went to do algebraic geometry.
Roger Penrose: So I wasn't trying to do physics at all.
Roger Penrose: Uh. And I, I'd encountered a friend of my brothers, Dennis
Roger Penrose: Shama when I think I was at university college as an undergraduate, and he gave him the series of talks on a cosmology, but started
Roger Penrose: with the the earth. And then he sort of worked his way out and then talked about what was then. Referred to as the steady state theory, uh, where
Roger Penrose: the galaxies, the universe expands and expands and expands.
Roger Penrose: But it doesn't, it doesn't change because all the time there was new Matta created
Roger Penrose: hydrogen and the universe expands. And then you've got new material and it. Keeps replenishing, uh, what's gets lost.
Roger Penrose: And I thought it was quite an intriguing, I mean, Dennis was a great fan of this model, and so I was really taken by us.
Roger Penrose: So the,
Roger Penrose: well, the story was that I was in Cambridge visiting my brother, my older brother Oliver. Who did statistical mechanics, and he
Roger Penrose: was actually much more precocious than I was. He was two years ahead, and he was, I think, finishing his research there. But, um,
Roger Penrose: I had been listening to these talks by Fred Hoyle, and he was talking, I think in his last talk about how in the steady state model, the galaxies expands it way expands
Roger Penrose: away.
Roger Penrose: And then when they reached the speed of light, they disappear. And I thought, that can't be quite right. And I started drawing pictures with light cones and things like
Roger Penrose: this, and I thought, well, they would sit, they would fade, gradually fade, but they wouldn't just disappear. And when I visited Cambridge, eventually my brother and we were at
Roger Penrose: this.
Roger Penrose: The Kingswood restaurant in Cambridge, and I said to my brother, I said, well, look, I don't understand what Fred was saying. It doesn't sort of make sense to me. And he said, well, I
Roger Penrose: don't know about cosmology, but sitting over there on the table is a friend of mine. He knows all the answers to these things.
Roger Penrose: And that was Dennis Shama. And so I explained this problem
Roger Penrose: I had to Dennis, and he was pretty impressed because he didn't, he said he didn't know the answer, but he would ask Fred, Fred Hoyle, and the main thing
Roger Penrose: was that when I did come up to do graduate work in gen, in. Algebra, geometry, uh, Dennis decided
Roger Penrose: to take me under his wing and try to persuade me to change my subject, and I'd do
Eric Weinstein: cosmology simultaneously under the great, uh, geometer
Eric Weinstein: Hodge as well as Dennis Shama.
Roger Penrose: Well Hodge was my supervisor. See, a dentist was just a friend. I see how she was my supervisor originally until he threw me out and
Roger Penrose: talk, became my supervisor. That's another little story, but uh, but Dennis just wanted to get me
Roger Penrose: interested, do working cosmology. This was it. I never, you wanted me to change my subject.
Roger Penrose: I learned an awful lot from Dennis about physics because Dennis
Roger Penrose: sort of knew everything and everybody, and he had a real knack. Of getting, if he thought two people should meet each other, he
Roger Penrose: got made sure they did meet each other. In one case it was Stephen Hawking, but, uh, Dennis was actually,
Roger Penrose: when you mentioned Dirac, Dennis was actually the last graduate with, at the time, he was the only graduate student of Dereks.
Eric Weinstein: Is that right?
Roger Penrose: Yes. Dennis was,
Eric Weinstein: was director,
Eric Weinstein: was famously sort of a. Difficult. I think that, you know, in recent years, this book came out of grant from Ella, the strangest man that puts, directs
Eric Weinstein: bizarreness uh,
Roger Penrose: difficult to get to know. But there's a bit of an irony here. I mean, suddenly he was hard
Roger Penrose: for physicists and so on to get to know him.
Roger Penrose: Now there were two people.
Eric Weinstein: And actually maybe if I could just say one thing to our listeners. Yes. In my
Eric Weinstein: estimation, if not yours, Dereck would be neck and neck with Einstein for the greatest of 20th century physicists.
Roger Penrose: I think I wouldn't be far off that,
Roger Penrose: that description.
Eric Weinstein: For some reason, his press wasn't nearly as good.
Eric Weinstein: Maybe because of his hair. I don't know.
Roger Penrose: Well, he didn't talk much. This is one of the problems. No, I agree. I
Roger Penrose: think he was, um, I mean, you think about, Oh, me, quantum mechanics, people who develop that amazing subject and direct was really the one who
Roger Penrose: put it all in order and so on.
Eric Weinstein: But it is, is, is, uh, and this gets to a very odd issue, which is that you have wielded taste and beauty as a weapon your entire
Eric Weinstein: life.
Eric Weinstein: Your drawings are among the most compelling. I remember the first time. Well, one of the things I've done using our friend Joe Rogan's program
Eric Weinstein: is to push out discussion of the hop fibrations because it's, it's the only nontrivial principle bundle that can be visually seen. And
Eric Weinstein: since the world seems to be about principle bundles, it's a bit odd that the general population doesn't know that stuff of which we are.
Roger Penrose: They help fibrations or the cliff parallels. Was instrumental in the subject of Trista theory.
Eric Weinstein: Well, but the first time I ever saw a diagram, it was
Eric Weinstein: somebody reproducing a diagram they had seen of yours. And so the way in which you have used art and sketches,
Roger Penrose: it was drawn by hand
Roger Penrose: largely. I mean, there were, I think, some circles involved who tell you use a compass for, but basically I draped my hand.
Roger Penrose: There were two versions of it. The first one was more.
Roger Penrose: I sort of threaded a first one was, had more circles in it, and I thought I'd draw a little more simply in the second
Roger Penrose: version, but actually I had three versions. The fed version is in the, uh, road to reality, but, um, I'm not sure
Roger Penrose: it's the best. I think the second version perhaps is the best.
Eric Weinstein: So, so Dirac. Getting back to it had this elegance of mind that was unrelenting.
Eric Weinstein: Yes. And he famously brought in these bizarre objects with which some of us are obsessed. Others of us don't understand the obsession
Eric Weinstein: called spinners, which is sort of a prerequisite to getting to twister theory, which you've popularized.
Roger Penrose: Well sort of. And I went to
Roger Penrose: the UC direct, gave a course of lectures in quantum mechanics, and the first course was sort of basic quantum mechanics.
Roger Penrose: And the second course was on quantum field theory, but also spinners. And there's an interesting story about that, which I don't know the answer to
Roger Penrose: in the second course.
Roger Penrose: He deviated from his normal course of lectures. Now, I understood when I talked to
Roger Penrose: Graham , who wrote this biography of Dereck, um, I understand from grand formula that when I described it.
Roger Penrose: Direct deviated from his nor course to give two or three lectures on two components, spinous, which for me were absolutely
Roger Penrose: what I needed.
Roger Penrose: You see, I learned from my work on algebraic geometry, geometry, which ended up by trying to understand. Tenseness systems as abs
Roger Penrose: abstract systems and things which you can't represent in terms of
Eric Weinstein: compounding. I should just say that in terms of these two components, spin as you're talking, you know, for the lay audience,
Eric Weinstein: all of the matter that they think about whether it's in bound up in electrons or.
Eric Weinstein: The quirks that make up protons and neutrons. If you think of these things
Eric Weinstein: as waves, which many people in our audience will be familiar with that concept. The question is, what are they? Wait, what medium are they waves in? And there the medium would be a medium of
Eric Weinstein: spinners, which is not something that's easy for people to understand.
Roger Penrose: Yeah. When it's, they're not, and certainly the formulism. You see, Dennis, I told him I
Roger Penrose: need to understand about spinners, and particularly the simplest ones are these two components. Spinners. And he suggested, I read this book by, and so I got the book
Roger Penrose: my course, and I found it completely incomprehensible.
Roger Penrose: Just the, I mean it was fascinating book cause it, it was very comprehensive. It
Roger Penrose: described all these different spins fields and different things like that and using a lot of two components, spinners, which is the right way to do it. But. To introduce what these
Roger Penrose: objects were, was almost incomprehensible. I found, mainly because you have these translation symbols all over the place and they
Roger Penrose: mess up the appearance of the formula.
Roger Penrose: So I just found this thing very complicated and an incomprehensible, but then I went to directs.
Roger Penrose: Second course. It may have been not the same year. I think he went one year. I did the first, and maybe the second course was when I was a research fellow rather than when I was a graduate student. I can't quite remember.
Roger Penrose: I think must've been when I was a graduate research fellow. Anyway, he, this was a course on quantum field theory and things like that, but he sort of
Roger Penrose: deviated from his normal. A course in one week to talk about two components, minutes and fame. For me, this was
Roger Penrose: exactly when I needed it, made the whole subject clear from this complete confusion that I had before.
Roger Penrose: Now, then you see, many years later, I talked to Graham
Roger Penrose: Fama and I told him the story and he said, that's very strange. Durag would never deviate from his course. He just. He thought, well, when are you going to this course? Perfect. It was
Roger Penrose: perfect. He would never change, and this was true of his first. Yeah, of course.
Roger Penrose: The shorter the initial course, which I went to,
Roger Penrose: which people often said to me, well, it's not such a great course. It's exactly like his book. Well, I hadn't read this book, so to me this was, sure. The book is
Roger Penrose: amazing too, but not having read the book, I found this course absolutely stunning and it made things
Eric Weinstein: up.
Eric Weinstein: Do you think, Dereck actually understand? Understood.
Eric Weinstein: These objects is most mysterious of
Roger Penrose: all components, minutes,
Eric Weinstein: spinners in general. I mean, he brought them into physics. They'd been previously found inside of
Eric Weinstein: mathematics, I think, by people like killing and Lee, or I'm not sure who, but cartoon perhaps. I don't think, I mean, let me throw out
Eric Weinstein: a really dangerous idea.
Eric Weinstein: I don't think any of us understand them at all. And the part of the problem was, is that he understood very well what could be said about them. Yeah.
Eric Weinstein: But that, you know, I asked you before about like your favorite film, you said 2001. You could make an argument that spinners are in mathematics and physics, like the
Eric Weinstein: monolith.
Eric Weinstein: It's always encountered. Nobody ever understands exactly what it means, but it always grabs your attention because it seems so absolutely bizarre and highly conserved.
Roger Penrose: Well,
Roger Penrose: I always like to think of things geometrically and. At least for the two component ones. You see, when you go up to higher dimensions, you still have spinners
Roger Penrose: about the spinners.
Roger Penrose: The dimension of the spinous goes up exponentially. So each time you add the two to the dimension of the space and the dimension, that's fitness. It's multiplied
Roger Penrose: by two. So
Eric Weinstein: think I mentioned to D for example. Yeah, you'd get spinners of dimension. To do the D over two. Yeah.
Roger Penrose: That's the sort of thing. That's right.
Roger Penrose: And so they, they were the usually ones talks about the direct spinners, which are the Fordham, the fog,
Eric Weinstein: the folds minutes.
Roger Penrose: But they split into these two,
Eric Weinstein: two, and
Eric Weinstein: two, and even dimensions.
Roger Penrose: Yes, that's right. And even dimensions. And, uh, I like to understand these things geometrically so you could
Roger Penrose: see what the two components spinner represented.
Roger Penrose: And I had this picture of a, of a flag. So you have the pole, it goes along the light cone. So that's, uh,
Eric Weinstein: that's the
Eric Weinstein: vector like piece of it.
Roger Penrose: Yeah. It's Avec. Uh,
Eric Weinstein: now you have an extra piece of data,
Roger Penrose: an extra piece, which is this flag plane. And you, you get a pretty good
Roger Penrose: geometrical understanding there. One little catch to it is that if you rotate it through a hundred, 300, 360 degrees, so you might think
Roger Penrose: just to where it started, it's not the same as it was before.
Roger Penrose: It's, it's changed its sign. And then you rotate it again. So
Eric Weinstein: that won't make any
Eric Weinstein: sense to anyone. But if, I mean, one way of looking at that is if you have a Klein bottle for those of, some people will be listening to this in audio as I'm watching it and video
Eric Weinstein: Klein bottle in a certain sense that can be made precise, has a square root.
Eric Weinstein: That would be a Taurus. That is a double cover. So it seems like a very weird thing to take a
Eric Weinstein: square root of a strange topological Mobius like object. But there you are. Yeah. So it's really the square root of the rotations that has this
Eric Weinstein: double effect, but we say it linguistically in a way that makes it almost impossible for anyone to
Roger Penrose: understand.
Roger Penrose: This was a mystery. I mean, I understood that it's been, I was the square
Roger Penrose: root of a vector. You see? And I couldn't make head or tail of that idea. And it was when I went to directs course, it did become clear. And he made, he
Roger Penrose: gave this very impressive illustration, which I thought was due to rock. I learnt later it was due to Hammon vile that you imagine a cone
Roger Penrose: circular cones space like that circular cross section and another equal cone.
Roger Penrose: Which rolls on it. So one is fixed and the other one rolls
Roger Penrose: around on it. Now you see, when you imagine initially the cone is almost, it's just this little spike. I mean, you've got a tiny circle at the end, and
Roger Penrose: when you row one on the other, it's like really one coin on the other coin. So, and you can see when you roll one coin, another coin, it goes around twice because.
Roger Penrose: 720 degrees you've been around. Okay. Now, when you imagine gradually increasing the angle, the semi angle of the cone,
Roger Penrose: and you do it again, you keep thinking of that motion until it becomes almost flat. And then what's the other one? It's just a little wobble, right? So when it becomes
Roger Penrose: flat, this motion goes to nothing.
Roger Penrose: So this illustrates how. A rotation through four PI, two complete rotations.
Roger Penrose: Gradually it can be deformed into no rotation at all. However, with single rotation, it doesn't disappear.
Eric Weinstein: Well, I think with a, with a police system in a
Eric Weinstein: wheel, we don't have any trouble imagining a wheel that rotates twice as fast, half as fast, not at all hooked up to one particular crank wheel.
Eric Weinstein: Right. The problem comes when. Um, that, that's not the generic case. The generic cases usually encountered one dimension higher three and up has
Eric Weinstein: a familiar, because something called the fundamental group as it's structured to, yeah. Um, rather than the Z in dimension two. So there is
Eric Weinstein: something where in the place where you can see this most easily, it's slightly misleading.
Eric Weinstein: And then. In higher dimensions, you have to learn how to tutor your intuition,
Eric Weinstein: which is this problem that all of us who try to think about higher dimensional objects and counters that we have to use, the visual cortex we're handed. And then we have to trick it into
Eric Weinstein: imagining worlds beyond where we've seen.
Roger Penrose: But you see, Dereck has another thing that's not a . There's a thing about the directs is his problem. So
Roger Penrose: you imagine a chair with which has the. Um, pieces of wood going out like this, and you have a, a pair of scissors. I think this is directs the joke that Jamie was a pair of
Roger Penrose: scissors and through the, the, uh, when you put your fingers, you have a piece of string which goes through this, and then it goes around the chair and then comes back through.
Roger Penrose: The other one goes back again. Right now the
Roger Penrose: problem is you take the scissors and you rotate them. Through
Eric Weinstein: three 6,360 degrees
Roger Penrose: and the strings all tangled up. We can't, and whatever you do, you kind of untangle it.
Roger Penrose: You're allowed to move assistance around parallel, not rotate them, and you can move the string around it and you can't undo it, but you do it twice, 300 400
Roger Penrose: 720 degrees, two complete rotations, and then you find you can untangle it.
Roger Penrose: So this was the direct scissors problem. And I think that the joke was, it's a pair of
Roger Penrose: scissors, so if you get too frustrated, you've just . And he wrote a paper explaining, I think max Newman.
Eric Weinstein: Yeah.
Roger Penrose: Wrote a paper.
Roger Penrose: Dirac did this as an illustration, how you can undo it when it's minutes, right. For a pie, for someone on trainees degrees.
Roger Penrose: But to prove that you couldn't do it with.
Roger Penrose: This is, I think, actually in
Eric Weinstein: my head, if you've seen this video called air on the Dirac string, which illustrates this in video form, I haven't seen them. I would highly recommend it because it, it
Eric Weinstein: shows this off, is the similarity to the belt trick, the Philippine wineglass and all different versions.
Roger Penrose: I find that I could do that one. Actually.
Eric Weinstein: I had
Eric Weinstein: Joe Rogan try it and I think he got almost all the way around.
Roger Penrose: Yeah, no, I have, I've done it with a glass. Yeah. Yes, you could like that and it comes back.
Eric Weinstein: Very
Eric Weinstein: stylish. Yes.
Roger Penrose: So you can do two, two complete rotations, complete rotation.
Eric Weinstein: So this is a very fundamental property of the world that
Eric Weinstein: is somehow not discussed.
Eric Weinstein: I think. I find it very interesting that people want to talk to me about the multiverse. Sometimes they want to talk to me, but quantum measurement problem. But
Eric Weinstein: the idea that we are somehow based on a square root, and I would disagree with you slightly if you would permit it. It's not just a question of the square root of the.
Eric Weinstein: Of the vectors. It's a square root
Eric Weinstein: of the, the algebra generated by the vectors that really the S the spinners are this exterior or Clifford algebra. This object has fascinated me my
Eric Weinstein: entire life, and it's very strange that all of you know the stability of matter and, and matters. Strange properties with electron shells are all coming out of
Eric Weinstein: this weird, not that it appears everywhere in the universe, and it's not universally known that it's even there.
Roger Penrose: Yeah. I suppose the difference between the family islands in the Bose ones, so
Roger Penrose: the particles which have a spin, which is. Half an odd number, right, which, which have this curious property that you
Roger Penrose: rotate them and they get back to manage themselves. And it's crucial for for Matta because the exclusion principle depends on the,
Roger Penrose: the family statistics, which is to do with the, this exact, this property
Eric Weinstein: does not OCDness and the scissor trick or whatever you want to call it.
Eric Weinstein: We wouldn't have
Eric Weinstein: a periodic table. Chemical elements.
Roger Penrose: You wouldn't have anything, anything. Yeah. You wouldn't have it. You wouldn't have fermions in. Otherwise you wouldn't have things which have an
Roger Penrose: exclusion principle. So, and the Bose ons, which are the opposite, they they like to be on, if you have. To both zones.
Roger Penrose: You can have them in the same state and they rather like to be in the same state. So you get these things called Bose-Einstein condensates where you're getting the very cold. They all flop together into the same state. But
Roger Penrose: for the family islands, it's completely the opposite. They hate to be in the same state where they can't be, and this is what sort of pushes them apart.
Roger Penrose: So you've got the family principle.
Eric Weinstein: So you have this
Eric Weinstein: strange thing called the spins statistics theory that says that if things have a nodded ness of a particular kind, then they either are highly
Eric Weinstein: individualistic or highly communistic, whatever you want to call it. My question would be, there's another aspect of that that I've been very curious about, which is when we have to treat these
Eric Weinstein: objects quantum mechanically, and you've of course thought a great deal about quantum theory, we have two totally different prescriptions.
Eric Weinstein: For how to
Eric Weinstein: make these different objects, quantum mechanical, but there's a one-to-one correspondence between these two utterly different treatments that matter in
Eric Weinstein: force. Get quantum mechanically. It's the darndest thing
Roger Penrose: when you get these two kinds of . Popsicle are two kinds of Athens Bose ones and the family owns,
Roger Penrose: and it has to do with the make a complete rotation.
Roger Penrose: Do they come back to themselves or do they come back to minus? And so
Eric Weinstein: that's the top. Illogical. Yeah. But then there's this whole
Eric Weinstein: thing out. You go under ocean, like bear is in a integration, which is no integration at all. I mean you're, you're effectively almost lying about what you're doing to
Eric Weinstein: the, from to make them look like.
Eric Weinstein: Bose ons. And yet what we, what we seem to get out of this is that
Eric Weinstein: nobody. I don't think anyone could have anticipated that there would be a dictionary of two totally different structures, which are, it seems to be almost word for word,
Roger Penrose: and
Roger Penrose: it's because they're not totally different in the sense that you'd take two, two family out in system and you get to both zones.
Roger Penrose: So you, well, they haven't had the same load.
Roger Penrose: Yes, that's right
Eric Weinstein: now. Yeah. Maybe I could ask you a little bit about that. Um, . So I want to get to supersymmetry, but before I do,
Roger Penrose: I
Roger Penrose: see. Yes. Okay. Go on.
Eric Weinstein: We're going to make you work this morning so
Roger Penrose: I can understand that.
Eric Weinstein: Yeah. Um, so here, here's my question. Am I correct
Eric Weinstein: that you've lived through two errors, an era of fairly rapid development in testable fundamental physics
Eric Weinstein: coming from theory.
Eric Weinstein: I've tried to be very careful about setting that up, so I don't walk into a trap and a stagnant
Eric Weinstein: theory, uh, era in which theoretical predictions coming, uh, at the level of fundamental theory have not been
Eric Weinstein: rapidly confirmed. Um, by experiment.
Roger Penrose: You're thinking of things like string theory.
Eric Weinstein: I'm thinking about a regime before the
Eric Weinstein: early seventies and a regime following the earliest
Roger Penrose: supersymmetry.
Roger Penrose: Is that what you
Eric Weinstein: meant? Well, it could be grand unified theory. Supersymmetry Technicolor. It could be as some .
Eric Weinstein: It could be any one of a number of speculative theories from Luke, quantum gravity, Reggie calculus,
Roger Penrose: next string theory. It's
Roger Penrose: like
Eric Weinstein: the kitchen sink. We've tried a million different things that don't.
Roger Penrose: Yeah. It didn't really pan out, you mean?
Eric Weinstein: Well, it seems like, well, if you'll permit an American metaphor,
Eric Weinstein: um, we've been waved into third base and we've been waiting for the signal to come home for about 50 years, and we're not even sure that anyone's still, uh,
Eric Weinstein: you know, they're at home plate.
Roger Penrose: Well, you see, you might be around playing the wrong game.
Roger Penrose: That's the trouble.
Eric Weinstein: You think rounders would do it?
Roger Penrose: Well, I mean, there's a lot of intriguing ideas
Roger Penrose: you mentioned. Basically, I think you were hinting it super symmetry is one of them. Which
Eric Weinstein: maybe I've thrown off close to 10 I pre, I could
Eric Weinstein: do it pretty easily,
Roger Penrose: but I guess you hadn't, there's nothing new about that.
Roger Penrose: They were, the people were playing around with not something I'm Kelvin was
Roger Penrose: the idea that not smart be
Eric Weinstein: at the basis of political identity. Yeah.
Roger Penrose: I mean, these ideas come back again and in a different form, but certainly
Roger Penrose: in the, I guess the 19th century people were playing with. Well, I guess you can go back further from that flood, Justin.
Eric Weinstein: Well, that's
Eric Weinstein: true, but I would say that Maxwell was the first great condensation of a theoretical ideas where an enormous
Eric Weinstein: amount of theory surrounding, yeah. Magnetism, electricity, visible light, invisible light.
Roger Penrose: Well, that was a huge, huge
Eric Weinstein: revolution. And
Eric Weinstein: that all of those things now, um, can be unpacked from a single geometric
Roger Penrose: equation that that's the thing.
Roger Penrose: I mean, people know about Galileo, they know about
Roger Penrose: Newton. I know about Keppra a no, but I understand and they may know about, and the modern
Roger Penrose: quantum field theory, Heisenberg, Schrodinger people. How many people know about Maxwell?
Eric Weinstein: Not enough,
Roger Penrose: not enough.
Eric Weinstein: Or the map will do have Maxwell's equations
Eric Weinstein: tattooed on their backsides.
Roger Penrose: Let some people do that. That sort of general public don't know about maximum, but Maxwell equations
Roger Penrose: completely. Changed our way of looking at the world and, uh, we live off it without thinking, you know, you've got these lights here.
Roger Penrose: Well, these are visible lights, so we, we know you knew about visible light, but we didn't know anything about x-rays, x-rays, radio waves, they're all part of
Roger Penrose: the same scheme, electromagnetism, dynamo.
Roger Penrose: Well, some of this goes back to Pharaoh day, just before max shore. So Faraday had a lot of the.
Roger Penrose: Influential ideas, electromagnetism. Well, well, a little bit of that was known before. Erstad knew that if you had an electric current, then you guys are magnetic
Roger Penrose: field. But it was the other way around with Maxwell.
Roger Penrose: Now, if you have a varying magnetic field, you're going to current and you combine these ideas, you can make a dynamo. So these, these things go to
Roger Penrose: Faraday and he had sort of clues that there might be some connection with. Right. But he didn't have the equations and,
Eric Weinstein: but even max, you know, I'm very
Eric Weinstein: partial to this book on orchids that followed Darwin's origin of species.
Eric Weinstein: Oh yeah. That was the book he wrote. The title is a, and I was . I love
Eric Weinstein: reciting it. It's a on the various contrivances by which British and foreign orchids are fertilized by insects. And so you think, well, why would he write a damn fool book like that after origin of species? And the answer is he
Eric Weinstein: wanted to test whether he understood his own theory.
Eric Weinstein: And in fact it's revealed that he didn't understand the full implications. I would say that the same thing is true of Maxwell's equations, which is, this is
Eric Weinstein: perhaps the best dress rehearsal for unification we've ever seen. You know, full unification. And on the other hand, it's not until the late
Eric Weinstein: fifties that we actually unpack the last trivial consequence of the theory with the, this bizarre effect of passing an
Eric Weinstein: electron beam around an insulated.
Eric Weinstein: A wire
Roger Penrose: had enough.
Eric Weinstein: Yeah. In fact, we, we had dinner last night. We, we asked yacker
Eric Weinstein: Aronoff if he wanted to come, but he's in Israel and he sends his regards,
Roger Penrose: send mine back. We will do, he's great fun. I always,
Eric Weinstein: but that was a, that was a very weird thing where we learned that, um, if you have, uh, an insulated solenoid
Eric Weinstein: that the.
Eric Weinstein: Phase of the electron beam going in a circle around it would be shifted despite the fact that the electromagnetic
Eric Weinstein: field could be treated to zero because the electromagnetic potential, this precursor turned out to carry the actual content that it. Before that, it had been thought that that was
Eric Weinstein: just a sort of a convenience product to recover electromagnetism, and it turned out that that geometric object was more important.
Eric Weinstein: And you know, in
Eric Weinstein: part, the reason I bring this up is that we would have no way of visualizing this effect if it were not for your interaction with MC Escher.
Roger Penrose: And now you have to explain that one. Well,
Eric Weinstein: you know this, this, this etching called ascending and descending, which
Eric Weinstein: is sometimes referred to as the Penrose stairs.
Roger Penrose: Yes. Well, you want that story.
Eric Weinstein: Well, I do, but yeah. What I was going to say about
Eric Weinstein: why I'm asking. Yeah, yeah. Is that the photon is really best represented in some sense. As the angles of a set of
Eric Weinstein: stairs like that with this very mysterious property. Then what you're really talking about is what we would call horizontal sub spaces pictured to stairs, and the fact that there's a
Eric Weinstein: paradox of going around.
Eric Weinstein: And you seem to be going up all the time, but you're back to where you came is the same thing as saying, I never go up and yet I come back higher or lower. And that's called Hala
Eric Weinstein: Nomi. And we don't have a means of visualizing that except for like either rock, paper, scissors, or your work with usher. Is that a fair comment?
Roger Penrose: Well, I had,
Eric Weinstein: cause this is the first
Eric Weinstein: time you've ever heard somebody say this.
Roger Penrose: Well, let me, I mean, there's a, it's quite complicated story here. You see, when I was a graduate student
Roger Penrose: in Cambridge, um, I think it was in my second year when the international Congress of mathematicians took place in Amsterdam.
Roger Penrose: And so I, and a few friends decided that we would go to this meeting. And I remember, uh, I think I was just about to get on a bus or a tram or
Roger Penrose: something. And Sean Wiley, who was a lecturer in the algebraic topology, um, it was just about to get off the bus. I was getting
Roger Penrose: on. He had this catalog in his hand.
Roger Penrose: Of, uh, an exhibition and the van cock museum. And this was a picture.
Roger Penrose: Yeah. The, the one called night and day with birds flying on. Huh. In into the day and the nights. And they, cha cha Lubbers change into the spaces between the birds.
Roger Penrose: When Megan and I slipped in the summer, I had some amazing, what is that?
Roger Penrose: Where did that come from? You know, well, as you'd be very interested, this is this, uh, in the find cock museum, there
Roger Penrose: is this exhibition by an artist school Escher. So I'd never heard of him before, and I went to this exhibition and I was absolutely. Blown away. I thought it was
Roger Penrose: most amazing thing. I remember particularly the one called relativity where people walk up the stairs, gravity directions at two different ways, and I
Roger Penrose: thought, this is hugely impressive.
Roger Penrose: And I went away thinking, well, I'd like to do something impossible. You see? And I didn't. See, I had an
Roger Penrose: idea about an impossible structure with bridges and roads and things like that, so it locally makes sense, but as a whole, it was inconsistent and I didn't think
Roger Penrose: I'd seen anything quite like that in his exhibition.
Roger Penrose: So I played around with this. And then I sort of whittled it down to the triangle, which people refer to as the
Roger Penrose: tri-bar. So it's triangle, which is locally, completely consistent picture, but as a whole, it's impossible. And I showed this to my
Roger Penrose: father, and then he started drawing impossible buildings, and then he came up with this staircase.
Roger Penrose: So we decided we'd like to write a paper
Roger Penrose: together on this, and we had no idea. What the subject was. I mean, w w Gina sent a paper like this to what journal. So he decided, since he
Roger Penrose: knew the editor of the British journal of psychology and he thought he'd be able to get through, we decided the subject was psychology.
Roger Penrose: Of course, it's, as you say, it's
Roger Penrose: not, it's more in a way mathematics because it's illustrates ideas well of co homology. And other things like that, which, which, uh, I didn't quite know I
Roger Penrose: was illustrating at the time. But anyway, he wrote this paper and, uh, we gave. Some reference to ESHA, I think
Roger Penrose: reference to the catalog.
Roger Penrose: And my father sent a copy to a Dutch friend who says the managed to get the tuition. And then my father and had
Roger Penrose: a correspondence. Um,
Eric Weinstein: so that was Lionel pen?
Roger Penrose: No, no, no. My phone. Atlanta. Penn Rose. Yes. But it's, I actually. This is Adesha then
Roger Penrose: and, and um, he had sent to print to my father with a dedication to it, and he gave me another, so I don't have
Roger Penrose: in the Bodleian, but in some sense I actually own a museum
Eric Weinstein: cause I'm very indebted to you for this, for this reason.
Eric Weinstein: Because when I, when I have to
Eric Weinstein: describe what general relativity is, yeah. And I don't wish to lie the way everyone else lies. From an alignment and do it differently. I say
Eric Weinstein: that you have to begin with four degrees of freedom, and then you have to put rulers and protractors, uh, into that system so that you can measure length and angle
Eric Weinstein: that gives rise miraculously to a derivative operator that measures rise over run.
Eric Weinstein: That rise is measured from a reference level.
Eric Weinstein: Those reference levels don't knit together and they form Penrose stairs and the degree of or Penrose. Snus is what is measured by the curvature tensor,
Eric Weinstein: which breaks into three pieces. You throw one of them away called the vial curvature, and you readjust the proportions of the other two and you set that equal to the amount of stuff.
Eric Weinstein: Now that's a very long
Eric Weinstein: causal chain, but it is linguistically and accurate description of what general relativity actually is.
Roger Penrose: Yeah. What do you do? Let's stretch that. It's also illustrates
Roger Penrose: cosmology, which I was being interviewed. Oh, ages ago by, I don't know whether it's BBC, I can't remember what it was.
Roger Penrose: There was an interview, but for some reason they
Roger Penrose: were interested in twists. The theory now.
Eric Weinstein: They think they're interested,
Roger Penrose: whether they thought me, well, I guess it had the word or something, and at one point they say, well, surprisingly none. At the
Roger Penrose: beginning, they asked me what good it was. You see, what can you use it for?
Roger Penrose: So I said, Oh, you can use it to solve Maxwell's equations. You see, that's the equations of
Roger Penrose: Christy and magnetism and license. So they got a bit interested and they said, Oh, how'd you do that? Well. It's actually involves an idea that I couldn't really explain here. It's, it's not possible to,
Roger Penrose: in a, in a sort of popular talk like this.
Roger Penrose: No, no. What is it exactly? No, no, no. I couldn't do it. No. What's that? It's an idea. It's a thing called comb. Ology. No, I could explain that. So
Roger Penrose: then I went back and home and I was lying. My benefits. I think I can't, you know, it's this impossible trying, that's exactly it. And illustration of . So I went back the
Roger Penrose: next day and told them that they weren't interested.
Roger Penrose: They didn't use it. I think I may have tried to explain. Yes, we have a little something which is
Roger Penrose: locally consistent, but with an ambiguity about it. So here the ambiguity is you're not quite sure. You draw a picture of it. The ambiguity is that you don't know how far away it is.
Roger Penrose: It could be bigger and further away, or smaller and closer, and the picture was consistent, but you get.
Roger Penrose: An inconsistency if you go around
Roger Penrose: locally because you have a freedom and you misuse this freedom in a sense. So the glitch in it is this impossible structure.
Eric Weinstein: Well. Oh,
Eric Weinstein: I had this. So this is actually my son and my 14 year old son's copy of the book, and I was having to describe this to him. Cole would call him ology was, and I
Eric Weinstein: said, yeah.
Eric Weinstein: Um, that one forms, which is a piece of technology, uh. In mathematics that you can analogize to radar
Eric Weinstein: guns so that while you're driving in, the policeman shoots your car with the radar gun. He's measuring the component of speed in the direction of his gun. And so that's something
Eric Weinstein: that eats the vector of speed and spits out a number.
Eric Weinstein: And then you could imagine it a race track that wanted to have a circular.
Eric Weinstein: A series of radar guns to measure the speed of cars going around. Now the question is, you also recognize that you could build a
Eric Weinstein: poor man's version of a speed system by heating the track to some temperature and measuring how quickly the temperature changes.
Eric Weinstein: The car went over,
Eric Weinstein: but you can't actually have the one thing that you want, which is the series of radar guns that are always measuring. The speed going around the track,
Eric Weinstein: because at some point, if the temperature is going down, down, down, down, down, down, down, then it's going to be 10 degrees below wherever it started.
Eric Weinstein: Which is your paradox again. Yes.
Roger Penrose: Well, there's a nice example. Somebody may remember who, where you accompany, you have a bowl going up the stairs or down at whichever it is, and you accompany that with a, with a.
Roger Penrose: Uh, a note going up or down and you can make it sound is that keeps on going all the way up, all the way up, all the time by, by the
Roger Penrose: harmonics.
Roger Penrose: You bring a dent, new home only can as you go around
Eric Weinstein: below sub perceptual. So there, there's this auditory illusion that
Roger Penrose: captures these. Yes, you'd have an auditory version at the same
Roger Penrose: thing. You had this bowl bouncing around with that.
Eric Weinstein: That's not real, but that's a bit of a cheat. I mean, my point would be that your S your stairs or your Penrose stairs.
Eric Weinstein: Are the, the cheat is that it appears to be flat. In other words, it's very easy to achieve that on a curved object.
Eric Weinstein: But that what you did was to create the illusion as taking place in a plane. Or
Roger Penrose: maybe you can,
Eric Weinstein: George and I played a rectal linear SIS.
Roger Penrose: Do you have an interpretation of a three
Roger Penrose: dimensional thing, which, which in an ambiguous,
Eric Weinstein: so you saw the movie inception of course, where they, they realize this actually,
Roger Penrose: yes, they're there.
Roger Penrose: They have an instruction of that then. That's right. Yeah,
Roger Penrose: but, but
Eric Weinstein: that effect is the soul of the Aronoff Boehm effect, which surprised the world in the late fifties because it was discovered so late
Eric Weinstein: into the game.
Roger Penrose: It's just a, it's just a company. Same sort of thing. That's right. Well, of course, like so many things people point out that.
Roger Penrose: This Oscar righteous fart who is a, who is a Swedish artist that drawn things like this before I think roundabout the year I was born, he had a picture, which is all
Roger Penrose: with cubes going around. It wasn't exactly the same, but it was,
Eric Weinstein: I think I've seen these floaters.
Roger Penrose: The cubes, yes, but then he had versions with stairs.
Roger Penrose: Staircases too. Let me
Roger Penrose: never put any, it never put any perspective in it. We seemed to me that was a
Eric Weinstein: something missed opportunity.
Roger Penrose: Yes. No. And my triangle, I did put some perspective. Yeah. So there's
Roger Penrose: slightly, you can see, but you can do it with a perspective and it's still still works.
Eric Weinstein: So what I want to get at is.
Eric Weinstein: I think also that we have
Eric Weinstein: this very funny thing that happened recently is starting from the early seventies where we started miss telling our own physics history
Eric Weinstein: because of the needs of the community to look like we were succeeding when we weren't, or we were succeeding at something different than we were trying to succeed at.
Eric Weinstein: And. In part, one of the reasons that I want to use this podcast to discuss science is to give alternate versions of what's happened, and I
Eric Weinstein: want to explore one or two of them with you. Now, you and I have a very funny relationship, which we don't really know each other, but you were quite close to Michael the T at
Eric Weinstein: various points.
Eric Weinstein: Yeah. And I was,
Roger Penrose: well, we have graduate students again in
Eric Weinstein: the same group, same year,
Roger Penrose: same year. He asked me the same supervisor. Incredible. Yes, that's right.
Eric Weinstein: And then you
Eric Weinstein: continue to cross pollinate ideas through the years. For, for listeners who don't know, Michael was one of the absolutely most
Eric Weinstein: dominant and generative.
Eric Weinstein: Um, I don't even know what to call them. It's like beyond genius, a sear of type.
Roger Penrose: But he sh she had such a broad
Roger Penrose: understanding of mathematics. It's
Eric Weinstein: partly in geometry, more generally, and analysis, I mean, just credible and algebra. I mean, he wrote a book on, on communitive algebra, the, um,
Eric Weinstein: now he had a partner, uh, for much of his career, his adore singer, who I was quite close to for a period of time.
Eric Weinstein: And is was again,
Eric Weinstein: another one of these figures that if I'd never met one, I wouldn't know that the human mind was capable of that level of repeated insight. Yeah.
Eric Weinstein: And they came up with something called the singer index theorem, which governs worlds in which there are no time dimensions, but only space dimensions or no space dimensions
Eric Weinstein: and only time dimensions, but there's
Roger Penrose: no just equations without any differential equations,
Eric Weinstein: differential equations.
Eric Weinstein: If you think about differential equations as coming very often in
Eric Weinstein: three main fields of study. Yeah. Elliptic hyperbolic and parabolic. Then the idea is that wave equations would be hyperbolic, the type that you're
Eric Weinstein: worried about in physics, but things like soap films. Look like elliptic equations and TN singer had this incredible insight into the
Eric Weinstein: nature of elliptic equations.
Roger Penrose: Do you, go ahead. Sorry. No, I was going to say it's an extremely general fear on which covers goes over all sorts of different areas in
Roger Penrose: mathematics and it has applications.
Eric Weinstein: It sort of tells you that the. The nodded Agnes of some beautiful space that you might be exploring, like some kind
Eric Weinstein: of high dimensional donut that's nodded many times around itself.
Eric Weinstein: Whatever you want that that topological nodded Ignace tells you
Eric Weinstein: something about the kinds of waves that can dance on that space.
Roger Penrose: Yeah, no, I see. It's very remarkable. Theorem
Eric Weinstein: does that theorem. In the so-called elliptic category, a world of space, and no time. Let's say
Eric Weinstein: relate strongly in your estimation to the most important hyperbolic equations that govern the waves that make up our physical world due to the
Eric Weinstein: constraints of relativity in a world with one time and three spatial dimensions.
Roger Penrose: All I can say, if I used the therapy. And at least two different con
Roger Penrose: contexts. Yes, maybe more so. I mean, I'm not an expert in that area at all. And it was mainly when I was trying to solve a particular problem. I don't know how
Roger Penrose: much detail you want to go into these things. It had to do with, um, how to make twist the theory work in curved spaces.
Roger Penrose: But I ran up into a question. Which had to do, it has to do with complex geometry. So you've got geometry in which instead of
Roger Penrose: using real numbers to use, you think of measuring with Roula say and the re the ruler is one dimensional.
Roger Penrose: The numbers go along. One dimension, if you like, and complex numbers where you have the square root of minus one incorporated in each the number system, they're really
Roger Penrose: two-dimensional.
Roger Penrose: So the geometry of complex numbers has twice as many as the real numbers, but the geometry of complex numbers. Is particularly
Roger Penrose: fascinating or not the algae, or he might sit in the analysis or whatever it is. It's particularly fascinating. And I was sort of, when I learned about this when I was at,
Roger Penrose: um, an undergraduate doing mathematics, and I thought it was an incredibly beautiful, because when you talk about real numbers, you have,
Roger Penrose: um.
Roger Penrose: You can have a thick draw co, which is a function. So this, this Cove has some shake and you might want to see what is
Roger Penrose: it, a smooth curve. That means you have a tangent direction as you go around it. Maybe it jumps. So you slept not even continuous or maybe smooth, or it may
Roger Penrose: be you have to have a curvature of this curve and you might, might not be smooth enough to have curvature.
Roger Penrose: See, so if there's one degree of smoothness or two degrees, or you, or you can have three
Roger Penrose: degrees or four degrees and they're all different or an infinite number of degrees. Or that you can expand your function in the power series. They're all different.
Roger Penrose: And then we learned about complex. You see, Oh, we're not doing it all over again.
Roger Penrose: And you've got your analysis on algebra. If you like geometry
Roger Penrose: where the, it uses complex numbers and then suddenly you find that if it's smooth. Everything comes with it. You can differentiate as
Roger Penrose: many times as you like. You can expand as the power series, and I thought, that's incredible. Re magic. You just have to do it once rather than this old Craig.
Roger Penrose: All these different kinds of
Eric Weinstein: mathematicians.
Roger Penrose: Yes.
Eric Weinstein: Quite often view the complex case, the ne the case of complex numbers as
Eric Weinstein: the natural case and the case of real numbers as artificially tortured. Yes. Which is a complete reversal from how most engineers and physicists
Eric Weinstein: and you actually have been quite instrumental.
Eric Weinstein: In making the case for the fundamentally complex nature, that it's not just a
Eric Weinstein: convenience that we use complex numbers in physics, but that nature appears to be essentially complex.
Roger Penrose: I think you see, by just hearing this nature
Roger Penrose: of complex analysis and how beautiful it struck me as being, and I had this sort of feeling, wouldn't they be wonderful if these numbers were
Roger Penrose: somehow the basis of way.
Roger Penrose: Physical world operates. I have no reason to think that. And then I learned about quantum mechanics and I was maze to find,
Roger Penrose: yeah, that, yeah, they're not just useful convenience. You can use them to simplify ideas and mathematics. You can, you know, might have an integral,
Eric Weinstein: you'd have to work awfully hard to
Eric Weinstein: get rid of.
Roger Penrose: Yes. But the things you find that your little trick to do it, these four to me come. With continental goals and they drop out in an amazing way. And I thought, well, that's a piece of magic, but it
Roger Penrose: doesn't tell you anything about the world. It just tells you this is a neat way of doing things. And then on and on about quantum mechanics, and suddenly these numbers, they're right there, the basis of the
Roger Penrose: whole subject.
Roger Penrose: And I thought that was an amazing thing. Maybe these complex numbers are really there at the root of everything.
Eric Weinstein: I mean, I think you wanted to
Eric Weinstein: talk about twisters and maybe I can intro that and then try to fit that into this history that I'm claiming. We don't tell now. One of the ways of
Eric Weinstein: describing what twister theory is, and of course it's a, it's a bit of a tall order for a podcast, is that you are replacing Einstein space time
Eric Weinstein: with a larger.
Eric Weinstein: Structure that incense, in some sense implies space time, where you can take all the data that roams
Eric Weinstein: around on space-time and the waves, the force, the matter what have you, and you can, as mathematicians might say, pull it upstairs to this larger
Eric Weinstein: twister space where you might have a couple of extra tricks up your sleeve because the extra space that you've created to augment space time with
Eric Weinstein: has this.
Eric Weinstein: Kind of complex number aspect baked into it.
Roger Penrose: Yes. Really, it was something I just to go back for a moment to explain the a T a
Roger Penrose: signature and that's why it was, you sort of come to that in a minute because it's, it's a very interesting story. The way these things sort of come together and take many, many years sometimes for what they come
Roger Penrose: together.
Roger Penrose: But I was really intrigued by these complex numbers and there is. Well something. Let me tell you, it was
Roger Penrose: sort of the origin of the twists or idea. I was struck by the fact that you see, people know that
Roger Penrose: when things travel with a great speed and in, in according to. Einstein special relativity. They get sort of flattened in the
Roger Penrose: direction of motion.
Roger Penrose: Now this is a way of talking about it and you get this Lawrence contraction as it's called now, I was playing around with
Roger Penrose: a relativity and thinking about it was this two two components, spinners and thinking of how the geometry of it worked, and I realized if you think of
Roger Penrose: the sky, you see the sky is is.
Roger Penrose: Where you have vectors in four dimensions. I think of a
Roger Penrose: vector or something which has a, has a, a magnitude in the direction to it as well. And in ordinary three space, you've got this idea of a vector, which is quite
Roger Penrose: common to people know about, but when you're in four dimensions, then you have. Space and time together.
Roger Penrose: But do you have particular vectors
Roger Penrose: which are called on these other ones along the light cones? So these, this is, see an ordinary vector might representative velocity. So you have a particle
Roger Penrose: moving along with a certain speed and you know, four dimensional vector would point along the. Philosophy or the momentum of that particle.
Roger Penrose: So
Eric Weinstein: weirdly
Eric Weinstein: in the space time metric of Einstein. Yeah. These are vectors that are not zero, but if you used Einstein, special rulers and
Eric Weinstein: protractors, what would the length of these
Roger Penrose: vectors.
Eric Weinstein: They wouldn't. So, so it's a really, it's a, it's linguistically tricky to talk about these things because they're
Eric Weinstein: zero things that would be measured to be zero length if that concept of length was in fact.
Eric Weinstein: Um,
Eric Weinstein: yeah. Extended from your normal concept of like,
Roger Penrose: yes. The idea that something of length zero means it's two points. The distance between them is
Roger Penrose: zero. You think of them ran on top of each other, or if the distance is very, very small, they're pretty close to each other. But in the kind of geometry, we'll call it Midkowski geometry, cause although it's
Roger Penrose: describing and science special relativity, the gym geometry was not Einstein.
Roger Penrose: People often say, Oh, well, Einstein introduced this four dimensional space time. That's not
Roger Penrose: true. It was Makowski and I son
Eric Weinstein: said that this is real. This is not just a sort of a weird artifact of the
Eric Weinstein: description of, um, various processes that were being entertained,
Roger Penrose: but it's a kind of geometry and Makowski showed that the, the space of
Roger Penrose: special relativity is really four-dimensional.
Roger Penrose: And it's this kind of geometry in which you can have distances, which is zero. Although the points are sort of long
Roger Penrose: way away from each other, and this represents a light Ray. So you'd have one event say, and then the light through that vent reaches
Roger Penrose: another event. When I say event, I mean not just as special.
Roger Penrose: Position, but at the time as well. So
Eric Weinstein: you mean a position in space, time,
Roger Penrose: space, time. So you
Roger Penrose: need four coordinates, three space in, one time going in. So that's when we call them an event. And so you have a point or an event in space time and managing the
Roger Penrose: particle, moving of the speed of light to another such event.
Roger Penrose: Now the distance between those two in these kind of geometry that bean coffee introduced is zero.
Roger Penrose: So, and he made cos he played around with different kinds of geometry and he realized that special relativity is really best described by this kind of, what
Roger Penrose: we call them in Kowski and geometry. So you can have zero distances, and yet the points are not on top of each other.
Eric Weinstein: So your idea was to take all the
Eric Weinstein: points that are bizarrely zero distance away and then make those the new points in a new space.
Roger Penrose: Well, it wasn't quite that I have, I, I, I had to come up to this
Roger Penrose: slowly because, all right. Yes, but the initial idea isn't so hot to understand reading. You see, if you look out at the sky,
Roger Penrose: what do you see when you're seeing.
Roger Penrose: Light rays, or you're seeing photons coming to your eye, which have traveled with the speed of light. So the world line
Roger Penrose: in four dimensions of that photon is tilted over at what represents the speed of light. Now in this Makowski
Roger Penrose: geometry, that distance has a clear meaning. So let me, let me give that the.
Roger Penrose: Suppose the the photon is emitted at one
Roger Penrose: point when event and received as another event. Now to that photon, the time between well on the other is zero and that time
Roger Penrose: measure is exactly the distance measure. In Minkovski geometry. Suppose the particle was not traveling, the speed of light. Suppose it traveled with half the speed of light or some other speed.
Roger Penrose: Then. It's time. Experience of time is exactly the distance. According to Minkovski is geometry. So you say if it
Roger Penrose: travels with very, very, very great speeds. Suppose you travel to a planet, which is four light years away and you travel with, I won't do the
Roger Penrose: calculation right here, but with half the speed of light, then you would the experience that you would.
Roger Penrose: Of time you experienced is less than the time that somebody here
Roger Penrose: on earth would think that it took you to get there. So as you travel faster, you, your experience of the passage of time slows down. In a sense, you
Roger Penrose: don't think it's as long, and if you actually travel, the speed's blood, that experience would be zero.
Roger Penrose: So this is the experience of the length of time. If you add weight, you could have a very,
Roger Penrose: very good clock you carry with you and you see how, what, how.
Eric Weinstein: How the clock made of pure light. It all gets pretty, pretty heady out here.
Roger Penrose: Well, you don't make another, you can imagine a clock,
Roger Penrose: say a nuclear clock or something, and you're not traveling with the speed of light because you can't get to this.
Roger Penrose: But the time measured by that nuclear clock would be the
Roger Penrose: distance in the cuffs. I
Eric Weinstein: should point out, just for our listeners, this even. People who do this field of a differential geometry morning, noon and night in
Eric Weinstein: math departments almost never choose to work in worlds with some temporal and some spatial dimension because it just, it breaks your head.
Roger Penrose: It's a
Roger Penrose: very difficult, different intuition,
Eric Weinstein: very different
Roger Penrose: intuition. You go back and you think about the puzzles that people had when Einstein introduced his special, and then most particularly general
Roger Penrose: tendency. They find it very puzzling. You can see, look at the arguments, people that
Eric Weinstein: well, we keep using these words like time and length and all of these things that have become,
Eric Weinstein: we, we don't recognize that in that one innocent decision to break off one degree of freedom and treat it differently.
Eric Weinstein: All
Eric Weinstein: of our linguistic intuition goes out without all over again.
Roger Penrose: Yeah. Well, it was a curious experience I had because I was giving a series of lectures, um,
Roger Penrose: and Seattle, it was, these were the Battelle lecture has given him, what was it, the, um. I forget exactly what the dates were. Maybe this
Roger Penrose: roundabout nine 1970 or something like that, and there was a collection of mathematicians in the collection.
Roger Penrose: Physicist John Wheeler and Cecelia were to organize
Roger Penrose: this. It was a very interesting meeting. Well, people from both areas of expertise were brought together and at that time, it's hard to believe now, but at that time, mathematicians
Roger Penrose: and physicists were barely talking to each other. And they got me to give a series of lectures,
Eric Weinstein: and this was before, um, Jim Simons and CN
Eric Weinstein: yang get together and
Roger Penrose: there is a good question.
Roger Penrose: When was the I,
Eric Weinstein: I'm, that was 75. 77
Roger Penrose: was before that. Okay. Wow. New before that.
Roger Penrose: Is that right? I think so, yes. I really have to, my memory is dates.
Eric Weinstein: If I know you're, you're hot on the, on the trail of this, but
Eric Weinstein: just to, to 11 something in Roman at MIT once beautifully said. Um, and he, I don't think he wrote it down.
Eric Weinstein: He said, we used, we didn't
Eric Weinstein: understand. The partnership that was possible between mathematics and physics because we, the physicists used to talk to the analysts and he said, the analysts
Eric Weinstein: either told us things that were absolutely trivial and irrelevant or things that we already had. He said, when we talked to the geometers, we, we started to learn new
Eric Weinstein: things that we'd never considered.
Roger Penrose: Yes, well, it was trust grow very much cross fertilization there, but I was going to say, I gave these lectures that I think it was 12 lectures
Roger Penrose: and I wasted my time on something that you weren't going to until I left myself. Only three lectures to describe. The Singularity's, the
Roger Penrose: black hole idea, which wasn't the term black hole wasn't used as then, but the collapse,
Eric Weinstein: you just called the Schwartz, Jill singulars.
Roger Penrose: Well, it was called a singularity when it, that was the
Roger Penrose: thing, people call it the Schwartz at singularity, where it's what we now call the horizon. Right. And I remember in my third lecture from the end describing
Roger Penrose: the . Basically what, what can we call a black hole that's talking about the Schwab shots and clarity?
Roger Penrose: And I was explaining that the Z, it was basically to do with a zero
Roger Penrose: length business. And, and Steen rod was a very distinguished mathematician. He,
Eric Weinstein: Norman steam.
Roger Penrose: Yeah. And he had written this book on five bundles, which is
Roger Penrose: absolutely impenetrable. Impenetrable, but also fundamental to the subject.
Eric Weinstein: Yes. But it's so impenetrable that I never got to the point.
Roger Penrose: But anyway, he was there at the back of the room and I
Roger Penrose: remember telling him about us, and he was absolutely dumbfounded. They say, here's somebody who's a real expert at this kind of geometry, Manny and geometry, whatever you call it, where you have
Roger Penrose: the notion of. When the distance is a small than the points are close together and here you have is other kinds of geometry and the intuition you need for that geometry
Roger Penrose: was completely foreign.
Roger Penrose: It's the point you were just making
Eric Weinstein: because yeah, we do have this weird way of talking about something that sounds like this. We might call it like non Hausdorff
Eric Weinstein: topology, but it is a Hausdorff typology.
Roger Penrose: Yes,
Eric Weinstein: it's, it's. So the problem is, is it's pulling apart two different notions of the word
Eric Weinstein: close.
Roger Penrose: That's right. Exactly. That's right. Because you think of close means a small distance. Right? So you imagine a little tiny bowl where they distance from that
Eric Weinstein: point is small.
Eric Weinstein: You know, mathematics makes you pay for every attempt to sort of intuitively encode something that isn't precise. We've been discussing the fact that this intuition is
Eric Weinstein: very, very strange and involving how to think about, um, spaces of the type that Einstein and Midkowski and pong Correy were considering.
Eric Weinstein: How does that begin to lead us towards these more speculative ideas of yours surrounding complex numbers and the twister
Eric Weinstein: program? I don't think many people, uh, many, many of them may have heard of it, but even in a, even in mathematics, you have to know that you got, you were sort of seen as leading edge.
Eric Weinstein: Cult. It had its own
Eric Weinstein: newsletter, its own bizarre drawings. It was very difficult to communicate to members of the twister cult because they didn't speak like other people
Roger Penrose: where we had this twist, the newsletter, which
Roger Penrose: was a, it started off by, it's just in handwriting and it was duplicated and then that's not going to that for the
Roger Penrose: moment.
Roger Penrose: Very good. Talk about the base, the origin of twists here. If you're like, where did it come from?
Eric Weinstein: It was really, in fact, your big bet in physics.
Eric Weinstein: Do you think.
Roger Penrose: Yeah, I think so. Well, you see, it's between that and the cosmology, but the cosmology is a bit different because that's not such a wild idea,
Roger Penrose: but it's not a whole body of wild ideas, which twists the theory more is all right.
Roger Penrose: Um, but it has lots of connections with mathematics as pure
Roger Penrose: mathematics and connections with physics. Let, let me describe the basis of it, because I think we've got most of the things we need. You see the light cone.
Roger Penrose: Describes how from a one point to one event in space time, all the different points of zero distance from it or another, it was all the light rays from that point.
Roger Penrose: Now, let me think of it the other way around. That is my past light cone. So I'm sitting at a certain point in space time
Roger Penrose: and I look out at the universe and all the light rays that get to me as a particular instance. Moment of my time come along this
Roger Penrose: past like her. So that's, you mentioned this stretching out into the past and getting bigger and bigger as it goes back in time.
Roger Penrose: And that's
Roger Penrose: all of the events, which are one moment of my time I read, I see those events. So I see a lot of stars in the sky. Now
Roger Penrose: let's suppose that. I mean the stars in the sky look like points. You see, so that you have the sphere, the celestial sphere, which is my field division.
Roger Penrose: If I'm imagining myself out in,
Eric Weinstein: so imagine that the earth was transparent, so you weren't.
Eric Weinstein: That's why my,
Roger Penrose: Oh, let's go out into space. Then I can be looking at the world
Roger Penrose: around me. Now let's imagine that another astronauts comes whizzing past me at nearly the speed of light. And just as we pass each other, he
Roger Penrose: looks, he or she looks out at the sky at the same moment as I do now because of a phenomenon known as aberration.
Roger Penrose: The stars will be
Roger Penrose: slightly. Not in the same place with regard to that astronauts as me. Um, this guy is somewhat
Roger Penrose: distorted, but it's distorted in a very particular way, which is what's called conformal. Uh, two way. Say this in a simple way. Suppose I
Roger Penrose: happened to see a configuration of stars that happened to be on a circle.
Roger Penrose: Suppose they were can cyclic SIS then this astronaut passing by me. We'd also see these
Roger Penrose: in a circle. Even though the transformation would not be a rotation of the spheres, sky would be squashed up more on one end and stretched out at the other end. But the thing about that
Roger Penrose: transformation, it's something which I knew about from my complex analysis days.
Roger Penrose: Do you think of the what's called the remand sphere? This is the.
Roger Penrose: The plane of points is it's the complex plane or the vessel plane or the point play. The points represent the complex numbers.
Roger Penrose: So zero is in the middle if you like, and then you've got one and then you've got minus one and I, and mine is either all on the circle and you go out and
Roger Penrose: infinity is way out to infinity.
Roger Penrose: But the Raymond sphere foes all this up into a sphere. So infinity is not point.
Eric Weinstein: This is a little bit like if you have a. If you have
Eric Weinstein: a caramel coating around an Apple, you're folding that
Roger Penrose: and
Eric Weinstein: at the point where the stick would go into the Apple, all of the.
Eric Weinstein: Boundary of that, a candy would come together.
Roger Penrose: Yes. And it's what's called a Steria graphic projection. You can project from the North pole and all the other points flattening
Roger Penrose: that into the plane.
Eric Weinstein: So you can see all the points on the sphere except for the point from which you're projecting.
Roger Penrose: Exactly. And that's called a stearic graphic projection. And it has this remarkable property that it sends
Roger Penrose: circles to circles, or you could say it's conformal.
Roger Penrose: That is angles preserved. And it's a very beautiful transmit. I used to play around with these things just for fun often.
Roger Penrose: Now the thing is that it transformations of this sphere to itself, which preserve. The angles.
Roger Penrose: It's also transformation, which is what's called analytical column, Hala morphic. It's, it's the most smooth transformation you can have.
Roger Penrose: So
Eric Weinstein: just the analog of smooth, but for complex objects rather than real objects. Real and complex means the types of numbers.
Roger Penrose: Yes, that's right. So
Roger Penrose: it's what smooth is and complex analysis and those transformations which sent the spheres and sphere. Are exactly those in relativity.
Roger Penrose: So the . Different observers passing me at different speeds, looking at the same sky.
Roger Penrose: The map from my sky to their skies is
Roger Penrose: exactly these complex transformations in the sphere. And this actually is what you exactly get when you use two components, spinners, and you see the
Roger Penrose: description when you move from one observer to another is exactly those ones which transformed the sky in this conformal way to itself.
Roger Penrose: And.
Roger Penrose: Often people find this puzzling. I find it puzzling originally because suppose you had a sphere which is whizzing, you know, an alien spaceship, which is a
Roger Penrose: sphere shooting past you at nearly the speed of light. Well, you see the direction of motion. It will be contracted by the Lorenz contraction. So when you look at it, you should see it sort of
Roger Penrose: flattened out.
Roger Penrose: You don't, because the sphere goes a circle. It goes to a circle. If you see it as a circle, when it's not moving, you will still see it as a circle. I'm the boundary of the thing will
Roger Penrose: look like a circle way. It is moving and you work away and think about it. Well, you see where the lightweight is. Go in the front of it and the back of eighth and all that, and you see really, you don't see the flattening.
Roger Penrose: It really is, doesn't look like a, like I said, circle it's boundary. It looks like a circle. So I wrote a paper on this. Almost simultaneously, there was
Roger Penrose: somebody else who had a paper. I'm mainly thinking of the small circles and spheres. Um, but this
Roger Penrose: transformation, that's really what started me off.
Eric Weinstein: If I understand correctly, maybe I don't.
Eric Weinstein: Yeah. Um, we have another mutual acquaintance, uh, or friend
Eric Weinstein: Raul bought, and
Roger Penrose: yes,
Eric Weinstein: he showed us that the world seems to repeat every eight dimensions in a certain way. But during the first cycle of what you might call
Eric Weinstein: bot periodicity from zero to seven or one to eight, depending on how you like to camp, you get these things called low dimensional coincidences.
Eric Weinstein: And
Eric Weinstein: so that they don't. Recur because of your point earlier about spinners that spinners grow exponentially, whereas vectors grow linearly
Eric Weinstein: and, but during the first period where these things are of comparable strength, yes, you've get all of these, um, objects where depending upon, you
Eric Weinstein: defined in two different contexts, you turn out to be the same object you're making use of that.
Eric Weinstein: Here
Roger Penrose: it is that it's the, uh. Well, the Lauren's group
Eric Weinstein: or like you know
Eric Weinstein: that the rotations of space and time, which we might call three are son three double cover would be equal to something else called SL
Eric Weinstein: to see which would mention complex numbers, even though there's no complex numbers to be seen in space and time.
Roger Penrose: Yeah. It depends on that one of those coincidences.
Roger Penrose: Triple coincidence. I think you said they get a cut. Which one is depending upon, and this description, but the point I'm making here
Roger Penrose: is that it has certain sense relativity. It's described when you do it in the two spinner form, which is really expressed in this fact that
Roger Penrose: it's the transformation of the Raymond sphere to itself, which is a complex transformation.
Roger Penrose: This is the most general transformation of the sphere to itself. When
Roger Penrose: you think of that sphere as a Raymond sphere. So it's a complex one dimensional space, you might say, surely it's two dimensional. Well, it's two dimensional in real numbers,
Roger Penrose: but one dimensional in complex numbers, cause they're complex.
Roger Penrose: Each complex numbers carries the information of two real numbers.
Eric Weinstein: So for example, mathematicians would call what most people call
Eric Weinstein: the complex plane. They might call it a complex line.
Roger Penrose: It's complex line. That's
Eric Weinstein: right. Yeah. And so the language, again, is intended to make things very hostile to the newbie.
Roger Penrose: Yes.
Roger Penrose: That's true. But you have to get used to the idea that when you're thinking complex, when you think of it sort of really sort of concretely and in the real terms,
Roger Penrose: that you have to double the number of real dimensions to get the number of complex
Eric Weinstein: lives. I want my audience, but I don't want them to feel stupid for making a mistake that everyone where a person,
Roger Penrose: you have the number of course.
Roger Penrose: So we have the. Complex numbers playing a fundamental role in relativity. That's a really point you want to make, and it's the
Roger Penrose: complex sphere, sorry, the remand sphere, which is this one dimensional in in complex sense, two dimensional in the real sense
Roger Penrose: object, which is fundamental. Now this reman sphere appears in the most basic way in quantum mechanics too.
Roger Penrose: You think of the,
Roger Penrose: the spin now, that's the practically the most direct complex, the most direct quantum mechanical thing. If in a certain sentence where you
Roger Penrose: see quantum mechanics playing a real role as quantum mechanics, which is hard to grasp normally, but you can see it here. The geometry reworks.
Roger Penrose: You see, if you have an object of spin half, that's the smallest non-zero spin.
Roger Penrose: You can have such an electron. So think of an electron. It hasn't been half.
Roger Penrose: Now what that means is that it's basically two States of spin, which people call it spin up and spin down.
Roger Penrose: Well, what does that mean? Right? Hey, put your thumb up like that, right handed spin is where your fingers go, and that's.
Roger Penrose: Spin up means right-hand is about
Roger Penrose: up. Spin down is right-handed, is about Donna has left-handed about that. And those are the two basic States. But what's special about up and down? Nothing. So you think of what
Roger Penrose: about right? Left forwards, backwards, all those are combinations of happened down. And they're complex combinations through these complex numbers,
Roger Penrose: which lie at the basis of quantum mechanics.
Roger Penrose: But here you can see in a visual way what they're doing. You see, you can say up down what's
Roger Penrose: left and right where these are com combinations of up and down. So you add this much of up to that much of down and you get. To the, to the right
Roger Penrose: and you minus it, you get some of that too. At times you get forwards or back, whichever it is, and the complex numbers come in to describe these possible
Roger Penrose: directions of spin.
Roger Penrose: And it's the Raymond sphere again. So. But you were relating these complex numbers of quantum mechanics do the directions in space, so you have a
Roger Penrose: connection between these rather abstract numbers, which are fundamental to quantum against, and the much more concrete picture of directions in
Roger Penrose: space.
Eric Weinstein: But Roger, I think you're both, well, let me be challenging slightly ever so slightly.
Eric Weinstein: Yes. What you're really talking about
Eric Weinstein: is a very important fork in the road for physics. Do you wed yourself to the world that we're actually given? And you know, Mach was
Eric Weinstein: famous for having said this phrase, the world is given only once. And so we happened to know that there does exist a world. That appears to be well modeled by three spatial in one temporal
Eric Weinstein: dimension.
Eric Weinstein: And then the key question is, do you wish to have a more general theory, which it works in all dimensions or work torques for all
Eric Weinstein: different divisions between how many spacial and how many temporal dimensions? And what I see you as having done, which I think is incredibly noble, brave, and scientifically
Eric Weinstein: valid, is to work with mathematics that are really pretty.
Eric Weinstein: Particular Ising themselves to the world we're
Eric Weinstein: given, rather than sort of keeping some kind of, I mean, like you're getting married to the world we live in, in a way that other people are just dating it
Eric Weinstein: and wishing to keep their options open.
Roger Penrose: I think you've hit on a very crucial point. Absolutely right. I mean, for example, with string theory and all that, people talk about.
Roger Penrose: 26 dimensions or 10 special dominion or 11 or 12 and things like that. And sure, the mathematics, we've got mathematics to handle these things,
Roger Penrose: and maybe that's important to the way the world works, but I was never attracted by that for basically two reasons. One was the reason I'm just trying to subscribe here,
Roger Penrose: and it's exactly what you're saying, that I'm looking for a way in which.
Roger Penrose: You find the mathematics to describe the world, which is very
Roger Penrose: particular to the dimensionality we see. So the three space dimensions and one time dimension. Is described in this formalism
Roger Penrose: very directly, and if you're a crunch to try and talk about other numbers of dimensions of space and time, it doesn't work
Eric Weinstein: as much as I really like to stick it to the string theory.
Eric Weinstein: That's not exactly their problem either. Because 26 is really, because it's two more than 24 and 10 is really because it's two more than eight and an eight you have something
Eric Weinstein: special called . Yes. And so what they were really doing was figuring out how to build different theories around different highly
Eric Weinstein: specific targets.
Roger Penrose: But you see there, it's the beauty and the mathematics, which sure is a good guide, but it has to be. Well,
Eric Weinstein: the
Eric Weinstein: reason they never grow up to playing with reality.
Roger Penrose: That's the sort of thing, I mean it's, it's perfectly good to explore all these different things and it's very
Roger Penrose: valuable. But I'm trying to follow a route which is viewed, I think in many quotas is very narrow.
Roger Penrose: I'm looking for a route which is
Roger Penrose: work specifically for the number of space, time, dimensions that we have, and is. If I'm, there are aspects of twisted theory, which do work in other
Roger Penrose: dimensions, but they run out very quickly and you can see analogs of these things, but they kind of
Eric Weinstein: the wrong version of the anthropic principle, which
Eric Weinstein: is that if there weren't a beautiful mathematics to catch you.
Eric Weinstein: I mean in some sense, despite the fact that you're in your late eighties it's like you're stage diving and a punk
Eric Weinstein: concert where you're kind of hope that the mathematics catches you because you're willing to actually marry in a very deep level. The world. That
Eric Weinstein: we do observe, and I find that what, what's very disturbing to me, um, is that the political economy of science means that fewer
Eric Weinstein: people are willing to make strong speculations, strong predictions.
Eric Weinstein: To explore things that don't give them the flexibility in case things that don't work
Eric Weinstein: out to say, um, well, it could be like this. It could be like that. And so in part, I see you as part of a dying breed of people who are willing to
Eric Weinstein: go down with a ship for the privilege of commanding it as its captain.
Roger Penrose: Well, you can use it that way if you like. My claim is that the ship isn't actually sinking. You meant
Eric Weinstein: thinking, no, no, no, I'm not. I'm not claiming that. I think that one of the things that that's happened is has been that yours has been one of the most important idiosyncratic
Eric Weinstein: programs that in fact got a huge.
Eric Weinstein: Lease on life from the fact that it has positive extra now and is because it was absolutely solid mathematics.
Eric Weinstein: It turned out that even if it doesn't give us a fundamental description of the world, it is at least a deep insight into, um, how to transform one
Eric Weinstein: problem into another to allow solutions that wouldn't have been easily gleaned in the, in the original formulation.
Roger Penrose: Yeah.
Eric Weinstein: I'm not saying that it's, it's knocked out of the park for a fundamental
Eric Weinstein: theory, but I, I don't actually know whether, do you believe twisters are a more fundamental description of the world.
Roger Penrose: Well, I do. Yes. I mean, you know, I
Roger Penrose: don't normally say that out loud, but now you've put me in a position. Yes. No, I do think that's
Eric Weinstein: fucking great.
Eric Weinstein: I mean, in other words, it's like you have to say this, I believe in, in general,
Eric Weinstein: people won't
Roger Penrose: say it. I think the thing is that I have been driven in directions. I as just as you're pointing out in directions, which, uh, picking out the
Roger Penrose: particular rather than the general, right. So, sure. You have mathematics, which.
Roger Penrose: One of the huge aims in mathematics is being more and more general.
Roger Penrose: And you mentioned the and that's a beautiful example of that, where it simply generalizes over areas, which you would never thought,
Eric Weinstein: but it also particular eyes.
Eric Weinstein: So for example, yes. It is only in low dimensions where you get to play the game with what are called defamation complexes, where the
Eric Weinstein: first term is the symmetries and the problem.
Eric Weinstein: The second term is the fields are the waves in the problem. And the third term is the equations in the problem. And then you get to cut it off at that
Eric Weinstein: point and have that be this magical concept of an elliptic complex. So, for example, in dimension four, um. We gleaned
Eric Weinstein: something bizarre, which is that there are an infinite number of different ways to do calculus in four dimensional space and only one way to do it in every other dimension.
Roger Penrose: Yes, yes. Well, there's something special there about Fala.
Roger Penrose: Certainly. That's true. And the connections. Maybe not that clear at the moment, but maybe we will see that this
Eric Weinstein: is maybe differentiable structures or part of part of
Eric Weinstein: physics. It's quite possible. How amazing that I'll give you another very bizarre one.
Eric Weinstein: I don't know whether this has ever come up. If you have two sets of symmetries
Eric Weinstein: known as lead groups that act transitively on the same sphere in usual position, then either their
Eric Weinstein: intersection acts transitively on that sphere or the dimension of that sphere is 15 and I believe that the intersection of the groups looks like the electro
Eric Weinstein: strong group.
Eric Weinstein: So it's very close to the particle spectrum of theoretical physics pulled out of nowhere, just from talking about, um, sphere transitive
Eric Weinstein: group and yeah.
Roger Penrose: Well, I, it's clear that one, I mean, in particle physics, I mean, I've never really been somebody who studied particle physics closely.
Eric Weinstein: Is that right? I didn't know.
Roger Penrose: Well, I mean, in general way I have met, but I suppose I felt we may be a long way from really understanding what's going on there. I dunno.
Roger Penrose: I mean, I hope, I hope that it was, well, you know, we have no, it's a complete, I often, I will have different views from these things.
Eric Weinstein: I think we're
Eric Weinstein: almost at the end.
Roger Penrose: Well, that's an interesting thing.
Eric Weinstein: So how do you come to the idea that we may be quite far? I'm
Roger Penrose: not saying that we're necessarily far. I think it's understanding why the groups
Roger Penrose: are the groups that we see. Um, and people have different theories about these.
Eric Weinstein: Let me ask you then, a couple of questions go on.
Eric Weinstein: Very early in this new stagnation post, the standard model. People like, uh, Glashow and George, I and
Eric Weinstein: putty and Salaam put forward these unifying symmetries that remain very odd, um, because they're so
Eric Weinstein: attractive and powerful. The prettiest of them being something called . Spin 10 which physicists persistent calling.
Eric Weinstein: So 10 for reasons that escape me.
Roger Penrose: Yeah. This is the one which doesn't exist or isn't that not that one?
Eric Weinstein: Well, the original SU five which sits inside of
Eric Weinstein: spin 10 was disproven in its most basic form. And at that point, George, I and Glashow had been trained in the previous culture of
Eric Weinstein: physics, which is that you fell on your sword.
Eric Weinstein: When you predicted something and it wasn't true, and I think that they sort of rushed to commit ritual suicide far too quickly.
Roger Penrose: Yeah. I just, um,
Roger Penrose: maybe if I'd worked in the subject, I form a clearer view. It's just that from the outside, I'm not convinced that
Roger Penrose: I'm clearly there. There are things which people have discovered, which are absolutely.
Roger Penrose: Fundamental in particle physics, but somehow
Roger Penrose: it hasn't got to the basic level, which I feel, I can see why these groups are what they are. And so on that, let me not talk about it cause I'm not an expert at that. And I'm only giving you an impression.
Roger Penrose: And I, I suspect that we will be, maybe not too long from now a better understanding.
Roger Penrose: I'm hoping that twister theory might have something to say about it,
Roger Penrose: but at the moment, uh. The area which needs to be explored here hasn't been explored. The things we did at one time, I'm
Roger Penrose: sort of deviating a bit from the general trend, but there was a question of how do we try, try it. How we treat massive particles and twisted theory and
Roger Penrose: naturally twisted theory describes massless things.
Roger Penrose: Uh, things go along the light cone and that sort of thing
Eric Weinstein: because you privileged the light cones. Then the treatment
Eric Weinstein: of particles that were massless. Got it. Privileged tram
Roger Penrose: and privileged treatment and not just that. Do you find transformations? There is
Roger Penrose: a way of representing the maximal equations. This is the thing I was mentioning about the TV program.
Roger Penrose: We're describing the Maxwell equations, which you
Roger Penrose: get out of the truths of theory and it comes directly out the, what about the direct equation? You want to talk about massive particles? Well, the way it seems to lead you,
Roger Penrose: as you think of. The well, you see a massive particle has a momentum that, uh, which is timeline.
Roger Penrose: So it points within the cone.
Roger Penrose: And one way you can describe a timeline. One is think of two, no one, a two light light. Once you think of a zigzag, so it's got a Zig and zag.
Roger Penrose: And that's why I'm convenient way of Jay, where you might have one, which she's made a three zigzag dog, something like that. And you can get the timeline line out of
Eric Weinstein: she, you can build it up from there.
Eric Weinstein: From primitive. That's right.
Roger Penrose: So the argument is that you have a twist of for each of these zigs and zags. And so you might have two of them, you might have three of them,
Roger Penrose: and you see how many of them give you the same. And then you get these groups and twisted theory. And these groups look like the Popsicle.
Roger Penrose: The next group say you've got two, and as you three,
Roger Penrose: and the idea we had is, Oh, well that's the basis for these.
Eric Weinstein: doesn't impress me much because it's ubiquitous, but that's, you three
Eric Weinstein: is a . This is the group that represents the strong force that holds our, uh, yeah.
Eric Weinstein: Well,
Roger Penrose: you see that as a thing that SU
Roger Penrose: three gives you this.
Roger Penrose: Um. Gay, you've engage it. So you have a, um, there is a difference between the and the that
Roger Penrose: the quantum chroma dynamics, if you like, which is the theory which comes from gauging se three is a genuine gauge theory. But when you try and do it for, I see to
Roger Penrose: the left for the electrons and, um,
Eric Weinstein: you,
Roger Penrose: you the gazing, it doesn't really work because you've got a, you've
Roger Penrose: got a special.
Roger Penrose: It's not the full group, so on. So there's something funny about it. Okay. And there are other theories, which might be a more promising way to go. Let's not go into that cause this is all
Roger Penrose: guessing. But the idea is that you could develop a particle physics using many choices
Eric Weinstein: and have it. In other words, if I'm not misunderstanding you,
Eric Weinstein: the idea is that the extra data.
Eric Weinstein: I mean we have a problem in the standard model in that we have effectively a an origin story with two gods.
Eric Weinstein: There's the God of Einstein that gives us space in time. And then there's this other God that gives us SU three cross, SU two quests, you one which give us the non gravitational
Eric Weinstein: forces and all of these particle properties we call quantum numbers.
Eric Weinstein: And this has no connection
Eric Weinstein: to the space
Eric Weinstein: and time data.
Roger Penrose: Well, that's the sort of thing. Yeah. Yeah. It looks as though it's quite separate. I mean, they must be tied up at some stage, but we haven't got to that. But the idea here was to
Roger Penrose: try and do it via to assist. Well, I'm just trying to say that we had, we haven't got very excited about this for awhile, and then it was a long time ago because when people discover
Roger Penrose: charm, I think it was charming and suddenly this didn't fit.
Roger Penrose: And so we gave up, but blah, blah.
Eric Weinstein: And so by charm, you mean the quality of entirely.
Eric Weinstein: Separate versions of the familiar family of matter. So we now think we have three copies of matter where the second two are repeated at higher mask,
Roger Penrose: that sort of thing. Yes. Yeah, that's
Roger Penrose: right. And so people would go, it didn't seem so simple at that point.
Roger Penrose: So, and, and the various things didn't seem to fit so well, but I think we should go back to that
Roger Penrose: from the insights that going from general relativity . I mean, there's a long story which should be probably hard to describe here, but the, uh,
Roger Penrose: construction, she twisted theory, starts off as a theory about space, flat space time.
Eric Weinstein: That's what
Eric Weinstein: bothers me about it.
Roger Penrose: Exactly. And it's what bothered a lot of people. When you see I'm in good company, then. I was
Roger Penrose: at the time at the university of Texas for a year, and this Alfred sheltered, put a lot of people together who were relative generativity
Roger Penrose: experts, hoping that something would come out of it, I guess.
Roger Penrose: And I had an office next to Ingleburn trucking, whom I learnt a lot from,
Roger Penrose: uh. And on the other side, I had an office that was Roy Kerr's office and Ray Sachs was a little way down.
Roger Penrose: And I have to backtrack because the question is where did, where did the theory come from? Now. I had
Roger Penrose: lots and lots of ideas. I was trying to fit together.
Roger Penrose: Part of it is we're trying to combine the Raymond sphere of relativity with the Raymond sphere of quantum mechanics and various
Roger Penrose: other mathematical ideas which come into quantum field theory. And I, they were sort of floating around and I remember drawing a big piece of paper with all these ideas, which were
Roger Penrose: roughly speaking of the nature that the world we see.
Roger Penrose: It's described by real numbers, but sort of hiding behind it is a world of complex numbers and
Roger Penrose: they somehow control this world of real numbers. So the dynamics is somehow controlled. By the way, the complex numbers work, and this was a sort of
Roger Penrose: vague thought I had, and I couldn't think of a picture in which you added.
Roger Penrose: You see space time as four dimensions. And I needed to add
Roger Penrose: basically one more dimension because I wanted to incorporate that idea. Again, this is difficult to describe these things on a sort of popular program, but it
Roger Penrose: was an idea fundamental to quantum field theory. Which has to do with splitting your field amplitudes into positive and negative frequencies.
Roger Penrose: And it's angled birth
Roger Penrose: and impressed upon me that this was very fundamental to quantum field theory. Most people weren't stressing it at that time. And the way to think about this is to think of the reman sphere
Roger Penrose: again, and you have the equator of the Raymond sphere describing the real numbers together with an infinity, and you've got this complex numbers.
Roger Penrose: On
Roger Penrose: one side, one hemisphere, and also now I have this there and the ones which are positive for frequency, which is the fundamental thing for quantum field theory
Roger Penrose: extend into one half. So this to me was a very beautiful way of thinking about it, rather than splitting everything into Fourier components and taking, taking half of them.
Roger Penrose: And that was
Roger Penrose: seen to me,
Eric Weinstein: four degrees of freedom with one extra real degree of
Roger Penrose: freedom. One extra dimension, like the Raymond sphere, going from the to the whole sphere.
Roger Penrose: And I wanted it to divide it into two halves. And that was the picture I wanted. And you tried to do with the space time. It doesn't work was the first space time is four dimensional, and if
Roger Penrose: you complexify it's eight dimensional.
Roger Penrose: That doesn't divide in two. That's just something else. So I, I knew that wasn't right. Okay. Now I was in
Roger Penrose: Austin, Texas. I had friends in Dallas. Now this was the year in which Kennedy was assassinated. And my friends in Dallas where to dinner
Roger Penrose: and it was the next place that Kennedy was to go to and he was going to give a speech and they all got worried because he didn't turn up and they were January
Roger Penrose: quite right to be worried because he'd been shot.
Roger Penrose: And this was a great shock to us all. And so we decided we wanted to calm ourselves down and we went to trip to
Roger Penrose: trip from Austin. Mary was in Dallas where the others were, and we went off in a few costs to San Antonio and maybe to the coast. And this was to
Roger Penrose: try and recover from the shock and coming back.
Roger Penrose: Well, the women folk wanted to gossip and so on. And I was, uh, with pitch to Ashford who isn't nice
Roger Penrose: fellow. And I like him a lot. And Gary in, but he didn't speak much. So all their others wanted to gossip. And I was sort of leftover and we, the two of us went in the car driving
Roger Penrose: back to Austin. And so I had a nice silent drive coming back and I started to think about these
Roger Penrose: constructions that I've a Robinson, he was in Dallas at the time, an English fellow who lived in Dallas, and he constructed the solutions of the Maxwell equations, which had this
Roger Penrose: curious twist to them.
Roger Penrose: And I understood these things and I realized that they were described by, as you talked about the hops map or the
Roger Penrose: Clifford parallels. He's a, you can think of a sphere in four dimensions, three-dimensional sphere, four dimensions, and you have these circles which fill the whole space.
Roger Penrose: No two intersect. And they every two link, beautiful configuration.
Roger Penrose: And I realized that this was the thing that. Geometrically describe the
Roger Penrose: solutions that I've ever had found, and I tried to think about this and I thought, well, okay, these sort of describe,
Roger Penrose: well. The way I've all had to follow the bus and think of it. Think of a light Ray. Yeah. And then you think of all the light rays,
Roger Penrose: which meet that art Ray. So you've got to one light rain, all the other slash racers meet it. And that family of light rays, you can have Maxwell's solutions and maximum cause which
Roger Penrose: point along those rays.
Roger Penrose: So what he did, this was his trick. You move that light right into the complex, so you add a complex number two, the
Eric Weinstein: sort of two extra dimensions.
Roger Penrose: Well, it pushes the light Ray into the complex, and then you can construct this twisting. You don't see the light Ray anymore.
Roger Penrose: It's pushed into the complex, but you still got the complex family of light rays, which meet it in a certain sense.
Roger Penrose: So I try to understand what that looks like. And I thought this is you're, you're
Roger Penrose: pushing something into the complex and you describe it by means of this. Complicated twisting family, right? Race. So in the drive back, I thought, well, let's count the number of
Roger Penrose: dimensions. There are these, as I call them later, Robinson congruences, and I was gratified or Stoffels or whatever the
Roger Penrose: right word is, to find that the number, the number of dimensions of these con.
Roger Penrose: This, my family is right where it was six, six dimensional family. What's the dimension
Roger Penrose: of the family of light rays? Five. So the ones you actually see directly in the light rays, that's the real thing. And the thing which govern me in the
Roger Penrose: mysterious complex world, add one dimension. They can twist right-handed.
Roger Penrose: That's one way. Lefthanded it's the other way. Divisive thing into exactly what I was looking
Roger Penrose: for.
Eric Weinstein: Fantastic. So I got that. And then additionally had this structure of three complex dimensions.
Roger Penrose: Yes, yes. When I went, I had to go back and get hold of my Blackboard and
Roger Penrose: try to wake it up
Eric Weinstein: and I .
Roger Penrose: So it was, it was a complex project of three space.
Roger Penrose: You have these two twisters and I, no,
Roger Penrose: no. Pretty chuffed with myself. Didn't realize what this was. You have a five dimension space. We survives this six. Real dimensional space, which is really a three complex dementia space into two
Roger Penrose: half.
Eric Weinstein: So if I'm understanding you, you would start out off with a seven dimensional sphere.
Eric Weinstein: You take an action by a circle to get, see the
Eric Weinstein: complex project of three space, and then you could further quotient that out by two spheres to get. The four dimensional
Roger Penrose: sphere, right? It's, you have to have a, you
Roger Penrose: can think of it as a sphere and, um,
Eric Weinstein: maybe I'm not seeing it correct.
Roger Penrose: You can't think of it as, as a sphere.
Roger Penrose: And, um,
Eric Weinstein: but you had a
Eric Weinstein: complex projected, yeah.
Roger Penrose: You can think of a seventh sphere.
Eric Weinstein: Let me just tell you what I find fascinating about this story is that you're talking about a. Period,
Eric Weinstein: traveling between two cities where you realize something is the hop vibration.
Roger Penrose: Well, I knew it was a hot five patient, but I hadn't actually thought of it.
Eric Weinstein: You may not know. The following
Eric Weinstein: is adores singer took the work of Jim Simons and, um.
Eric Weinstein: Uh, Frank Yang and on the trip to Oxford where you Michael,
Roger Penrose: where
Eric Weinstein: he said, Oh my God, this is the quaternary ionic rather than the
Eric Weinstein: complex hop vibration. He said it was when he realized that the self dual instant tonic equations were going to be a revolution.
Eric Weinstein: And so it was the exact
Eric Weinstein: moment of the relationship to something is non trivial. In his case as the quote turning ionic rather than the complex hop vibration. So this is almost an exact
Eric Weinstein: parallel between two stories because I've never heard yours before.
Roger Penrose: That's very interesting. It also has relevant direct relevance.
Roger Penrose: Direct. Yes. Because as I think as you were just saying, cause you think of the
Roger Penrose: vector space for which the complex three spaces and of course that's for complex dimensions. And then. That means
Roger Penrose: eight real,
Eric Weinstein: and this is, look, I want to tie this into a bigger thread, which I think is fascinating. I am not a
Eric Weinstein: devotee of string theory, nor am I of loop quantum gravity.
Eric Weinstein: I think that most of what has been said about supersymmetry has been overbearing and
Roger Penrose: wrong. I completely agree with all those things
Roger Penrose: you're saying
Eric Weinstein: and. I think that the intellectual carnage from these adventures in political, in, um,
Eric Weinstein: political economy or public relations or whatever you want to call it, are not being born by the people who benefited from them, but by those who have to clean up after
Roger Penrose: something
Eric Weinstein: to be sad.
Eric Weinstein: Well, you don't have to say it. I can say it because I'm not inside of the university. So now what I would claim is, is that while these people, I think did a tremendous disservice for all of us.
Eric Weinstein: Taking what I consider to be our most accomplished intellectual community in the history of academics, theoretical physics.
Eric Weinstein: It is not the case that these people
Eric Weinstein: did nothing for 45 plus years, but what they did do has never been told properly. So I claimed to you at dinner the other night,
Eric Weinstein: like if you just look at the role of curvature. In our understanding of not only general relativity where it's been for over a
Eric Weinstein: hundred years, but now in particle theory.
Eric Weinstein: So we had a first revolution around the mid 1970s with what's called the Wu yang dictionary, where a
Eric Weinstein: particular geometer who becomes the most successful hedge fund manager in, in human history, meets arguably the most accomplished theoretical physics
Eric Weinstein: physicist. If it's not Weinberg, it might be yang in terms of what has been proven as contributions.
Eric Weinstein: They have an unbelievable.
Eric Weinstein: Uh, interaction, which shows that the classical theory underneath particle physics is as, or more geometric than the theory of Einstein using steam rods,
Eric Weinstein: fiber bundles, and Eris months connections or vector potentials or what have you. Then you have a second revolution. Again involving, so
Eric Weinstein: that was the first one that his singer takes from Stony Brook to
Roger Penrose: Oxford.
Eric Weinstein: Do you have another one, which is the geometric quantization revolution with your colleague
Eric Weinstein: Nick Woodhouse writing the Bible there? Yes. Yes. In which Heisenberg's uncertainty relations. Strangely come out of curvature rather than
Eric Weinstein: there just being some
Roger Penrose: sort of looking in connection to the Bumble.
Eric Weinstein: Well that there's this thing called the pre quantum line bundle where line is against one of these planes.
Eric Weinstein: So
Eric Weinstein: the terminology is all screwed up. Nevertheless, the key point is, is that what we had previously treated as the annoyance of the Heisenberg
Eric Weinstein: uncertainty principle became the beauty. Of a geometric quantum. So now you had the underlying classical theory is geometric.
Eric Weinstein: The underlying quantum theory is now geometric.
Eric Weinstein: And then again with your English group. Uh, particularly Graham
Eric Weinstein: seagulls is a, is a real hero with Michael Latiya, um, pointing the pointing the way. You guys figure out that this weird grab bag that was
Eric Weinstein: called quantum field theory, which is this thing above quantum mechanics that is needed for, if you're going to have particles that change regimes in which the number of particles changes.
Eric Weinstein: Like
Eric Weinstein: something emits a photon unique quantum field theory. You can't do it in quantum mechanics. So that world was a grab bag that made absolutely no effing sense
Eric Weinstein: pedagogically to anybody coming from outside of the discipline and what they taught us. And this is coming from the 1980s on is the quantum field theory
Eric Weinstein: would have been discovered by typology, wrists, and geometers, even if the physical world had never used it, because it was actually a naturally occurring augmentation
Eric Weinstein: of what's called boredom theory, which is an enhancement of what you've previously referred to as comb ology.
Eric Weinstein: So these are three separate revolutions with people that
Eric Weinstein: almost nobody's ever heard of. Like Luis Alvarez Gamay. Um, you know, and, um, Dan Quillan, who I think is the
Eric Weinstein: world's greatest accidental quantum field theorist. For some reason the physics community is still telling us stories about entanglement and about
Eric Weinstein: multi versus, and many worlds.
Eric Weinstein: And this actual thing that happened, which is as gorgeous as anything I've ever seen, has been a revolution that's been.
Eric Weinstein: Plowing through mathematics and physics is covered up because they want to tell a story about quantum gravity, which just doesn't hang together. What the
Eric Weinstein: F?
Roger Penrose: Yeah, well, I think,
Eric Weinstein: first of all, my wildly off,
Roger Penrose: no, I don't think you are.
Roger Penrose: You see. Um, I mean, a lot of these things I,
Roger Penrose: I wish I knew more about you seeing, for example, Quillin theory and so on, which, which, uh, you know, life is too short, but, but, uh, the, these asks comes
Eric Weinstein: out of the a T a singer theory where he, he finds these determinant lines, which are coming out of non-local spectral
Eric Weinstein: information.
Eric Weinstein: And building the basis maybe for pre quantum line bundles in which the functions in that world become the waves that give us the
Eric Weinstein: theory.
Roger Penrose: I think the trouble here, you see mathematics is full of all sorts of beautiful deep theory and. Most
Roger Penrose: of mathematics as it exists now in the sense of what's written in journals and so on has almost no bearing on the physical world.
Roger Penrose: Now, you see, I feel
Roger Penrose: totally convinced, and I think you're expressing something similar, that if you find the right route through this stuff, you will. Really find the key to what we're seeing in
Roger Penrose: the physical world. Now we've found many such keys and general relativity to the Lorencia version of Romanian
Eric Weinstein: semi Romani and her suit of Ramani
Roger Penrose: suit and Romanian geometry.
Roger Penrose: So that's picked up a beautiful area of mathematics intended into, into, into physics.
Roger Penrose: And then in reverse is, has, um. Given a lot back to mathematics and also with quantum
Roger Penrose: quantum theory clearly and quantum few theory, but I think there are things that are hiding there, which are very beautiful mathematics and which will reveal themselves
Roger Penrose: as important in the physics.
Roger Penrose: We haven't got to it
Eric Weinstein: yet. What do you make of the fact that we now have three separate geometries. So
Eric Weinstein: you have Ramani in geometry as the parent of general relativity. You have Eris money in geometry, which is based on sort of these Penrose
Eric Weinstein: stairs coming from fiber bundle theory, which is the parent of the Maxwell classical theory, but also the classical theory that would be underneath the
Eric Weinstein: strong force holding protons together, which want to repel, and the weak force, which causes beta decay.
Eric Weinstein: Yeah. All right. And then you've got this other geometric theory, which is
Eric Weinstein: the geometric quantum, and they're not the same geometry. So for example, the geometry that that Jim
Eric Weinstein: Simons and a CN yang find has this property called gauge symmetry. You have the opportunity for gauge
Eric Weinstein: symmetry in the Einstein theory, but because Einstein.
Eric Weinstein: Takes curvature and uses something called
Eric Weinstein: linear algebra to project all of the curvature information into a smaller subset, killing off something called vial curvature. If you gauge symmetry rise and
Eric Weinstein: then project, it's not the same as projecting and then gauge symmetry rising. So the opportunity to use gauge theory is lost by the specific
Eric Weinstein: genius of minds.
Roger Penrose: Well, you see, there's a good example because he did this amazing thing by producing general relativity, but then in his later years, he tried
Roger Penrose: to develop the theory and these unified field theories, which from a mathematical point of view was not really a very. Listen, not likely to give much new
Roger Penrose: insights, but you know, he was right to think that you should find that unified scheme and so on and bring the, well, he troubled.
Roger Penrose: One trouble is he didn't really, he considered
Roger Penrose: electromagnetism, but the particle physics didn't play much of a role in what he was doing when he
Eric Weinstein: died, before quirks were in. But he never, he was innocent of
Eric Weinstein: SU three and it's various.
Roger Penrose: I think the thing is there's. Huge, beautiful things in mathematics, and
Roger Penrose: we'd like to think, and I like to think that they do have a role in.
Roger Penrose: Fundamental role roles that we've not yet discovered in
Roger Penrose: operating. Whether w w the way the world works is dependent on very deep mathematics. The trouble is that there's so many wrong steps in the sense that.
Roger Penrose: Many beautiful things in mathematics, which are guided in certain directions, which from the point of view of mathematics are great.
Roger Penrose: And they can be generalizing
Roger Penrose: ideas and, and um, revealing all sorts of previously unknown beauties. But the proportion of these which we find has relevance to
Roger Penrose: physics. It's so it's very small at the moment. No, I think that in some ways, maybe the most powerful, the most, I'm
Roger Penrose: sure, I mean complex numbers and the analysis of complex numbers is one example where he wants, does seem to see a role
Roger Penrose: in operating the way the world works, and I'm sure that we will find other things.
Roger Penrose: It's just, there are so many temptations in directions, which are not
Roger Penrose: particularly to do with fear.
Eric Weinstein: But what I don't understand and what I'm absolutely unsympathetic with, is that. We have a lot of people who once
Eric Weinstein: upon a time had a lot of different ideas. Now, most of the ideas at the moment, if we're brutally honest, it, we are so constrained by this point in our story
Eric Weinstein: in theoretical physics that almost every new idea is dead on arrival unless you specifically keep it from predicting things that we don't
Eric Weinstein: see.
Eric Weinstein: Yeah. Yeah. Right. And so what I see is, is that you've got different, and this is a sociological and economic critique, is that you have. A
Eric Weinstein: class of naughty boys who are very badly behaved, who get to make all sorts of, um, claims, talk to the press incessantly
Eric Weinstein: over decades about all the wonderful things they're going to do, which they don't do.
Eric Weinstein: And then you haven't got another group of people whose feet are held to the fire, where the instant they start to
Eric Weinstein: consider something that might, for example, violate a no-go theorem. Uh, they're roundly humiliated. Now, what I see you as having done is to carve out a very
Eric Weinstein: unusual niche. Twister theory is, at a minimum, an incredibly valuable tool for generating
Eric Weinstein: solutions on one space from solutions on another, let's say.
Eric Weinstein: However, it's also somewhat tolerated within the system. It's a
Eric Weinstein: minority point of view. It's a minority community. But it is allowed to play a parallel game to the string world where the string theorists
Eric Weinstein: have lived for years, in my estimation, on externalities. There are lots of positive externalities of having, and I do think that's the smartest community out there.
Eric Weinstein: I do think that in general, they're smarter than the relativists. They're even smarter than most of the geometers. They're in sufferable.
Roger Penrose: Oh, they're very clever people.
Eric Weinstein: Very clever people, and
Eric Weinstein: very insufferable. And the problem with that community is, is that it's actually accomplished a great deal
Eric Weinstein: that isn't of a stringy nature.
Roger Penrose: That's true. That's
Eric Weinstein: true. And I do think that what they've done is they've, instead of quantizing geometry, which is what quantum
Eric Weinstein: gravity was supposed to be, they, it backfired. And they, they had the geometry. Um, geometry is the quantum, and that's the main
Eric Weinstein: legacy of these people is it's an, the, the, the, uh,
Eric Weinstein: No, they, they took off for, uh, for Paris and landed in Tokyo, which is very
Eric Weinstein: impressive as a feat, but it wasn't what they were setting out to
Roger Penrose: do. No, I think basically I agree with that and certainly string theory has had a big influence in various areas of mathematics,
Roger Penrose: but the influence directly in physics has been pretty minimal.
Roger Penrose: I think.
Eric Weinstein: What do you think about the legacy of something like supersymmetry, which is,
Roger Penrose: that's an interesting question, isn't it?
Roger Penrose: Yes. Well, it's very interesting, partly from a personal point of view, because when I first heard about it, and a lot of it was on conformal
Roger Penrose: supersymmetry, right. And I could see there was a lot of connection with Twista theory.
Roger Penrose: The only thing I didn't like was you were led to these algebras, which didn't commute and uh,
Roger Penrose: well, there was the square or something was zero or something, whatever. I mean, they weren't the kind of algebra that you needed and twist a theory. You need a complex
Roger Penrose: analysis. But anyway, I, I went, I visited Zunino.
Roger Penrose: At one point, and I was in verse intrigued, cause I could, this is
Eric Weinstein: half of the duo that came up
Eric Weinstein: with the sort of original, originally original deep. Yes. A supersymmetric model.
Roger Penrose: Absolutely. Yes. And so I thought there's enough connections here. I'd like to understand it better.
Roger Penrose: And yeah, I think I understood a bit more.
Roger Penrose: But one thing I remember particularly, this is a little bit of a side point, but I was talking to him about two components, spinners, and I realized
Roger Penrose: he was somebody who understands it. Understood it perfectly well, and he told me this story. He said he once written the paper in which he used two
Roger Penrose: component spinners and it was worked out very well.
Roger Penrose: A few months later, Abdusalam did the same thing, but using four components mirrors and he
Roger Penrose: said, everybody referred to ABIs allows paper and nobody referred to his paper and he said, well, that from then on he said he vowed never to write a paper using the two spinner
Roger Penrose: formalism, which I thought was pretty ironic, particularly since Dirac himself intriguing that a lot of people in the early days of looking at.
Roger Penrose: Generalizing the Dirac equation for high spins and so on. And there were, you know, Duffin comer, and we're the only, the ones from, I forget what they were all
Roger Penrose: called, different names for all the different spins, and they were all in course and spoke, I remember, and Dereck wrote this, had written this I think earlier, I can't remember the history of which is which,
Roger Penrose: but I think earlier this paper where he did a whole lot using two spinners.
Roger Penrose: I'm direct using two spinners where you see, clearly he knew about them. So as I was concerned, because he
Roger Penrose: had acted on them, but this was much earlier than that. He had this paper in the Royal society describing all the different spins with two spinners, much more clear, a much
Roger Penrose: more general, simple, systematic.
Roger Penrose: And again, nobody seemed to refer to directs paper, which is quite curious because he'd. I mean, there's a huge
Roger Penrose: irony there because he wrote his initial paper using these four spinners and he didn't realize until maybe pointed out by Vanderbilt, and I have no idea where he got it from. He realized that you could write
Roger Penrose: all this in two spinners, and in some ways it was simpler and use this to generalize to all the spins, but for some.
Roger Penrose: Curious reason, nobody or very
Roger Penrose: few people seem to refer to direct paper.
Eric Weinstein: Well, you know about this famous, uh, situation where Fineman found effectively the path integral
Eric Weinstein: formalism in some paper had published in the Soviet union and the fireman, you know, was trembling. I think in the end
Eric Weinstein: as director, you realize when you said that these two things were analogous, that they're in fact proportional and direct said.
Eric Weinstein: Are they,
Roger Penrose: you have to be
Roger Penrose: careful with your right, cause I had to. When I'd first written things in two spinners and I'd written generativity with two spinners, and I found certain things came
Roger Penrose: out very beautifully. And this thing that everybody was worrying about, calling them at that time called the bell Robinson tensor, right?
Roger Penrose: And you could, it's dropped out of use to
Roger Penrose: spinous and the principal Nell directions and all sorts of things. And the thing is, you have this equation, which is the Banky identities written in two spinners. And you
Roger Penrose: can see it's just. The same equation that you write for masters fields, Maxwell's equations.
Roger Penrose: It's the same you Trina, if it had no mass, just to say they're just the same, you have it in a more
Roger Penrose: engine. The more the higher the spin, the more indices, but it's the same equation and you can see it's conformity in variant or the justice.
Eric Weinstein: Part of the problem that you're going to get into with all of these things is I would
Eric Weinstein: venture to argue that even the lowly Biyanki identity, which is at the heart of how Einstein figured out how to do his equations.
Eric Weinstein: Yes. To make sure that, um,
Eric Weinstein: effectively his vectors pointed perpendicular to the orbits of the symmetries that he was considering that we don't really even
Eric Weinstein: understand the things that are given to us for free fully. There's an old paper of Jerry Kasdan, I believe in which he actually reduces the
Eric Weinstein: Bianca identity from much more fundamental principles.
Eric Weinstein: And the same thing is true with the sudden appearance of a version of the calculus due to, um, levy Chivita
Eric Weinstein: from merely choosing, um, rulers and protractors. Yeah, I really. Worry that we never actually grounded these fields properly. I don't know if
Eric Weinstein: you're familiar. I think it's checkoff who said that if a, if a gun is placed above the mantle place, uh, in the first act, it must be fired by seeing
Eric Weinstein: for, well, for example, we have this thing called the torsion tensor.
Eric Weinstein: Oh God. That everybody's introduced to on the first day of Ramani in geometry, and then they.
Eric Weinstein: Properly or encouraged to forget about thereafter. Never really seems to show up in any meaningful way anywhere,
Roger Penrose: man. It's always a puzzle. I know, and I've never
Roger Penrose: quite made up my mind about it. And let's not go into that story that yes, I don't use it or do I once wrote a paper, but
Eric Weinstein: to ask you just in terms of the path
Eric Weinstein: forward, um, it strikes me that what we have learned.
Eric Weinstein: About our physical world
Eric Weinstein: and what comes up in this book is of a very frightening nature that Einstein's equations, when you really understand them through Hilbert's
Eric Weinstein: insight, come from the simplest possible thing we could minimize.
Roger Penrose: Oh yeah.
Eric Weinstein: Oh yes. Same thing for Maxwell's
Eric Weinstein: equations. They spread from the electromagnetism to the weak force into the strong force because it was the simplest possible thing that could be optimized.
Eric Weinstein: The Lagrangian. I'm trying to avoid saying those words,
Roger Penrose: and then there's the
Eric Weinstein: and then . Yes. Third equation
Eric Weinstein: to complete. This triptych is. The equation for matter, which generates all of something calledK theory,
Eric Weinstein: which is absolutely fundamental. So I could make an excellent argument that the three major equations to be supplemented by one for the Higgs field.
Eric Weinstein: Now that we found
Eric Weinstein: it, um. Are the simplest and best possible equations of their type. Not that we've found so far, but provably.
Eric Weinstein: So
Roger Penrose: yeah, I think the trouble with simplicity arguments, which I agree with, is that it's simple in one context and much simpler context.
Roger Penrose: It may be,
Eric Weinstein: but nature is shown such. I mean, the thing that I can't get over is that her taste in mathematics.
Eric Weinstein: You know, I, I've
Eric Weinstein: analogize this to rating a jewelry store with millions of pieces and in under half a minute finding all the best stuff.
Roger Penrose: I wanted to finish a story that you see, which I didn't quite finish. It relates to something you were saying earlier, which I one point. You
Roger Penrose: see, Dereck was at the same college as I was st John's college and Cambridge where I was a fellow.
Roger Penrose: And I happened to be sitting opposite him at one point. And I had been working on
Roger Penrose: these two spinner ways of looking at gender relativity. And so I said to him, I thought, you know, I thought something he might be interested in, could I, would he have opportunities to talk me about it? So .
Roger Penrose: So he reserved a room and I had a little discussion with him, and then I wrote down this equation, which was this wave equation which you, which represents the Banky identities,
Roger Penrose: and I wrote this thing down and direct.
Roger Penrose: I thought he would instantly recognize it because it's basically the same equation that he had in his paper with all
Roger Penrose: these different spins. And he asked me these. I wrote down the question is where does that equation come from? So I said, it comes from the Bianchi
Roger Penrose: identities, and he said, what does it be?
Roger Penrose: Yankee identities.
Eric Weinstein: Holy cow.
Roger Penrose: And I thought, well, he's been writing all these papers and general relativity. He must
Roger Penrose: know perfectly well. The explanation presumably is you simply rediscovered them himself. He just didn't know they were calling the Bianca as entities. I
Roger Penrose: don't know. It's a very curious story,
Eric Weinstein: and this was in the form that the derivative of the curvature in terms of the natural derivative is equal to zero.
Eric Weinstein: That's
Roger Penrose: in vacuum. Say yes, and you take the vial coverture chair, which is all that's left of every curvature, and you write that in spinners
Roger Penrose: and it's a spinner with four indices completely symmetrical. And then when you write the derivative, it's the derivative acting on those four things. In one
Roger Penrose: contraction, the jury has got two indices and you can track one of those, and that's their equation.
Roger Penrose: That's banishes. That's the equation. Same as the maximal equation, the same as you train. Now, if you had one
Roger Penrose: index and no mass, and it's the way I think about these things and the conformal invariance is very crucial. That leaves me to all sorts of ideas that
Roger Penrose: I wouldn't have thought of otherwise. And it was clearly the sort of thing direct with it played with himself because his equation, all the highest equations,
Roger Penrose: although curiously, in his paper, he did the massless case a different way, which I never quite understood why.
Roger Penrose: But anyway, so is there clearly things that he
Roger Penrose: understood completely and somehow maybe never connected? I don't know what it was.
Eric Weinstein: Do you, did you read his 1963 article in
Eric Weinstein: scientific American where he makes a very interesting case against, um, naive application of the scientific method?
Roger Penrose: No, I don't. That's the
Roger Penrose: rec center in Saturday.
Eric Weinstein: Absolutely. And his point
Roger Penrose: should have seen that.
Eric Weinstein: Um, yeah, he makes the point in the case of Schrodinger and he says, Schrodinger would not have been led
Eric Weinstein: into error if he had not been pressed for agreement with experiment because Schrodinger then. Uh, after publishing, there was a period
Eric Weinstein: of time where it wasn't understood that spins somehow entered the picture and complicated the theoretical prediction with its experimental verification.
Eric Weinstein: But I think secretly
Eric Weinstein: he was actually talking about himself where he had introduced the equation. There had to be positively and negatively charged. Particles. And at that time the
Eric Weinstein: electron and the proton were known, but the positron and the anti-proton were not. And so he linked those two. And Heisenberg immediately dinged him and said, wouldn't those be
Eric Weinstein: of the same mass?
Eric Weinstein: And you're obviously making an error. And he didn't stick to his guns or have the courage of his convictions to predict the new particles. And I think that that 1963
Eric Weinstein: paper from scientific American is direct trying to give us a gift from Mount Olympus to say. Stop with the incessant
Eric Weinstein: insistent on the naive scientific method.
Eric Weinstein: Give yourself more room to imagine more room to play, more room to be wrong.
Roger Penrose: I think that's a crucial thing. He said
Roger Penrose: he, that was the thing about Dirac he just didn't want to be wrong. Yeah. He was very worried about saying things that were wrong. And so often he would say
Roger Penrose: nothing rather than anything. So this is a big thing with him, and I think he was disturbed by, yeah, you're right.
Roger Penrose: I mean, he could have predicted instantly,
Eric Weinstein: I think he needed
Eric Weinstein: more freedom and he didn't have it, and he tried to give
Roger Penrose: that fade away. Being too timid. Yes, I should. What I'm impression. Yeah.
Eric Weinstein: Let me ask you a harder question.
Roger Penrose: All
Roger Penrose: right.
Eric Weinstein: Um, because we haven't asked you any hard questions to begin with. Um, you're going to be in your 90s soon
Roger Penrose: if you were to
Roger Penrose: come working.
Eric Weinstein: Yes. If you were to point. To younger people. There seems to be a failure to pass torches that I've
Eric Weinstein: noticed. And you don't seem to be the sort of a person I would imagine to have that problem. Who would you be pointing to?
Roger Penrose: A human being.
Eric Weinstein: Individuals.
Roger Penrose: Ooh, that's a tricky one. I don't, I,
Eric Weinstein: you don't have to poach.
Eric Weinstein: Push anyone down, but who would you, who would you build up an. Who's young and vital, who might be,
Eric Weinstein: you might say, look, if anyone's got the scent, this might be a person to look at.
Roger Penrose: I think I'm not going to take
Eric Weinstein: you up on that one. I'll decline jell declined to
Eric Weinstein: push further.
Roger Penrose: Yes. It's just a, it's not so obvious.
Roger Penrose: I mean, I've certainly had people clearly good and inspirational ways and think
Roger Penrose: of things I'd never thought of. It is. It's hard. It's, I don't know enough people. I think it's probably somebody I don't know. Let me see. Yes.
Eric Weinstein: Do you, um, do you
Eric Weinstein: worry that the glory that is the Oxford, um, school of geometry and physics may not continue.
Eric Weinstein: Without.
Roger Penrose: Do
Roger Penrose: worry a bit about that. Yes. I mean, there was
Eric Weinstein: an unbelievable nucleus of people.
Roger Penrose: Absolutely right. Very rockabilly,
Eric Weinstein: and I worry that the U K doesn't value itself
Eric Weinstein: enough. I think that you guys are so idiosyncratic and so weird and badly behave. I don't know what to call it, but the UK is punched
Eric Weinstein: way above its weight by tolerance, tolerating and encouraging personalities, idiosyncrasies.
Eric Weinstein: That.
Roger Penrose: I think that there, there is a point there. I, I,
Roger Penrose: I wouldn't know how to generalize across countries cause maybe, uh, but I think, I think you're right to some degree there is
Roger Penrose: tolerance of Accenture city, which rich is specifically kind of intense kind of tolerance, which is specifically English or British, I should say.
Roger Penrose: British.
Roger Penrose: I don't know. I, I'm nervous about saying things like that cause you find somebody Springs up somewhere else
Eric Weinstein: or somebody else. Somebody will hate you for it. But quite honestly, what are they going to do? Make you pay with
Eric Weinstein: your career? I don't think it's going to happen.
Roger Penrose: Yeah. But I think, I think, what'd you say about the geometry developed in Oxford is pretty distinctive.
Roger Penrose: Yes.
Roger Penrose: Um, but then the people moved out too. I mean, Michael went back to Cambridge.
Eric Weinstein: Well, that's, well, but the Oxbridge system, I mean, if, if I, I don't, I don't have
Eric Weinstein: to make it so peculiar to Oxford, but you know, even if I think about like a Nigel Hitchen. Um, or a Mason, I guess, has been in
Eric Weinstein: that system.
Roger Penrose: Yes. Not that I grew up a very agro P completely.
Roger Penrose: Yeah.
Eric Weinstein: They very jealous.
Roger Penrose: No doubt about that. Yes. Yeah. But it's, I mean, you're asking me to
Roger Penrose: have big a thing then.
Eric Weinstein: Let me just,
Roger Penrose: yeah. One final thing.
Eric Weinstein: Have you been to the, um, courtyard.
Eric Weinstein: Of the Simon center for geometry and physics at Stony Brook, which is tiled with Penrose tiles.
Roger Penrose: I have not been there. I've seen photographs at the tiling.
Roger Penrose: Yes,
Eric Weinstein: ma'am. Recommend
Eric Weinstein: a pilgrimage. They have a wall there as well. Yes. And the so called iconic wall, which because Jim Simon's made so much money, he was
Eric Weinstein: able to chisel, um, some of the world's most important equations and principles that you and I probably think of as
Eric Weinstein: being the hallmarks of . Of being alive, uh, you know, just contact with these things.
Eric Weinstein: They're actually in a place that can be visited with a key. And I always think about
Eric Weinstein: in a fan, fantastic world, unlocking that wall and seeing whether it's in fact a gateway to something else.
Roger Penrose: Yeah, it was a long time since I've been there and I haven't been there since the
Roger Penrose: war over. Pavings
Eric Weinstein: I recommended, let me ask you one final question to pose out.
Eric Weinstein: Um, we all
Eric Weinstein: worry. When we've gotten this far along, uh, your road to reality, if you will, that we're not going to live to see
Eric Weinstein: the final chapter a completion, that this is a mystery, like none other. That probably in some sense does have an
Eric Weinstein: explanation in it and it kind of end. Is that something that. That occupies you.
Eric Weinstein: I mean, I find you absolutely vital and, and
Eric Weinstein: um, sharp as a tech, but like I, I'm worried about this at age 54. That what if, what if I don't get a chance to see the end? Is that something that animates?
Roger Penrose: So there's a huge amount of
Roger Penrose: chance involved in these things. So it's a gamble, I think, you know, to see a real end til this eye is too remote for that.
Roger Penrose: But on the other hand. Easy. We didn't really discuss where twisted theory is stuck or has stuck for 40
Roger Penrose: years and where I think it's got somewhat unstuck.
Eric Weinstein: You think it will be the answer?
Roger Penrose: Well, I'm not sure how fragile take us. You said that's another question,
Roger Penrose: but the main problem as I saw it in twister theory.
Roger Penrose: It's a sort of rather surprisingly things which worked surprisingly well. And one of these
Roger Penrose: is to construct solutions of the unsigned equations or the Richie flat four dimensional space times, which were completely
Roger Penrose: generic, provided they were anti self deal. Now what that means is you've got a complex solution of AdSense vacuum equations, which.
Roger Penrose: Uh,
Roger Penrose: lefthanded in some sense. Now, why do we want complex solutions anyway? You know, you want the real solutions. When you say, I thought at one point, well, one useful way of thinking about the complex ones
Roger Penrose: as these are wave functions. Cause my functions are naturally complex. So I thought, well this is a wave function, but it's a nonlinear way function.
Roger Penrose: So I call it the non linear
Roger Penrose: graviton and it seemed to be a big step forward and understanding how quantum mechanics and gravity fits in together. But it got stuck. It got stuck with what I call the googly
Roger Penrose: problem. Now you have to, if you're not a member of the former British empire, you probably won't know what a googly is.
Roger Penrose: It's a, it's a bowl both in the game of
Roger Penrose: cricket. You see in cricket, unlike baseball, you'd like to spin the ball about its axis, the direction it spins about the direction, which it's moving, cause it
Roger Penrose: bounces. And that's a key thing. So it bounces one way or the other. And to make it spin lefthanded. Is has a certain action with your hand.
Roger Penrose: And there's a
Roger Penrose: clever thing that people do who are really good at this, who can looks as though they're using the same action, but it's very cleverly done that the ball spins the other way, and you throw occasional
Roger Penrose: one of these in and it gets the batsman completely bamboozled. And that's called a Googley.
Roger Penrose: So using the same action, the spins, the ball lefthanded, you spin it
Roger Penrose: right-handed. So I use that term because he's very an apt. You have the frame, the twist of framework, which naturally gives you the left-handed Gravitt. Tom, make it do the
Roger Penrose: right hand one. And I struggled and struggled and struggled and have all sorts of wild ideas for how to do this.
Roger Penrose: And I came up with one, which I was very proud
Roger Penrose: of, but it needed a cosmological constant to be zero. And so I thought there is no cosmological constant. And then I had a discussion with Jerry Ostreicher, who was a
Roger Penrose: very distinguished, uh, astrophysicist, and I was talking about the observations that there seem to be a
Roger Penrose: It's
Roger Penrose: exponential expansion of the universe, which seemed to indicate the presence of a positive, cosmological constant. So I said, well, you know, surely that's not really there. It's dust
Roger Penrose: or something. And he looked at me, he said, that's not the point. There are so many things in cosmology. Which works so much better if you put this customer logical constant in.
Roger Penrose: So I had to retract my view. I threw out my construction, but it took me many years to see when you have a cosmological constant, you could do
Roger Penrose: something that didn't work without it, and this enables you to have it. Construction, which I think solves this googly problem. The trouble is, from my point of view, it
Roger Penrose: translates into algebra rather than geometry.
Roger Penrose: Oh, there you can get back to geometry by thinking of it as a connection on the bundle. So that is a geometrical thing. It isn't a thick connection. And then you
Roger Penrose: talk about this algebra, and then instead of patching spaces together to make a Cove manifold, you patch the algebras together. Then they have to be non-competitive.
Roger Penrose: The point that made clear to me by
Roger Penrose: Michael a T at one point, and this is the proposal, you just construct me the algebras and they are connections on bundles and this enables you, at least
Roger Penrose: in principle, to find a generic solution of the Einstein vacuum equations with cosmological cancer. When I say find it's,
Eric Weinstein: you need it, what would
Eric Weinstein: be called an Einstein manifold?
Eric Weinstein: The Ricci scaler shots then did none zero.
Roger Penrose: Constantly nonzero. That's right. That's right. Exactly what people call Einstein space. But this is
Roger Penrose: Lorencia. They're not positive. Definitely, but it's not a construction event that you should write in this for. I mean, Don, it's, you construct this algebra and then you've look
Roger Penrose: for sub algebras and the algebra, and that's not the thing I'm good at doing, but still it needs
Eric Weinstein: to be collaborated.
Roger Penrose: Oh, absolutely. And I got distracted
Roger Penrose: by cosmology and other things, and
Eric Weinstein: stay away from that consciousness stuff. It'll suck all your time.
Roger Penrose: Well, that is a problem actually. Yeah. But you see other people are
Roger Penrose: doing that. I'm not really doing that. They get me to give lectures on it, and I give the same old lecture, which I've given many, many.
Eric Weinstein: I have to say that if, if, uh, if you
Eric Weinstein: stick with what you've. What you've done in physics. Um, and keep trying to push that ball forward. I can't imagine a better use of your time. Um, you are invited
Eric Weinstein: anytime you want to come back and return to this program. This has been an extremely heavy load for our listeners.
Eric Weinstein: No, we don't apol. We don't apologize for
Eric Weinstein: that week. We have to start doing something different because people are hungry to know what does it actually sound like to hear people talking about where things are rather than some spoonfed prettified
Eric Weinstein: version that's like preach huge as if it were baby food.
Eric Weinstein: I don't think they want that anymore.
Roger Penrose: No, I, I agree. And I think even if you don't understand all the things that
Roger Penrose: they get, some feeling from some of the things people are trying to do is, is really important. We as important as the details or perhaps more
Eric Weinstein: part of it is just respecting our listeners.
Eric Weinstein: They know that we don't know how to get this to them in exactly the right way.
Eric Weinstein: And so I think we have the best listenership of any program out there because they've been habituated to recognize that not every
Eric Weinstein: program, and not every sentence is going to make sense. So Roger, um, thank you for coming through. We'll come back anytime and we'd love to continue the conversation about
Eric Weinstein: twisters or anything else you'd like to talk
Roger Penrose: about.
Roger Penrose: I've really enjoyed it. Thank you very much. Yes.
Eric Weinstein: All right. You've been through the portal with the surger Penrose. Hope you've enjoyed it. Please subscribe to
Eric Weinstein: us wherever you listen to podcasts. And if you are the sort of person who've used podcasts, navigate over to our YouTube channel, make sure that you subscribe and click the bell so you'll
Eric Weinstein: be, uh, informed the next time our next episode drops.
Roger Penrose: Be well.