The Portal podcast transcription series
- Peter Thiel
- What is The Portal?
- Werner Herzog
- Timur Kuran
- Rabbi David Wolpe
- Jocko Willink
- Bret Easton Ellis
- Andrew Yang
- Bryan Callen
- Julie Lindahl
- Sam Harris
- Vitalik Buterin
- Garry Kasparov
- London Tsai
- Garrett Lisi
- Tyler Cowen
- Anna Khachiyan
- Eric Weinstein – State of the Portal 2020
- Bret Weinstein
- Sir Roger Penrose
- Ashley Mathews (Riley Reid)
- Ben Greenfield
- Agnes Callard
- Kai Lenny
- The Construct: Jeffrey Epstein
Geometric Unity – a First Look
- James O’Keefe
- Daniel Schmachtenberger
- Eric Lewis
- Jamie Metzl
- Ross Douthat
- Ryan Holiday
The following transcript was generated by a machine and not edited by any human – so it’s full of of errors. I’m posting the transcript because the podcast is excellent and a crappy transcript is better than no transcript. Questions/comments: get me on Twitter @mgmobrien.
Eric Weinstein 0:00
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 Brett’s evolutionary prediction from first principles of elongated telomeres and laboratory rodents. I think it’s a significant enough episode and we’ve had so much feedback around it. Before we continue any kind of line of thinking surrounding that episode, we’ll wait for my brother and his wife Heather hiking, to return from the Amazon where they’re currently incommunicado. So thanks for all the feedback it’s been very interesting to process. The second piece of housekeeping surrounds today’s episode with Roger Penrose. Now I know what I’m supposed to do. I’m supposed to talk about quantum 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 back to his earliest work on singularities and general relativity with Stephen Hawking. What I instead want to do is to remind you what Roger is in fact famous for he’s one have the greatest geometric physicists now living. He’s perhaps the best descendant of Albert Einstein, currently still working in theoretical physics in this particular line of thought. I also think he’s a great example of what the UK does well, he has a very idiosyncratic approach to trying to solve the deepest problems in theoretical physics 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, you try to remember that 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’re being 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, you’re not going to get all of the waves. And in 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 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 understand each other. 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 chewed and spoon fed. Hope you enjoy it. Without further ado, sir Roger Penrose. 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. Hello. Good to be here. Good to have you. I’m extremely excited about having you here. There are lots of questions that you typically get asked these days, many of them about consciousness, some of them about art objects that come out of your thinking, but I know you in a professional capacity has one of the most important people at the nexus of geometry. 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 Leonard Cohen, quote, where from a song called the future where he says, You don’t know me from the wind, you never will you never did. But I’m the little Jew that wrote the Bible. And I have what I consider 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 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. And I think what I want to do is to introduce you to our audience, which has been habituated over perhaps 16 or so interviews, not to expect to understand everything 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 combination of allowing them to look up things In their own free time, if your game Shall we talk about the road to reality you can talk about that should be great. So, where, where are we, in the history of coming to understand what this places in which we find ourselves? What we are made out of? And what we know about our own context?
Roger Penrose 4:22
It’s a very tough question that I mean, when I wrote that book, it was more or less the state of the world at the time. I now feel I should rewrite part of it because things have changed. In one important way, in particular, as far as I’m concerned, whether other people agree with me is another question. But I don’t think I’m going to rewrite it because it was such an effort. And I don’t think I would be likely to live long enough to do a good job of it
Eric Weinstein 4:52
has that much really changed since you wrote the book, a lot of Level A
Roger Penrose 4:56
lot has not changed. The thing that has changed in my view, you see Whether people agree with me on this as another question is to do with cosmology. Right? You see, I have a proposal, which I didn’t have. I mean, it’s new since the book. It’s not all that new because it’s about 15 years old. But it’s new since I wrote that book
Eric Weinstein 5:16
in our time scales. That’s quite new. Now, that’s pretty new. Let’s just just to get some context. You were born in the early 1930s. You won. Yes. Okay, you, you got a chance to live through, if not the original general relativistic and quantum revolutions, their consequences. In particular, you were able to take classes from people like Paul Dirac, who scarcely seems like a human being sometimes more like a god.
Roger Penrose 5:48
Oh, yeah, that was an experience. Yes.
When I when I was at Cambridge as a graduate student, so I did my undergraduate work at London University. University College. And then I went to Cambridge graduate student and I went to do algebraic geometry. So I wasn’t trying to do physics at all. And I, I encountered a friend of my brothers Dennis Sharma when I think I was at University College as an undergraduate, and he given a series of talks on cosmology where it started 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. Where the galaxies the universe expands and expands and expands. But it doesn’t doesn’t change because all the time there is new matter created hydrogen, and the universe expands and then you get new material and it keeps replenishing what what’s got lost? And I thought it was quite interesting. breathing. I mean, I, Dennis was a great fan of this model. And so I was really taken by it. So that
well, the story was that I was in Cambridge,
visiting my brother, my older brother, Oliver, who did statistical mechanics. And he was actually much more precocious than I was. He was two years ahead. And he was, I think, finishing his research there. But 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 expanded away, expanding away and then when they reach 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 this. And I thought, well, they would, they would fade gradually fade, but they wouldn’t just disappear. And when I visited Cambridge, visiting my brother and we were at this Kingswood restaurant in Cambridge, And I said to my brother, I said, Well, look, I don’t understand what Fred was saying. He doesn’t sort of make sense to me. And he said, Well, I 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. And that was Dennis Sharma. And so I explained this problem 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 was that when I did come up to do graduate work in general in algebraic geometry, Dennis decided to take me under his wing, and try to persuade me to change my subjects and do cosmology. We’re
Eric Weinstein 8:43
simultaneously under the great geometer Hodge, as well as Dennis shum.
Roger Penrose 8:49
Well, Hodge was my supervisor. See, Dennis was just a friend. I see how she was my supervisor originally until he threw me out and taught became my supervisor. That’s another little story.
Eric Weinstein 9:04
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Roger Penrose 11:06
Dennis just wanted to get me interested, do working cosmology this was it. I never, you wanted me to change my subject. I learned an awful lot from Dennis about physics, because Dennis sort of knew everything and everybody. And he had a real knack of getting if he thought two people should meet each other. He got made sure they did meet each other. In one case, it was Stephen Hawking. But Dennis was actually I when you mentioned Iraq, Dennis was actually the last graduate with at the time he was the only graduate student of directs.
Eric Weinstein 11:47
Is that right?
Roger Penrose 11:48
Yes. Then this was was direct direct
Eric Weinstein 11:50
was famously sort of difficult. I think that you know, in recent years, this book came out of Graham Formella the strangest man that puts directs
Roger Penrose 12:03
difficult to get to know. But there’s a bit of an irony here. I mean, suddenly, it was hard for physicists and so on, to get to know him. Now there were two people.
Eric Weinstein 12:15
And actually, maybe if I could just say one thing to our listeners, yes. in my estimation, if not yours, direct would be neck and neck with Einstein for the greatest of 20th century physicists.
Roger Penrose 12:27
I think I wouldn’t be far off at that description.
Eric Weinstein 12:31
For some reason, his press wasn’t nearly as good maybe because of his hair. I don’t know. Well, he didn’t talk much. This is one of the problems. No, I agree. I think he was. I mean, you think about all the quantum mechanics, people who develop that amazing subject, and durack was really the one who put it all in order and so on is is and this gets to a very odd issue, which is that you have wielded taste and beauty as a weapon. Your entire Life your drawings are among the most compelling. I remember the first time. One of the things I’ve done using our friend Joe Rogan’s program is to push out discussion of the Hopf fibration. Because it’s the only non trivial principle bundle that can be visually seen. And 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 13:29
yes, well, they they have vibration, or the cliff, in parallels was instrumental in the subject of Twister theory.
Eric Weinstein 13:37
Well, but the first time I ever saw a diagram, it was somebody reproducing a diagram they had seen of yours. And so yeah, the way in which you have used art and sketches. Yeah, but
Roger Penrose 13:48
yeah, it was drawn by hand. Largely. I mean, there were, I think, some circles involved which I use a compass for. The basically I drink my hand. There were two versions of it. The first one was more I sort of threaded The first one was had more circles in it, and I thought I’d draw the most simply the second version, but actually, I had three versions. The third version is in the
road to reality, but
I’m not sure it’s the best. I think the second version perhaps is the best.
Eric Weinstein 14:23
So so darracq getting back to it had this elegance of mind. That was unrelenting. Yes. And he famously brought in these bizarre objects with which some of us are obsessed. Others of us don’t understand the obsession called spinners, which is sort of a prerequisite to getting to Twister theory, which you’ve popularized,
Roger Penrose 14:47
well, sort when I went to the sea direct gave a course of lectures in quantum mechanics. And the first course was sort of basic quantum mechanics 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. In the second course, he deviated from his normal course of lectures. Now, I understood when I talked to Graham farmer who wrote this biography of Dirac. I understand from grandfather that when I described that direct deviated from his normal course to give two or three lectures on two components spinners, which for me were absolutely what I needed.
Eric Weinstein 15:41
You see, I learned from my work on algebraic geometry geometry, which ended up by trying to understand tensor systems as ABS abstract systems and things which you can’t represent in terms of I should just say that in terms of these two components, spinners, you’re talking for the lay audience All of the matter that they think about whether it’s in bound up in electrons or the quarks that make up protons and neutrons, if you think of these things 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 they’re the medium would be a medium of spinners, which is not something that’s easy for people to understand.
Roger Penrose 16:23
Yeah, well, it’s they’re not. And certainly the formulism. If you Dennis, I told him I need to understand about spinners and particularly to the simplest ones are these two components spinners. And he suggested I read this book by corson. So I got the book by course. And I found it completely incomprehensible. Just, I mean, it was fascinating book because it was very comprehensive and described all these different spins, fields and different things like that. And using a lot of two components, minutes, which is the right way to do it, but to introduce what the objects were was almost incomprehensible I found, mainly because you have these translation symbols all over the place, and they mess up the appearance of the formula. So I just found this thing very complicated and incomprehensible. But then I went to directs. 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 it was when I was a research fellow rather than I was a graduate student I can’t quite remember, I think must have 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 deviated from his normal course, in one week to talk about two components, minutes and fame. For me this was exactly what I needed. It made the whole subject clear from this complete confusion that I had before. Now then, you see many years later, I talked to grandpa Pamela and I told him this story. And he said that’s very strange. Durang would never deviate from his course he just he thought when he got his course perfect, it was perfect he would never change. And this was true of his first yeah course. The shorter the initial course, which I went to which people often said to me well that’s not such a great course it’s exactly like his book but hadn’t read his book. So to me this was sure the book is amazing too. But not having read the book I found this course absolutely stunning and it made things up do you think direct actually understand Understood? These objects these most mysterious competitive spinners
Eric Weinstein 18:44
spinners in general? I mean, he brought them into physics they’d been previously found inside of mathematics, I think by people like killing and Lee I’m not sure yet but Katana car 10% perhaps. I don’t think I mean, let me throw out a really dangerous idea. 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. But that is, you know, I asked you before, but like your favorite film you said 2001. You could make an argument that spinners are in mathematics and physics, like the monolith, 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 19:29
Well, I always like to think of things geometrically. And least for the two component ones. You see, when you go up to high dimensions, you still have spinners. But the spinners, the dimension of the spinners goes up exponentially. So each time you add the two to the dimension of the space, and the dimension spinners, this multiplied by two.
Eric Weinstein 19:51
So think I mentioned 2d, for example, you’d get spinners of dimension, two to the D over two.
Roger Penrose 19:58
That’s the sort of thing that’s right. So they were the usually ones talks about the direct spinners, which are the for the for
Eric Weinstein 20:06
the false mean, right?
Roger Penrose 20:08
But they split into these two, two and two even dimensions. Yes, that’s right. And even dimensions. And I like to understand these things geometrically. So you could see what the two components been represented, I had this picture of a, of a flag. So you have the flagpole goes along the light cone. So that’s a,
Eric Weinstein 20:29
that’s the vector like piece of it, it’s a vector. And then you have an extra piece of date an extra piece, which is this flag plane.
Roger Penrose 20:37
And you get a pretty good geometrical understanding. The one little catch to it is that if you rotate it through, hundred 300 360 degrees, so you might think, just to where it started. It’s not the same as it was before it’s it’s changed that sign and then you rotate it again.
Eric Weinstein 20:58
So that won’t make any sense to anyone. But if I mean one way of looking at that is if you have a Klein bottle yeah for those of some people will be listening to this an audio so I’m watching a video, Klein bottle in a certain sense that can be made precise has a square root, that would be a Taurus that is a double cover. So it seems like a very weird thing to take a square root of a strange topological Mobius like object. There you are. Yeah, so it’s really the square root of the rotations that has this double effect. But we say it linguistically in a way that makes it almost impossible for anyone to understand. I
Roger Penrose 21:35
think this was a mystery. I mean, I understood that spinner was the square 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 became clear and he made he gave this very impressive illustration, which I thought was due to direct I learnt later it was just a human bio. Huh Did you imagine a cone can count space like that circular cross section, and another equal cone, which rolls on it. So one is fixed, and the other one rolls round on it. Now you see when you imagine initially the cone is almost just a little spike, you got a tiny circle at the end. And when you roll 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 round twice, because it’s 720 degrees around, okay? Now, when you imagine gradually increasing the angle, the semi angle of the cone, and you do it again, you keep thinking about motion until it becomes almost flat. And then what’s the other ones just a little wobble? Right, when it becomes flat, this motion goes to nothing. So this illustrates how a rotation through four pi right to complete rotations. Gradually can be deformed into no rotation at all.
However, with a single rotation, it doesn’t disappear. Well, I
Eric Weinstein 23:07
think with a with a pulley system in a 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, right? Yeah, the problem comes when that that’s not the generic case, the generic case is usually encountered one dimension higher three and up has a familiar because something called the fundamental group structure, you name it to rally the Z in dimension two. So there is something where in the place where you can see this most easily, it’s slightly misleading. And then, in higher dimensions, you have to learn how to tutor your intuition, which is this problem that all of us who try to think about higher dimensional objects encounters that we have to use the visual cortex were handed and then we have to trick it into imagining worlds beyond where we’ve seen portal welcomes back returning sponsor Athletic Greens, who knows we all seem to have two friends. One friend is bragging about perfect nutrition coming from popping a regime of between 12 to 14 different pills every day. The other is spending an inordinate amount of time either shopping for food or in the kitchen trying to eat their way to a perfect diet. Only problem is it can’t be done. So what’s the answer? Well, Athletic Greens has the ultimate daily All In One Health drink with 75 vitamins and minerals including prebiotics, probiotics, digestive enzymes, adaptogen, superfoods and more. Now what they do is they give you packets and you can dissolve these packets in water to come up with a delicious solution to your complete nutritional needs. So whether you’re taking steps towards a healthier lifestyle, or you’re an athlete pushing for better performance, Athletic Greens takes the guesswork out of everyday good health. Why not just try it jump over to Athletic Greens comm slash portal and claim our special offer today that’s 20 free travel packets valued at $79 with Your first purchase that’s Athletic Greens comm slash portal, you’ll be glad you did. The portal is pleased to welcome back returning sponsor Skillshare. They’ve got a website with lots of instructional classes taught through high quality videos, you can find almost everything there. But I want to talk about something that leaves most self teachers feeling very uncomfortable. We brag about self teaching, but in fact, the personal experience of it is often one of humiliation when we’re starting off in a new subject. So instead of taking something that I feel comfortable with, I went straight to what makes me feel uncomfortable. That is, I don’t know anything about hip hop music production. I chose a course in trap music production taught by k theory, because the instructional videos showed me how they use a computer where I would normally use instruments in order to produce a great sounding track. I was very pleased with the experience and in fact Skillshare is incredibly affordable because an annual subscription is less than $10 a month. So Skillshare will allow you to explore your creativity if you go to Skillshare comm slash portal you’ll get two free months of premium membership. That’s two whole months of unlimited access to Thousands of classes for free. So get started and joined today by heading to Skillshare comm slash portal that’s Skillshare comm slash portal.
Unknown Speaker 26:08
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Roger Penrose 26:13
But you see direct had another thing.
There’s a thing called the direct scissors problem. Hmm. So you imagine the chair with which has the pieces of wood going out like this? Yeah. And you have a pair of scissors. I think this is direct joke that it was a pair of scissors and through the, the way you put your fingers, you have a piece of string which goes through this and then goes around the chair and then comes back through the other one goes back again. Right. Now the problem is you take the scissors, and you rotate them through 360 360 degrees and the strings all tangled up. You can’t And whatever you do, you can’t untangle it. You’re allowed to move the scissors around parallel, not rotate them, and you can move the string around it and you can undo it, but you do twice. 300 words. For 720 degrees to complete rotations, and then you find you can untangle it. So this was the direct scissors problem. And I think the joke was it’s a pair of scissors. So if you get so frustrated you just and he wrote a paper explaining that, I think max Neumann yeah wrote a paper, Dirac did this illustration how you can undo it when it’s minutes, right, four pi, feminine treasuries to prove that you couldn’t do it with this is I think you
Eric Weinstein 27:32
Okay, well, Max Newman. Have you seen this video called air on the Dirac string which illustrates this in video for haven’t seen that I would highly recommend it because it shows this off as the similarity to the belt trick. The 15 wineglass Yeah, well, there’s all different versions.
Unknown Speaker 27:48
I find I could do that one actually.
Eric Weinstein 27:50
I had Joe Rogan try it and I think he got almost all the way around.
Roger Penrose 27:54
Yeah, I’ve done it with a glass. Yes. Yes, you could like that and it comes back Very stylish. Yes, you’re going to complete rotations in the rotation. Yes.
Eric Weinstein 28:06
So this is a very fundamental property of the world that is somehow not discussed. I think. I find it very interesting that people want to talk to me about the multiverse. Sometimes they want to talk to me about quantum Measurement Problem. But 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 of the vectors. It’s the square root of the the algebra generated by the vectors that really the the spinners are this exterior Clifford algebra. Oh, yeah, this object has fascinated me my entire life. And it’s very strange that all of you know the stability of matter and matters strange properties with electron shells are all coming out of this. Weird not that it appears everywhere in the universe. And it’s not universally known that it’s even there.
Roger Penrose 28:57
Yeah, I suppose the difference between the fermions and the bozos So the particles which have a spin, which is half an odd number, right, which which have this curious property that you rotate them, and they get back to manage themselves, and it’s crucial for for matter, because the Paoli exclusion principle depends on the the family statistics which is to do with the exact
Eric Weinstein 29:26
property. So without this not adness in the scissor trick or whatever you want to call it, we wouldn’t have a periodic table and chemical elements,
Roger Penrose 29:34
you wouldn’t have anything we’d have anything you wouldn’t have it you wouldn’t have fermions In other words, you wouldn’t have things which have an exclusion principle. So, and the bosons which are the opposite they they like to be on. If you have two bosons in you can have them in the same segment rather like to be in the sense that so you get these things called Bose Einstein condensates where you get the very cool they all flock together into the same time. But for the fans, 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. So you get to the family principle.
Eric Weinstein 30:10
So you have this strange thing called the spin statistics theorem. Yes, that says that if things have not adness of a particular kind than they either are highly 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 objects quantum mechanically, and you’ve, of course, thought a great deal of quantum theory. We have two totally different prescriptions for how to make these different objects quantum mechanical, but there’s a one to one correspondence between these two, utterly different treatments that matter in force, get quantum mechanically, it’s the
Roger Penrose 30:53
darndest thing. When you get these two kinds of political are two kinds of atoms, bosons and the I’m aeons, and it has to do with the make a complete rotation. Do they come back to themselves? Or do they come back to minus? And so
Eric Weinstein 31:07
that’s the topological. Yeah. But then there’s this whole layout right, go under ocean Barisan integration, which is no integration at all. I mean, you’re effectively almost lying about what you’re doing to the fermions. Yes, and make them look like bosons. And yet, what we what we seem to get out of this is that, nobody. I don’t think anyone could have anticipated that there would be a dictionary of two totally different structures, which are seems to be almost word for word,
Roger Penrose 31:41
because they’re not totally different in the sense that you take two family on system and you go to both zones, so they have the same length. Yes, that’s right.
Eric Weinstein 31:52
Now, yeah, maybe I could ask you a little bit about that. So I want to get to supersymmetry. But before Do I sit? Yes. Okay, go on. We’re gonna make you work this morning, sir. I can understand that. Yeah. So here’s my question, am I correct that you’ve lived through two errors, an era of fairly rapid development in testable, fundamental physics. Coming from theory. I’ve tried to be very careful about setting that up. So I don’t walk into a trap and a stagnant theory era, in which theoretical predictions coming at the level of fundamental theory have not been rapidly confirmed by experiment. Thinking things like string theory, I’m thinking about a regime before the early 70s and a regime following the earliest supersymmetry. Is that what you meant? Well, it could be grand unified theory supersymmetry, Technicolor asymptotic safety. It could be any one of a number of speculative theories from loop quantum gravity, Reggie calculus. extremely serious. Sure, sure. It’s like a kitchen sink. We’ve tried a million different things that don’t.
Roger Penrose 33:16
It didn’t really pan out.
Eric Weinstein 33:17
Well, it seems like well, if you’ll permit an American metaphor. 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, you know, they’re at home plate.
Roger Penrose 33:32
Well, you see might be wrong playing the wrong game. That’s the trouble
Eric Weinstein 33:35
you think rounders would do?
Roger Penrose 33:38
Well, I mean, there’s a lot of intriguing ideas. You mentioned, basically, I think you were hinting it. supersymmetry is one of them.
Eric Weinstein 33:48
maybe I’ve thrown off close to 10. I probably could do it pretty easily.
Roger Penrose 33:52
But I guess you hadn’t. There’s nothing new about that. They were the people we’re playing around with. Not something I’m Kelvin. With the idea that knots might be
Eric Weinstein 34:03
at the basis of particle identity.
Roger Penrose 34:06
Yeah, I mean, these ideas come back again in a different form. But certainly in the, I guess, the 19th century people were playing with. Well, I guess you can go back further than that. phlogiston.
Eric Weinstein 34:20
Well, that’s true. But I would say that Maxwell was the first great condensation of theoretical ideas where an enormous amount of theory surrounding magnetism, electricity, visible light, invisible light, that was a huge, huge revolution that all of those things now can be unpacked from a single geometric equation. That’s the thing I mean, people know about Galileo and
Roger Penrose 34:51
Newton, know about Kepler,
know about Einstein and they also may know about The modern quantum field theory Heisenberg, Schrodinger people. How many people know about Maxwell?
Eric Weinstein 35:07
Not enough, not enough, although max do have Maxwell’s equations tattooed on their backsides let some people do
Roger Penrose 35:14
that the general public don’t know about maximum. But Maxwell’s equations completely changed our way of looking at the world. And we live off it without thinking, you know, you’ve got these lights here. 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 the same scheme. electromagnetism, dynamite? Well, some of this goes back to Faraday just before max. Sure. So Faraday had a lot of the influential ideas, electromagnetism. Well, a little bit of that was known before arrested, knew that if you had an electric current Then you get a magnetic field. But it was the other way around with Maxwell. 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 Faraday any sort of clues that there might be some connection with light. But he didn’t have the equations. And it was even max. You know, I’m very partial to this book on orchids that followed Darwin’s Origin of Species.
Eric Weinstein 36:26
Oh, yeah, that was the book he wrote. The title is, and I always I love reciting it. It’s on the various contrivances by which British and foreign orchids are fertilized by insects. And so you think, Well, why would you write a damn fool book like that after Origin of Species? And the answer is he wanted to test whether he understood his own theory. 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 perhaps the best dress rehearsal for unification we’ve ever seen. Oh man, you know, full unification and on the other hand, it’s not until the Late 50s that we actually unpack the last trivial consequence of the theory with the this bizarre effect of passing an electron beam around an insulated wire, enough. Ah, yeah, in fact, we just had dinner last night we Yeah, we asked yaker Aronoff if he wanted to come but he’s in Israel, and he sends his regards. Oh, you know, send mine back Oh,
Roger Penrose 37:29
he’s great fun I always
Eric Weinstein 37:31
but that was a that was a very weird thing where we learned that if you have a an insulated solenoid that the phase of the electron beam going in a circle around it would be shifted despite the fact that the electromagnetic field could be treated as zero because the electromagnetic potential this precursor, yeah. Turned out to carry the actual content that it before that it have been thought that that was just a sort of convenience product to recover electromagnetism. And it turned out that that geometric object was more important. And you know, in 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 38:22
And now you have to explain that one. Well,
Eric Weinstein 38:25
um, you know, this this, this etching called ascending and descending.
Roger Penrose 38:29
Oh, yeah, sure.
Eric Weinstein 38:30
Yeah. Which is sometimes referred to as the Penrose stairs.
Roger Penrose 38:34
Yes. Well, you want that story?
Eric Weinstein 38:37
Well, I do but what I was gonna say about why I’m asked Yeah, right. Yeah, is that the photon is really best represented in some sense. As the angles of a set of stairs like that with this very mysterious property, then what you’re really talking about is what we would call horizontal subspaces. Picture the stairs and the fact that there’s a paradox of going around, 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 holonomic. And we don’t have a means of visualizing that except for like, either Rock, paper, scissors or your work with Escher. Is that a fair comment?
Roger Penrose 39:18
Well, I had,
Eric Weinstein 39:20
oh, there’s the first time you’ve ever heard somebody say this?
Roger Penrose 39:24
Well, let me I mean, there’s a quick, complicated story. You see, when I was a graduate student in Cambridge, I think it was in my second year, when the International Congress of Mathematicians took place in Amsterdam. And so I and a few friends decided we go to this meeting. And I remember I think I was just about to get on the bus or tram or something. And Sean Wiley, who is a lecturer in in algebraic topology. There’s just about get off the bus I was getting on here had this catalog in his hand of an exhibition in the Bangkok museum. And this was a picture of it the one called Night and day with birds flying aha you into the day and the night and they check the birds change into the spaces between the birds one week, and I look at this man, I’ve had some amazing what is that? Well, nothing to come from it Oh, well as you’d be very interested. This is this. In the Bangkok Museum, there is this exhibition by an artist called Asher. So I’d never heard of him before. And I went to this exhibition and I was absolutely blown away. I thought it was most amazing thing. I remember particularly one called relativity where people walk up the stairs and gravity directions in two different ways. And I thought this is hugely impressive and I went away, thinking Well, I’d like to do something impossible You see, and I didn’t see I had an idea about an impossible structure with bridges and roads and things like that. So locally makes sense. But as a whole, it was inconsistent. And I didn’t think I’d seen anything quite like that in his exhibition. So I played around with this, and sort of whittled it down to the triangle, which people refer to as a try bar. So it’s it. It’s triangle, which is locally completely consistent picture. But as a whole, it’s impossible. And I showed this to my father. And then he started drawing impossible buildings, and then he came up with this staircase. So we decided we’d like to write a paper together on this. And we had no idea what the subject was. I mean, what sent the paper like this to what journal, so he decided since he knew the editor of the British Journal of psychology, and he thought he’d be able to get it through. We decided the subject was psychology. Of course, it’s As you say, it’s not it’s more in a way mathematics because it’s illustrates ideas, well of CO homology, and other things like that, which, which I didn’t quite know I was illustrating at the time. But anyway, we wrote this paper. And we gave some reference to Russia, I think, reference to the catalog. And my father sent a copy to a Dutch friend that says, and he managed to get it to Russia. And then my father and he had a correspondence. So that was Lionel Penner. Now, my father in law says, but I actually visited Russia then. And he had sent to print to my father with a dedication to it, and he gave me another so I have in the Bodleian, but in some sense, so the Ashmolean Museum because
Eric Weinstein 42:56
I’m very indebted to you for this for this reason, because when I When I have to describe what general relativity is, yeah, and I don’t wish to lie the way everyone else lies from an alignment to do it differently, I say that you have to begin with four degrees of freedom. And then you have to put rulers and protractors into that system so that you can measure length and angle that gives rise miraculously, to a derivative operator that measures rise over run, that rise is measured from a reference level, those reference levels don’t knit together, and they form Penrose stairs. And the degree of Escher Ines or Penrose, and this is what is measured by the curvature tensor, which breaks into three pieces, you throw one of them away called the viol curvature and you readjust the proportions of the other two. And you set that equal to the amount of stuff now that’s a very long causal chain. Yeah, but it is linguistically an accurate description of what general relativity actually is. Yeah, what
Roger Penrose 43:58
is illustrates that it’s also Stretch comb ology which I was being interviewed Oh, ages ago, but I don’t know whether it’s BBC. I can’t remember what it was. There was an interview, but for some reason, they were interested in Twister theory now.
Eric Weinstein 44:13
They think they’re interested
Roger Penrose 44:14
where they thought they were, I guess they’d heard that word or something, right? And at one point, they say, well, surprisingly not at the beginning. They asked me what what good it was to see what can you use it for? So I said, Oh, you can use it to solve Maxwell’s equations. You say, that’s the equations of electricity and magnetism and light and so they got a bit interested. And they said, Oh, how do you do that? Well, it actually involves an idea that I couldn’t really explain here. It’s not possible to in a sort of popular talk like this. 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 then I went back home and I was like, my benefit. I think I can’t you know, it’s this impossible. Trying that’s exactly an illustration of comb ology. So I went back the next day and told them that they weren’t interested. They didn’t use it, I think I may have tried to explain. Yes, we have a look at something which is locally consistent, right? 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. It could be bigger and further away or smaller and closer, and the picture is consistent. But you get an inconsistency if you go around, right? Luckily, because you have a freedom. Yes, you misuse this freedom, in a sense. So the glitch in it is this impossible structure?
Eric Weinstein 45:39
Well, I had this so this is actually my son, and my 14 year old son’s copy of the book. Yes. And I was having to describe this to him called what cosmology was and I said, that one forms which is a piece of technology, in mathematics that you can analogize to radar guns so that while you’re driving in the policeman shoots your car with a radar gun, he’s measuring the component of speed in the direction of his gun. Yeah. And so that’s something that eats the vector of speed and spits out a number. And then you could imagine it a racetrack that wanted to have a circular series of radar guns to measure the speed of cars going around. Now the question is, you also recognize that you could build a poor man’s version of a speed system by heating the track to some temperature and measuring how quickly the temperature changes the car went over. 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, because at some point, the temperature is going down, down, down, down, down, down, down, then it’s going to be 10 degrees below wherever it started, which is your paradoxic
Roger Penrose 47:00
Yes, well, there’s a nice example. Somebody made I couldn’t remember where you accompany you have a ball going up or down it, whichever it is. And you accompany that with it with a, a note going up or down. And you can make it sound as though it keeps on going all the way up and all the way up all the time. By if I got the harmonics, you bring a new harmonic in as you go right below
Eric Weinstein 47:23
it, yes, sub perceptual. So there’s this auditory illusion that captures these
Roger Penrose 47:28
Yes, you’d have an auditory version of the same thing. It had this ball bouncing around with that.
Eric Weinstein 47:33
That’s not it, that’s a bit of a cheat. You have I mean, my point would be that your S your stairs or your Penrose stairs 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. But that what you did was to create the illusion as taking place in a plane or you can draw it in direct linear system. You have an interpretation. Have a three dimensional thing which which is an ambiguous and so you saw the movie inception of course where they they realize this actually yes
Roger Penrose 48:07
Eric Weinstein 48:10
but but that effect is the soul of the Aronoff Boehm effect which surprised the world in the late 50s because it was discovered so
Roger Penrose 48:20
late into the game it is it is a company same sort of thing. That’s right. Well, of course like so many things people point out that this Oscar right as far as who’s who’s a Swedish artist drawing things like this before? I think round about the year I was born he had a picture which is all with cubes going around it wasn’t exactly the same but it was I think I’ve seen these flows the one with the cubes, yes. And then he had versions with stairs staircases to put an issue. He never put any perspective in it, which seemed to me that was a
Eric Weinstein 48:55
something missed opportunity.
Roger Penrose 48:57
Yes. Now in my triangle, I did put some perspective Yeah. Slightly, you can see, but you can do it with a perspective and it still works.
Eric Weinstein 49:06
So what I want to get at is, I think also that we have this very funny thing that happened recently is starting from the early 70s, where we started Miss telling our own physics history, 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. 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 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 t at various points.
Roger Penrose 49:52
And I was we graduate students again in the same in the same group, same year. Absolutely same Yes. With the same supervisor.
Eric Weinstein 49:58
Incredible. Yes. right and then you continue to cross pollinate ideas. Yes.
Unknown Speaker 50:02
Over the years. Yes.
Eric Weinstein 50:04
So for, for listeners who don’t know Michael Tia was one of the absolutely most dominant and generative I don’t even know what to call him is like beyond genius a seer of type.
Roger Penrose 50:18
But he said she had such a broad understanding of mathematics it’s partly in geometry
Eric Weinstein 50:23
or generally and analysis, just incredible and algebra. He wrote a book on on commutative algebra. The now he had a partner for much of his career Isidore singer who I was quite close to for taco. Yeah. And is was, again 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. And they came up with something called the TS singer index theorem, which governs worlds in which there are no time dimensions, but only space dimensions are No space dimensions and only time dimensions, but there’s no equations without any differential equations with differential equation, if you think about differential equations is coming very often in three main fields of study, elliptic, hyperbolic, and parabolic. Then the idea is that wave equations would be hyperbolic the type that you’re worried about in physics, but things like soap films look like elliptic equations and tn singer had this incredible insight into the nature of elliptic equations. Do you go ahead. So now I’m going to say it’s extremely general theorem, which covers goes over all sorts of different areas of mathematics. And has application it sort of tells you that the, the non madness of some beautiful space that you might be exploring like some kind of high dimensional doughnut that’s knotted many times around itself, whatever you want, that that topological nod madness tells you something about the kinds of waves that can dance on that space.
Roger Penrose 52:06
Yeah. Nice. It’s very remarkable theorems.
Eric Weinstein 52:11
Does that theorem in the so called elliptic category, world of space and no time, let’s say relate strongly, in your estimation, to the most important hyperbolic equations that govern the waves that make up our physical world due to the constraints of relativity in a world with one time and three spatial dimensions.
Roger Penrose 52:33
I can say if I use the theorem,
and at least two different continent contexts, yes, maybe more. So I’m not an expert in that area at all. And it was mainly when I was trying to, I shouldn’t attend an auction.
I was trying to
solve a particular problem. I don’t know how much the All you want to go into these things, which had to do with how to make Twister theory work in curved spaces. But I ran up into a question
which had to do, how do I put this?
It has to do with complex geometry. So you’ve got geometry in which instead of using real numbers to use, you think of measuring with ruler, say and the ruler is one dimensional. The numbers go along one dimension if you like. And complex numbers where you have the square root of minus one incorporated into the number system. They’re really two dimensional. So the geometry of complex numbers has twice as many as the real numbers. But the geometry of complex numbers is particularly fascinating. or less the algebra you might say the unknown assessor, whatever it is, it’s particularly fascinating. And I was sort of when I learned about this when I was at an undergraduate doing mathematics. And I thought it was incredibly beautiful.
Because when you talk about real numbers you have
you can have a draw curve, which is a function. So this, this curve has some shape. And you might want to see what is it a smooth curve, that means you have a tangent direction as you go around it. Maybe it jumps. So it’s not even continuous or maybe smooth. Or it may be you have to have a curvature of this curve. And you might might not be smooth enough to have curvature. See, see there’s one degree of smoothness or two degrees or you or you can have three 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. And then we learn about complex you see all we know do it all over again. And you’ve got your analysis on algebra, if you like, geometry worthy, it uses complex numbers. And then suddenly you find that if it’s smooth, everything comes with it. You can differentiate as many times as you like, you can expand the power series, a lot of incredibly magic, you just have to do it once. Rather than this. Oh, Craig, all these different kinds
Eric Weinstein 55:27
of mathematicians. Yes. Quite often view the complex case, the the case of complex numbers as the natural case and the case of real numbers as artificially tortured, yes, which is a complete reversal from how most engineers Yes, and us actually have been quite instrumental in making the case for the fundamentally complex nature that it’s not just in science that we use complex numbers in physics, but that Nature appears to be essentially complex,
Roger Penrose 56:02
I think you see by just hearing this
nature of complex analysis, right, and how beautiful it struck me as being. And I had this sort of feeling. Wouldn’t it be wonderful if these numbers were somehow the basis of way physical world operates? I have no reason to think that. And then I learned about quantum mechanics. And I was amazed to find, 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 56:35
you’d have to work awfully hard to get rid of.
Roger Penrose 56:37
Yes, but the things you find it a little trick to do it now these follow me come with contour integrals, and they drop us an amazing way. And I thought, well, that’s a piece of magic, but it doesn’t tell you anything about the world. It just tells you. This is a neat way of doing things. And then I learn about quantum mechanics and suddenly these numbers are right there the basis of the whole subject, and I thought that was an amazing thing. Maybe these complex numbers are really they’re at the root of everything.
Eric Weinstein 57:05
Now one of the ways of describing what Twister theory is, and of course, it’s a bit of a tall order for a podcast is that you are replacing Einstein space time. With a larger structure that inset in some sense implies space time, where you can take all the data that roams around on space time, the waves, the force, the matter what have you. And you can, as mathematicians might say, pull it upstairs to this larger 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 has this kind of complex number aspect baked into it.
Roger Penrose 57:52
Yes, well, it was something just to go back for a moment to explain the TF singer. That’s why it was useful. I could 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 when they come together, but I was really intrigued by these complex numbers and there is well something, let me tell you so the origin of the Twister idea. I was struck by the fact that you see people know that that when things travel with a great speed, and in in according to Einstein special relativity, they get sort of flattened in the direction of motion. Now, this is a way of talking about it, and you get this Lorentz contraction as it’s called. Now, I was playing around with relativity and thinking about it was this to two component spinners and thinking about the geometry of it worked. And I realized if you think of the sky, you see the sky is is where you have vectors in four dimensions. Think of a vector or something which has has a magnitude and a direction to it as well. And into ordinary three space, you’ve got this idea of a vector, which is quite common to people know about. But when you’re in four dimensions, then you have space and time together. But do you have particular vectors, which are called now, and these are the ones along the light cone. So these this is an ordinary vector might represent a velocity. So you have a particle moving along with a certain speed, and your four dimensional vector would point along the velocity or the momentum of that particle. So
Eric Weinstein 59:46
weirdly, in the space time metric of Einstein, yeah, these are vectors that are not zero. But if you used Einstein’s special rulers and protractors, what would the length of these vector is So it’s a really, it’s a, it’s linguistically tricky to talk about these things because they’re nonzero things that would be measured to be of zero length. If that concept of length was in fact, yeah. extended from your normal concept of,
Roger Penrose 1:00:20
yes, the idea that something of length zero means it’s two points, the distance between them is zero. You think of them around 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 Minkowski geometry because although it’s describing Einstein’s special relativity, the gym geometry was not an Stein. People often say, oh, Einstein introduced this four dimensional space time. That’s not true. It was Minkowski. And I signed
Eric Weinstein 1:00:50
ahead that this is real. This is not just a sort of a weird artifact of the description of various processes. We’re being entertained, yes,
Roger Penrose 1:01:00
what’s the kind of geometry and makowski showed that the, the space of special relativity is really four dimensional. And it’s this kind of geometry in which you can have distances, which is zero, although the points are sort of long way away from each other, and this represents a light ray. So you have one event, say, and then the light through that event reaches another event. When I say event, I mean, not just a special position, but the time as well. So you mean a position in space time, space time, so you need four coordinates three space and one time coordinate. So that’s when we call an event. And so you have a point or an event in space time, and measuring the particle moving with the speed of light to another such event. And the distance between those two, in this kind of geometry that Minkowski introduced is zero. So and he Minkowski played around with different kinds of geometry. And he realized that special relativity is really best described by this kind of what we call Minkowski geometry. So you can have zero distances, and yet the points are not on top of each other.
Eric Weinstein 1:02:14
So your idea was to take all the points that are bizarrely zero distance away, and then make those the new points in the new space.
Roger Penrose 1:02:22
Well, it wasn’t quite that I could come up to this slowly because it took me two years. But the initial idea isn’t so hard to understand, really. You see, if you look at the sky, what do you see when you’re seeing light rays or you’re seeing photons coming to your eye which have traveled with the speed of light. So the world line in four dimensions of that photon is tilted over at what represents the speed of light. Now in this Minkowski geometry, that distance it It has a clear meaning. So, let me let me give that the suppose the the photon is emitted at 1.1 event and received at another event. Now to that photon, the time between one and the other is zero. And that time measure is exactly the distance measure in Minkowski geometry, suppose the particle was not traveling the speed of light, suppose it traveled with half the speed of light or some other speed, then it’s time experience of time is exactly the distance according to Minkowski geometry. So you say, if it travels with very, very, very great speed, suppose you traveled to a planet, which is four light years away, and you travel with wonder I won’t do the calculation right here, but with half the speed of light, then you would, the experience that you would have time you experience is less than the time that somebody here 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 don’t think it’s as long. And if you actually travel the speed of light, that experience would be zero. So this is the experience of the length of time if you have a very, very good clock you carry with you and you see how, what, how the clock made of pure light, it all gets pretty, pretty heady out here. Well, you don’t make enough. You can imagine the clock, say a nuclear clock or something and you’re not traveling with the speed of light because you can’t get to the time measured by that nuclear clock would be the distance in the cuff. I should point out just for our listeners,
Eric Weinstein 1:04:39
yes, even people who do this field of differential geometry morning noon and night in math departments, almost never choose to work in worlds with some temporal and some spatial dimension. Yeah, because it just it breaks your head.
Roger Penrose 1:04:56
It’s a very different different intuitions, very different when you Go
Eric Weinstein 1:05:00
back and you think about the puzzles that people had when Einstein reduced is special and then most particularly general relativity. They found it very puzzling. You could look at the arguments people that we keep using these words like, yeah, time and length and all of these things that have become. We don’t recognize that in that one innocent decision to break off one degree of freedom and treat it differently. It’s right that all of our linguistic intuition goes out
Roger Penrose 1:05:29
without all over again. Yeah. Well, it was a curious experience I had because I was giving a series of lectures. Seattle with these were the Mattel lectures given in what was it the I forget exactly what the dates were. Maybe this round about 919 70 or something. And there was a collection of mathematicians and the collection physicists, john Wheeler and Cecile the way to organize ism is a very interesting meeting. Well, people from Both areas of expertise were brought together and at that time is hard to believe now. But at that time mathematicians and physicists were barely talking to each other. And they got me to give a series of lectures.
Eric Weinstein 1:06:13
And as before, Jim Simons and cn Yang get together and
Roger Penrose 1:06:20
it’s a good question. When was that? 7570 say it was before that. Okay. Wow. Is that right? I think so. Yes.
I really have to.
Eric Weinstein 1:06:32
My memory is date says no, if you I know you’re, you’re hot on the other trail of this, but just to 11 something in Roman, Jackie’s at MIT once beautifully said. And he I don’t think you wrote it down. He said, we used we didn’t 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 either told us things that were absolutely trivial in there. relevant for things that we already said, when we talked to the geometers, we started to learn new things that we’d never considered.
Roger Penrose 1:07:09
It’s really it was very much cross fertilization there. But I was gonna say I gave these lectures that I think it was 12 lectures. And I wasted my time on Sunday should weren’t going to, until I left myself only three lectures to describe the singularities the black hole idea, which wasn’t the term black hole wasn’t used since then. But the
Eric Weinstein 1:07:31
collapse, just called the Schwarzschild singulars.
Roger Penrose 1:07:34
Well, it was called the singularity when that was the thing people call it the swatch of singularity where it’s what we now call a horizon right. And I remember in my third lecture from the end, describing the basically what what we call a black hole, I talked about the singularity. And I was explaining that the Z was basically to do with the zero length business and and Steen rod was a very distinguished mathematician he from Princeton, Norman’s didn’t know. Yeah. And he’d written this book on fiber bundles, which is absolutely impenetrable, impenetrable, but also fundamental to the subject. Yes.
Eric Weinstein 1:08:11
But it’s so impenetrable that I never got to the point.
Roger Penrose 1:08:13
But anyway, he was there at the back of the room. And I remember chatting about it, and he was absolutely dumbfounded. They see you as somebody who’s a real expert at this kind of German Romanian geometry, whatever call it where you have the notion of when the distances are small, then the points are close together. And here you have this other kind of geometry. And the intuition you need for that geometry is completely foreign as the point you were just making well, because yeah, we do have this weird way of talking about something that sounds like this. We might call it like non hausdorff topology, but it is it has Dorf topology. Yes,
Eric Weinstein 1:08:49
it is. But it’s, it’s it’s so the problem is, is it’s pulling apart two different notions of the word close.
Roger Penrose 1:08:57
That’s right. Exactly. Because you think of Close means a small distance, right? So you imagine a little tiny ball where the distance from that point is
Eric Weinstein 1:09:05
was small, you know, mathematics makes you pay for every attempt to sort of intuitively encode something that isn’t precise.
Roger Penrose 1:09:13
Yes. Now I wanted to say I got a bit distracted from leading up to the twist is because that was well, I needed the complex numbers. That’s right. I needed the lorentzian. Okay, we’ve got all that. Yeah. Okay. I can do that. Very goodness. Yes. So,
Eric Weinstein 1:09:30
Roger, now, we’ve we’ve been discussing the fact that this intuition is very, very strange, involving how to think about spaces of the type that Einstein and Minkowski and panca. Ray were considering, yes. How does that begin to lead us towards these more speculative ideas of your surrounding complex numbers? And the Twister program, I don’t think many people many, many of them have heard of it. But even in, even in mathematics, you have to know that you got you were sort of seen as leaving a cult. It had its own 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 1:10:14
When we had this twisted newsletter, which was a
Saturday started off by it’s just in handwriting. And it was duplicated. And then let’s not go into that for the moment are very good. Talk about the basic the origin of Twister theory like how where did it come from? It was really
Eric Weinstein 1:10:34
in fact, your big bet. In physics, do you think?
Roger Penrose 1:10:38
Yeah, I think so. Well, you see, it’s between that and the cosmology, but the cosmos is a bit different because that’s not such a, okay. It’s a wild idea. Yeah. But it’s not a whole body of wild ideas, which is a theory more is all right. But it has lots of connections with mathematics as pure mathematics and connections with physics. Let me describe the best Is it because I think we’ve got most of the things we need. You see, the light cone describes how from one point to one event and space time, all the different points of zero distance from it or another was all the light rays from that point. Now let me think about it the other way around that is my past like home. So I’m sitting at a certain point in space time, and I look out to the universe. And all the light rays that get to me at a particular instant moment of my time, come along this past lacquer. So that’s imagine this could be stretching out into the past and getting bigger and bigger as it goes back in time. And that’s all the events which are in one moment of my time I see those events. So I see a lot of stars in the sky. Now let’s suppose that I mean the star And look like points you see, so that you have this sphere, the celestial sphere, which is my field of vision if I’m measuring myself out and so
Eric Weinstein 1:12:08
imagine that the Earth was transparent, so you weren’t, that’s why my Oh,
Roger Penrose 1:12:11
just let’s go out into space. And I guess I can be looking at the the world around me. Now let’s imagine that another astronaut comes whizzing past me at nearly the speed of light. And just as we pass each other, he looks, he or she looks out at the sky, the same moment as I do. Now, because of a phenomenon known as aberration, the stars will be slightly, not in the same place with regard to that astronaut as me. The sky is somewhat distorted, but it’s distorted in a very particular way, which is what’s called conformal way to say this in a simple way. Suppose I happen to see a configuration of stars that happened to be A circle, suppose they were constructing this. And then this astronaut passing by me would also see these 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 transformation, it’s something which I knew about from my complex analysis days. Do you think of the, what’s called the Riemann sphere? This is the plane of points is it the complex plane or the vessel plane, the point of play, the points represent the complex numbers. So zero is in the middle of your life, and then you’ve got one and then you’ve got minus one, and I and minus either all on the circle, and you go out and infinity is way out to infinity. But the Riemann sphere falls all this up into a sphere. So infinity is not point.
Eric Weinstein 1:13:54
So it’s a little bit like if you have a if you have a caramel coating around an apple, you’re full That you’ve turned it around. And at the point where the stick would go into the apple, all of the boundary of that candy would come together.
Roger Penrose 1:14:09
Yes. And is it what’s called a stereographic projection you can project from the North Pole. And all the other points flatten that into the plane.
Eric Weinstein 1:14:18
So you can see all the points on the sphere except for the point from which you’re projecting Exactly.
Roger Penrose 1:14:22
And that’s called the stereographic projection. And it has this remarkable property that it sends circles to circles. Or you could say it’s conformal that his angles are preserved. And it’s a very beautiful transformation. I used to play around with these things for fun often. Now, the thing is that the transformations of this sphere to itself which preserve the angles, it’s also transformation, which is what’s called analytical column holomorphic. It’s, it’s the most smooth transformation you can have
Eric Weinstein 1:14:57
just the analog of smooth But for complex objects rather than real objects that were real and complex means the types of numbers Yes, that’s right.
Roger Penrose 1:15:06
So it’s so it’s what’s what smooth is and complex analysis. And those transformations which sent the spheres and sphere are exactly those in relativity. So the different observers passing me at different speeds looking at the same sky, the map from my sky to their skies, is exactly this complex transformations of the sphere. And this actually is what you exactly get when you use two components spinners and you see the description when you move from one observer to another is exactly those ones which transform the sky in this conformal way to itself and 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 sphere, shooting past you at nearly the speed of light. Well, you see the direction of motion, it will be contracted by the Lorentz contraction. So when you look at it, you should see it sort of flattened out. You don’t. Because a sphere goes a circle goes to a circle, if you see it as a circle, when it’s not moving, you’ll still see it as a circle. And the boundary of a thing will look like a circle it is moving. And you work away and think about it. Well, you see where the light waves go and the front of it and the back of it and all that you see, really you don’t see the flattening, it really is does look like a like a circle. It’s boundary looks like a circle. So I wrote a paper on this. almost simultaneously, there was somebody else wrote a paper on mainly thinking of the small circles and spheres. But this transformation, that’s really what started me off.
Eric Weinstein 1:16:49
If I understood correctly, maybe I don’t Yeah. We have another mutual acquaintance, or friend Raul bot, and yes, 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 bot periodicity from zero to seven, or one to eight, depending on how you like to capture, yeah, you get these things called low dimensional coincidences.
Unknown Speaker 1:17:15
Oh, yes. And so
Eric Weinstein 1:17:16
that they don’t recur because of your point earlier about spinners that spinners grow exponentially, whereas vectors grow linearly? That’s right. And but during the first period, where these things are of comparable strength, yes, you’ve get all of these objects where depending upon you defined in two different contexts, you turn out to be the same object. That’s right. You’re making use of that here
Roger Penrose 1:17:42
it is that it’s the mother Lorentz group,
Eric Weinstein 1:17:45
or like, you know that the rotations of space and time which we might call so one three or so and three double cover would be equal to something else called SL to C, which would mention complex numbers. Even though there’s no complex numbers to be seen in space and time,
Roger Penrose 1:18:03
yeah, it depends on that, that one of those coincidences was triple coincidence, I think you certainly get a coincidence. Which one is depending upon in this description. But the point I’m making here is that in a certain sense, relativity is described when you do it in a to spin a form, which is really expressed in this fact that it’s the transformation of a Riemann sphere to itself, which is a complex transformation. This is the most general transformation of the sphere to itself when you think of that sphere as a Riemann 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, but one dimensional in complex numbers, because the complex each complex numbers carries the information of two real numbers.
Eric Weinstein 1:18:54
So for example, mathematicians would call what most people call the complex plane, they might call it a complex line.
Roger Penrose 1:19:00
Complex line. That’s right.
Eric Weinstein 1:19:01
Yeah. And so the language, again, is intended to make things very hostile to the newbie.
Roger Penrose 1:19:07
Yes, but it’s 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 in in real terms that you have to double the number of real dimensions to get the number of
Eric Weinstein 1:19:20
complex I want my audience to watch, but I don’t want them to feel stupid for making the mistake. Everyone, person.
Roger Penrose 1:19:27
You have the number of course, yes. So we have the complex numbers playing a fundamental role in relativity, that’s really the point you want to make. And it’s the complex sphere. So, the Riemann sphere, which is this one dimensional, in complex sense, two dimensional in the real sense, object, which is fundamental. Now, this Riemann sphere appears in the most basic way in quantum mechanics to you think of the the spin now. That’s the pack. The most direct complex, the most direct quantum mechanical thing is in a certain sense, where you see quantum mechanics playing a real role as quantum mechanics, which is hard to grasp normally, but you can see it here is the geometry reworks. You see, if you have an object of spin half, that’s the smallest nonzero spin, you can have such an electron. So think of an electron it has been half. Now, what that means is that it’s basically two states of spin, which people call spin up and spin down. Well, what does that mean? Right? Put your thumb up like that right handed spin is where your fingers go. And that’s spin up means right handed about up, spin down is right handed about dinos 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 about right, left, forwards, backwards. All those are combinations of up and down. And their complex combinations through these complex numbers, which lie at the basis of quantum mechanics. then here you can see, in a visual way, what they’re doing, you see, you can say, up, down what’s left and right where these 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, right, and you minus it, you get to the left, oh, i times you go forwards about whatever it is. And the complex numbers come in to describe these possible directions of spin. And it’s the Riemann sphere again. So, but you were relating these complex numbers of quantum mechanics do the directions in space. So you have a connection between these rather abstract numbers, which are fundamental to quantum mechanics and the much more concrete picture of directions in space.
Eric Weinstein 1:21:57
Well, but Roger, I think You’re both. Well, let me be challenging slightly.
Roger Penrose 1:22:04
Eric Weinstein 1:22:04
Yes, what you’re really talking about is a very important fork in the road for physics, do you wed yourself to the world that were actually given. And you know, Mach was famous for having said this phrase, the world is given only once. And so we happen to know that there does exist a world that appears to be well modeled by three spatial and one temporal dimension, that and then the key question is, do you wish to have a more general theory, which works in all dimensions or works for all different divisions between how many spatial and how many temporal dimensions and what I see you as having done which I think is incredibly noble, brave and scientifically valid, is to work with mathematics that are really particularized themselves to the world were 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 and wishing to keep their options open.
Roger Penrose 1:23:09
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 26 dimensions, or 10, space ultimate, or 11, or 12, and things like that. And, sure, the mathematics we’ve got mathematics to handle these things. 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 describe here and this exactly what you’re saying that I’m looking for a way in which you find the mathematics to describe the world, which is very particular to the dimensionality we see to the three space dimensions and one time dimension is described in this formalism very directly. And if you’re going to try and talk about But other numbers of dimensions of space and time, it
Eric Weinstein 1:24:02
doesn’t work as much as I really like to stick it to the string theorists. 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 special called triviality. Yes. And so what they were really doing was figuring out how to build different theories around different highly specific targets.
Roger Penrose 1:24:28
But you see there, it’s the beauty in the mathematics, which sure is a good guide. But it has to be the theories and they never grow up to playing with reality. That’s the sort of thing I mean, it’s perfectly good to explore all these different things and it’s very valuable, but I’m trying to follow a route which is viewed I think, in many quarters is very narrow. I’m looking for a route which is work specifically for the number of Based on dimensions that we have, and is, if I’m there are aspects of Twister theory which do work in other dimensions, but they run out very quickly. And you can see analogs of these things. But they’re kind of the
Eric Weinstein 1:25:14
wrong version of the anthropic principle, which is that if there weren’t a beautiful mathematics to, to catch you, I mean, in some sense, despite the fact that you’re in your late 80s, it’s like you’re stage diving in a punk 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 we do observe and I find that what what’s very disturbing to me is that the Political Economy of science means that fewer people are willing to make strong speculations, strong predictions, to explore things that don’t give them the flexibility in case things don’t work out to say. 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 go down with a ship for the privilege of commanding it as its captain.
Roger Penrose 1:26:11
Well, you can use it that way, if you like. My claim is that the ship isn’t actually sinking, you might think you don’t know. No, I’m
Eric Weinstein 1:26:17
not claiming, I think that one of the things that that’s happened is has been that yours has been one of the most important idiosyncratic programs that in fact, got a huge lease on life from the fact that it has positive externalities, because it was absolutely solid mathematics. It turns out that even if it doesn’t give us a fundamental description of the world, it is at least a deep insight into how to transform one problem into another to allow solutions that wouldn’t have been easily gleaned in the original formulation. Yeah, I’m not saying that it’s it’s knocked out of the park for a fundamental theory, but I I don’t actually know whether Do you believe twisters are a more fundamental description of the world. Well, I do.
Roger Penrose 1:27:05
Yes. I mean, I don’t normally say that out loud. But now you put me in a position.
Eric Weinstein 1:27:09
Yes. No, I think that’s fucking great. I mean, in other words, it’s like you have to say this, I believe and in general people won’t say it.
Roger Penrose 1:27:18
I think the thing is that I have been driven in directions, as just as you’re pointing up in directions, which picking out the particular of the general, right, so sure you have mathematics, which one of the huge aims in mathematics is being more general? And you mentioned the testing a theory, that’s a beautiful example of that, where it simply generalizes over areas which you would never thought, but it also particularized.
Eric Weinstein 1:27:46
So for example, yes, it is only in low dimensions, where you get to play the game with what are called deformation complexes, where the first term is the symmetries of the problem. The second term The fields are the waves and the problem. And the third term is the equations and the problem. And then you get to cut it off at that point, and have that be this magical concept of an elliptic complex. So for example, in dimension four, we glean 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 and every other dimension. Yes, yes. Well, there’s something special there about four. Certainly, that’s true. And the connections, maybe not that clear at the moment. But maybe we’ll see that this is maybe differentiable structures are part of part of physics. It’s quite possible. How amazing that I’ll give you another very bizarre one. I don’t know whether this has ever come up. If you have two sets of symmetries known as Li groups, that act transitively on the same sphere, in usual position, then either their intersection acts transitively on that sphere. The dimension of that sphere is 15. And I believe that the intersection of the groups looks like the electro strong group. So it’s very close to the particle spectrum of theoretical physics pulled out of nowhere just from talking about sphere transitive group. And
Roger Penrose 1:29:17
well, it’s clear that when, I mean in particle physics, I mean, I’ve never really been somebody who studied particle physics closely. Is that right? I didn’t know. Well, I mean, in general, we have but but I suppose I felt we may be a long way from really understanding what’s going on there. I don’t know. I mean, I hope I hope that it was. Well, you know, we have no, it’s a complete I often have different views from Why do these things.
Eric Weinstein 1:29:45
I think we’re almost at the end. Well, that’s an interesting so how do you come to the idea that we may be quite far?
Roger Penrose 1:29:53
I’m not saying that we’re necessarily far I think it’s understanding why the groups are the groups that we see
Eric Weinstein 1:30:00
And people have different theories about these. Let me ask you that a couple of questions gone. So very early in this new stagnation post the standard model. People like Glasgow and George Chi and Putin Salaam, put forward these unifying symmetries that remain very odd. Because they’re so attractive and powerful. The the prettiest of them being something called spin 10 which physicists persist in calling so 10 for reasons that escaped me.
Roger Penrose 1:30:38
Yeah, whether this is the one which doesn’t exist, or is that not that one?
Eric Weinstein 1:30:42
Well, the original su five, which sits inside of spin 10 was disproven in its most basic form. And at that point, George I and Glasgow had been trained in the previous culture of physics, which is that you fell on your sword when you predicted Something that wasn’t true. I think that they sort of rushed to commit ritual suicide far too quickly.
Roger Penrose 1:31:05
Yeah, I just I’m, maybe if I’d worked in the subject i’d form of clear view. It’s just from the outside. I’m not convinced that I’m clearly there. There are things which people have discovered, which are absolutely fundamental in particle physics. But somehow it hasn’t got to the basic level, which I feel I can see why these groups are, what they are, and so on. Let me not talk about it, because I’m not an expert at that. And I’m only giving an impression. And I suspect that it will be maybe not too long from now a better understanding. I’m hoping that Twister theory might have something to say about it. But at the moment, the area which needs to be explored here hasn’t been explored. The things we did it one time. I’m sort of deviating a bit from the general trend. But there was a question of how we trade trade, how we treat massive particles and Twister theory. And naturally Twister theory describes massless things. Things go along the light cone and that sort of thing
Eric Weinstein 1:32:12
to others because you privileged, the light cones and then yeah, then the treatment of particles that we’re massless got a privilege tramming privilege treatment.
Roger Penrose 1:32:22
And not just that you find transformations. There is a way of representing the Maxwell equations. This is the thing I was mentioning about the TV program. we’re describing the Maxwell equations, which you get electricity theory, and it comes directly out there. What about the Dirac equation he wants to talk about massive particles? Well, the way it seems to lead you, as you think of the way you see a massive particle has a momentum that which is timeline points within the cone and one way you can describe a time Like one is think of to no one, so to light like once you think of a zigzag, so it’s got zig and zag. And that’s one convenient way j, where you might have one which is made a three zigzag dog, something like that. And you can get the timeline out of.
Eric Weinstein 1:33:16
So you can build it up from different primitive. That’s right.
Roger Penrose 1:33:19
So the argument is that you have a twister for each of these zigs and zags. And so you have might have two of them, you might have three of them. And you see how many of them give you the same amount. And then you get these groups in twisted theory. And these groups look like the particle physics groups. So you’ve got su two and Su three. And the idea we had Oh, well, that’s the basis for these positive things. So
Eric Weinstein 1:33:42
su two doesn’t impress me much because it’s ubiquitous, but su three is a is a very unusual, this is the group that represents the strong force that holds Are
Roger Penrose 1:33:55
you see there’s a thing that su three gives you this
You can gauge it. So you have
there is a difference between the SU two and the SU three that the Quantum chromodynamics, if you like, which is the theory, which comes from gauging su three is a genuine gauge theory. But when you try and do it for ice to the left for the electrons and we use week ISIS spin, either gauging it doesn’t really work because you’ve got a you’ve got a special it’s not the full group so and so there’s something funny about it. Okay. And there are other things which which might be a more promising way to go. Let’s not going to that because this is I’m guessing. But the idea is that you could develop a particle physics using many choices and
Eric Weinstein 1:34:44
have it in other words, if I’m not misunderstanding you, the idea is that the extra data mean we have a problem in the standard model. Yeah, in that we have effectively a an origin story with two gods. There’s the God of Einstein that gives us space into And then there’s this other guy that gives us su three cross su two, question one, which gives us the non gravitational forces and all of these particle properties we call quantum numbers. And this has no connection to the space and time data.
Roger Penrose 1:35:18
Well, that’s the sort of thing. Yeah, it looks as though it’s quite separate. I mean, it must be tied up at some stage. But we haven’t got to that. But the idea here was to try and do it by twist. Well, I’m just trying to say that we had, we’ve got very excited about this for a while. And then it was a long time ago, because when people discovered I think it was challenged, and suddenly this didn’t fit. And so we gave up a model.
Eric Weinstein 1:35:41
And so by charm you mean the, the addition of entirely separate versions of the familiar family of matter. So we now think we have three copies of matter. Yeah, where the second two are repeated at higher mask, that sort of thing. Yes. Yeah, that’s right. And so people got it didn’t seem to So simple at that point so, and various things didn’t seem to fit so well.
Roger Penrose 1:36:04
But I think we should go back to that, 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 construction she Twister theory starts off as a theory about space, flat space time. That’s what bothers me about it. Exactly. And it’s what bothers a lot of people when you see
Eric Weinstein 1:36:31
every big company that
Roger Penrose 1:36:35
I was at the time at the University of Texas for a year and this average children put a lot of people together who relative general relativity experts, hoping that something would come out of it, I guess. And I had an office next to Engelbart choking, whom I learnt a lot from and On the other side, I had an office, that was Roy curse office. And Ray Sachs was all the way down. And I have to backtrack, because the question is Where did Where did twisted theory come from? Now, I had lots and lots of ideas that I was trying to fit together. Part of these were trying to combine the Riemann sphere of relativity with the Riemann sphere of quantum mechanics, and various other mathematical ideas which come into quantum field theory. And they were sort of floating around. And I remember drawing a big piece of paper with all these ideas, which we’re roughly speaking of the nature that the world we see is described by real numbers, but sort of hiding behind it is a world of complex numbers. And 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 vague thought ahead. And I couldn’t think of A picture in which you added, you see, space time is four dimensions. And I needed to add basically one more dimension because I wanted to incorporate an idea. Again, it’s difficult to describe these things on sort of popular program. But it was an idea fundamental to quantum field theory, which has to do with splitting your field aptitudes into positive and negative frequencies. And its angle burthen impressed upon me that this was very fundamental to quantum field theory. Most people weren’t stressing it at that time. And the weird way to think about this is think of the Riemann sphere again, and you have the equator of the Riemann sphere, describing the real numbers together with an infinity. And you’ve got this complex numbers on one side, one hemisphere and also on the hemisphere, and the ones which are positive for frequency, which is the fundamental thing for quantum field theory. extend into one half so To me was a very beautiful way of thinking about it rather than splitting everything into Fourier components and taking taking half of them. And that was sent to me and you have four degrees of freedom with one extra real degree of freedom. one extra dimension like the Riemann sphere going from them. You have to the whole sphere. Yeah. And I wanted it to divide it into two halves. Yeah. And that was the picture I wanted. And you tried to do the space time it doesn’t work was first space time is four dimensional. And if you complexify eight dimensional, it doesn’t divide in two. That’s just something else. So I I knew that wasn’t right. Okay. Now, I was in Austin, Texas. I had friends in Dallas. Now, this was the year in which Kennedy was assassinated. And my friends in Dallas were to dinner. And that was the next place that Kennedy was to go to and he was going to give a speech. And they all got worried because it didn’t turn up and they were January ish, quite right to be wise, because he’d been shot. And this was a great shock to us all. And so we decided we wanted to calm ourselves down and went to a trip to trip from Austin Mary was in Dallas where the others were. And we went off in a few cars to San Antonio and maybe to the coast. And this was to try and recover from the shock and coming back. All the women folk wanted to gossip and so on. I was with pitch to Ashford who is a nice fellow, I like him a lot and Garen, but he didn’t speak much. So all the others wanted to gossip and I was sort of left over and we the two of us went in the car, driving back to Austin. And so I had a nice silent drive coming back. And I started think about these constructions that Ivan 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 curious twist to them. And I had understood these things. And I realized that they were described by as you talked about the hops map or the different parallels is you can think of a sphere in four dimensions, three dimensions here for dimensions. And you have these circles, which fill the whole space know to intersect, and they agree to link, beautiful configuration. And I realized that this was the thing that geometrically described the solutions that I ever had found. And I tried to think about this and I thought, Well, okay, these sorts of describe.
Well, the way I’ve all had to sit for the bus Think, think of a light ray. Yeah. And then you think of all the light rays which meet that light ray. So you’ve got one light ray and all the other slight tracers meet it, and that family of light rays, you can have Maxwell’s solutions and maximum because each point along those rays so what he did this Historic, you move that light right into the complex. So you add a complex number to the to extra dimensions. Well, it pushes the light rail into the complex. And then you can construct this twisting. You don’t see the light right anymore expression to the complex. But you’ve still got the complex family of lightweights which meet it in a certain sense. So I tried to understand what that looks like. And I thought this is you’re 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 dimensions there are these as I call them later, Robinson conferences, and I was gratified or stoffels or whatever the right word is to find that the number that never dimensions of this, this family right which was six, six dimensional family, what’s the dimension of family of light rays five. So the one You actually see directly in the light rays. That’s the real thing. And the thing which governing in the mysterious, complex world, at one dimension, they can twist right handed. That’s one way left handed and the other way divides the thing into exactly what I was looking for.
Eric Weinstein 1:43:17
Fantastic. So I got that and then additionally had this structure of three complex dimensions.
Roger Penrose 1:43:22
Yes, yes. Well, I went I had to go back and get hold of my Blackboard and try to work it out. No, I’m exhilarated. So it was it was a complex project of 3d space. You have these two twisters. And I know, ciao chuffed myself didn’t realize what this was. You have a five dimensional space which divides this six real Vanessa space, which is really a three complex dimension space into two half. So
Eric Weinstein 1:43:47
if I’m understanding you, you would start out off with a seven dimensional sphere, you take an action by a circle to get see the complex projective three space and then you could further quotient that out by two spheres to get the four dimensional sphere.
Roger Penrose 1:44:05
When it’s you have to have you can think of it as a sphere and
maybe I’m not seeing it correct. You can think of it as a sphere. And
Eric Weinstein 1:44:16
are you at a complex project? Yeah,
Roger Penrose 1:44:17
yeah, you can think of a seven sphere.
Eric Weinstein 1:44:20
Now, let me just tell you what I find fascinating about this story is that you’re talking about a period traveling between two cities where you realize something is the Hopf fibration.
Roger Penrose 1:44:31
Well, I knew it was the hot fashion, but I hadn’t actually thought of it.
Eric Weinstein 1:44:35
You may not know the following. No, go ahead. Yes.
Isidore singer, took the work of Jim Simons and Frank Yang. I mean, yeah, yeah, yeah. And on the trip to Oxford, where you, Michael? Yes. He said, oh my god. This is the attorney ionic rather than the complex. Hopf fibration. He said it was See, when he realized that the self dual instant on equations were going to be a revolution. And so it was the exact moment of the relationship to something as non trivial in his case as the attorney onic rather than the complex Hopf fibration. So this is almost an exact parallel between two stories, because I’ve never heard yours before. That’s very
Roger Penrose 1:45:20
interesting. It also has relevance direct relevance direct. Yes. Because I think as you were just saying, because you think of the vector space for which the complex three spaces and of course, that’s for complex dimensions, and then that means a real
Eric Weinstein 1:45:37
and this is, look, I want to tie this into a bigger thread, which I think is fascinating. I am not a devotee of string theory, nor am I of loop quantum gravity. I think that most of what has been said about supersymmetry has been overbearing and wrong. I completely agree with all those things you say. And I think that The intellectual Carnage from these adventures in political in political economy or public relations or whatever you want to call it are not being borne by the people who benefited from them. But by those who have to clean up after
Roger Penrose 1:46:15
something to be said.
Eric Weinstein 1:46:17
Well, you don’t have to say it. I can say it because I’m not inside of the universities. Yeah, no, yeah. Now what I would claim is, is that while these people I think, did a tremendous disservice for all of us taking what I consider to be our most accomplished intellectual community in the history of academics, theoretical physics. It is not the case that these people did nothing for 45 plus years, but what they did do has never been told properly. So I claimed to you and dinner the other night. Like if you just look at the role of curvature in our understanding of not only general relativity, where it’s been for over 100 years, but now in particle theory, So we had a first revolution around the mid 1970s with what’s called the Wu Yang dictionary, where a particular geometer who becomes the most successful hedge fund manager in human history meets arguably the most accomplished theoretical physics physicist if it’s not Weinberg, it might be Yang in terms of what has been proven this contributions they have an unbelievable interaction which shows that the classical theory underneath particle physics is as or more geometric than the theory of Einstein using steam rods, fiber bundles in Eris months connections or vector potentials or what have you. Then you have a second revolution again involving so that was the first one that is singer takes from Stony Brook to Oxford. Yes.
Roger Penrose 1:47:50
Isn’t you have another one?
Eric Weinstein 1:47:52
Yeah. Which is the geometric quantization revolution with your colleague Nick Woodhouse writing the Bible there. Yes. In which Heisenberg’s Uncertainty relations strangely come out of curvature, rather than then just being some sort of condo Kevin, you’re looking in connection to the bundle? Well, that there’s this thing called the pre quantum line bundle where line is against one of these planes. So the terminology is all screwed up. Yes. Nevertheless, the key point is is that what we had previously treated as the annoyance of the Heisenberg uncertainty principle became the beauty of a geometric quantum so now you had the underlying classical theory is geometric. The underlying quantum theory is now geometric. And then again with your English group, particularly Graham Siegel’s is that is a real hero with Michael lutea pointing pointing the way you guys figure out that this weird grab bag that was called quantum field theory which is this thing above Quantum mechanics that is needed for if you’re going to have particles that changed regimes in which the number of particles changes like something emits a photon, you need quantum field theory, you can’t do it in quantum mechanics. So that world was a grab bag that made absolutely no effing sense 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 would have been discovered by topologists and geometers. Even if the physical world had never used it, because it was actually a naturally occurring augmentation of what’s called board ism theory, which is an enhancement of what you previously referred to as co homology. So these are three separate revolutions with people that almost nobody’s ever heard of like Luis Alvarez Gamay, and, you know, and Dan quillin, who I think is the world’s greatest accidental quantum field theorist, For some reason, the physics community is still telling us stories about entanglement and about multiverses and many worlds. And this actual thing that happened, which is as gorgeous as anything I’ve ever seen has been a revolution that’s been 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 f?
Roger Penrose 1:50:27
Yeah, I think
Eric Weinstein 1:50:30
I mean, first of all my wildly off.
Roger Penrose 1:50:32
No, I don’t think you are, you see,
Eric Weinstein 1:50:36
I mean, a lot of these things that I wish I knew more about, you see, for example, Crillon theory and so on, which which is you know, life is too short, but, but these are things out of the singer theory, where he finds these determinant lines, which are coming out of non local spectral information and building the base. Maybe four pre quantum line bundles in which the functions in that world become the waves that give us
Roger Penrose 1:51:06
the theory. I think the trouble here you see, mathematics is full of all sorts of beautiful deep theory. And most of mathematics as it exists now, in a sense of what’s written in journals and so on, has almost no bearing on the physical world. Now, you see, I feel 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 the physical world. Now, we found many such keys and general relativity to the lorentzian version of Romanian,
Eric Weinstein 1:51:47
semi Romanian or pseudo Romani
Roger Penrose 1:51:48
pseudo Romanian geometry. So that’s picked up a beautiful area of mathematics and turns it into into into physics and it’s and then in reverses has given a lot back to mathematics and also with quantum quantum theory, clearly and quantum field theory, but I think there are things that are hiding there which are very beautiful mathematics and which will reveal themselves as important in the physics we haven’t
Eric Weinstein 1:52:20
got to it. What do you make of the fact that we now have three separate geometries? You have Romani and geometry as the parent of general relativity. Yes. You have Eris money and geometry, which is based on sort of these Penrose 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 strong force holding proton repel and the weak force which causes beta decay. All right. And then you’ve got this other geometric theory which is the geometric quantum And they’re not the same geometry. So for example, the geometry that the Jim Simons and cn Yang find has this property called gauge symmetry, you have the opportunity for gauge symmetry in the Einstein theory, but because Einstein takes curvature, and uses something called linear algebra, to project all of the curvature information into a smaller subset killing off something called viol curvature, if you gauge symmetrize, and then project it’s not the same as projecting and then gauge symmetrized. So the opportunity to use gauge theory is lost by the specific genius amongst
Roger Penrose 1:53:48
what you see there’s a good example because he did this amazing thing when producing general relativity. But then in his later years, he tried to develop the theory in these unified field theories which From a mathematical point of view was not really a very, was not likely to give much new insights. But you know, he was right to think you should find the unified scheme and so on and bring the well he traveled one travelers. He didn’t really, he considered electromagnetism. But the particle physics didn’t play much of a role in what he was
Eric Weinstein 1:54:22
what he died before quarks were in. But that’s true. He never he was innocent of su three. And it’s very assertions. Yes, sir.
Roger Penrose 1:54:30
I think the thing is, there’s huge, beautiful things in mathematics. And we’d like to think and I like to think that they do have a role in fundamental role roles that we’ve not yet discovered. In operating, whether we’re 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 many beautiful things in mathematics which you Guided in certain directions, which from the point of view of mathematics are great, and they can be generalizing ideas and, and revealing all sorts of previously unknown beauties. But the proportion of ease which we find has relevance to physics is so it’s very small at the moment. Now, I think that in some ways, maybe the most powerful the most Sure. I mean, complex numbers. And the analysis of complex numbers is one example we once does seem to see a role in operating the way the world works. And I’m sure that we will find other things. It’s just there are so many temptations interactions, which are not particularly to do with it. I understand
Eric Weinstein 1:55:48
that but what I don’t understand and what I’m absolutely unsympathetic with, is that we have a lot of people who once upon a time had a lot of different ideas. Most of the ideas at the moment for brutally honest, it we are so constrained by this point in our story in theoretical physics that almost every new idea is dead on arrival unless you specifically keep it from predicting things that we don’t see. 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 class of naughty boys who are very badly behaved, who get to make all sorts of claims, who talk to the press incessantly over decades about all the wonderful things they’re going to do, which they don’t do. And then you haven’t got another group of people whose feet are held to the fire where the instant they start to consider something that might, for example, violate a no go theorem. They’re roundly humiliated. Now what I see you as having done is to carve out a very unusual niche twist theory is, at a minimum, an incredibly valuable tool for generating solutions on one space from solutions on another, let’s say.
it’s also somewhat tolerated within the system. It’s a 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 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. I do think that in general, they’re smarter than the relativist. They’re even smarter than most of the geometers they’re insufferable. They’re very clever people. Yeah, very hateful. Very insufferable. Oh, yeah. And the problem with that community is is that it’s actually accomplished a great deal that isn’t of a stringy nature.
Unknown Speaker 1:58:00
Eric Weinstein 1:58:00
Yes. And I do think that what they’ve done is they’ve instead of quantizing geometry, which is what quantum gravity was supposed to be they it backfired. And they they had the geometry. geometry is the quantum. And that’s the main legacy of these people is it’s the the, you know, they took off for for Paris and landed in Tokyo, which is very impressive as a feat, but it wasn’t what they were setting
Roger Penrose 1:58:28
out to do. I think, basically, I agree with that. And certainly string theories had a big influence in various areas of mathematics. But the influence directly in physics has been pretty minimal, I think.
Eric Weinstein 1:58:41
What do you think about the legacy of something like supersymmetry,
Roger Penrose 1:58:44
which is? That’s an interesting question, isn’t it? Yes. It’s very interesting, partly from a personal point of view, because when I first heard about it, a lot of it was on conformal supersymmetry, right. And I could see there was a lot of connections. With twists of theory, the only thing I didn’t like was you were led to these algebras, which didn’t commute. And whether there was the square of something was zero or something, whatever. I mean, they weren’t the kind of algebra that you needed interesting theory, you need a complex analysis. But anyway, I went I visited zunino at one point, and I was most intrigued because I could
Eric Weinstein 1:59:25
this is half of the duo that came up with the sort of originally original deep. Yes, a super symmetric model. Absolutely. Yes.
Roger Penrose 1:59:33
And so I thought there’s enough connections here. I’d like to understand it better. And yeah, I think I understood a bit more. 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 he was somebody who understood and understood it perfectly well. And he told me this story he said he once written the paper, in which he used to component spinners and it was worked out very well. A few months later, after Salaam did the same thing, but using four components spinners, and he said everybody refer to Abacus 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 formalism, which I thought was pretty ironic, particularly since Dirac himself is intriguing that a lot of people in the early days of looking at generalizing the Dirac equation for higher spins and so on. And they were you know, Duffin Cameron were the only ones I forget where they were all called different names for all the different spins. And they were all in course and spoke I remember and Dirac wrote this headdress and I think earlier I can’t remember the history of which is which, but I think earlier, this paper he did a whole lot using two spinners and direct using two spinners. He’s he clearly knew about them. So as I was concerned, because he acted on them, but this was much earlier than that, yet. This paper in the Royal Society describing all the different spins with two spinners, much more, much clearer, much more general, simple, systematic. And again, nobody seems to refer to direct paper, which is quite curious because he, I mean, there’s a huge irony there because he wrote his initial paper using these four spinners and didn’t realize until maybe pointed out by van de Landa, I have no idea where he got it from, he realized that you could write all this into spinners. And in some ways, it was simpler and use this to generalize to all the spins. But for some curious reason, nobody or very few people seem to refer to direct paper.
Eric Weinstein 2:01:40
We know about this famous situation where Fineman found effectively the path integral formalism in some paper directed published Yes, in the Soviet Union. Right, right. And the fireman, you know, was trembling anything and as director you realize when you said that these Two things were analogous that they’re, in fact proportional. And direct said, are they?
Roger Penrose 2:02:06
Yeah, be careful with direct because I had a when I first written things in two spinners and I’d written general relativity with just two spinners and I’d find certain things came out very beautifully. And the thing that everybody was worrying about calling at that time called the bell Robinson tensor, right? And you could dropped out of us two spinners and the principal now directions and all sorts of things. And the thing is, you have this equation, which is the big identity is written into spinners. And you can see, it’s just the same equation that you write for masters fields. Maxwell’s equations is the thing you train if it had no mass, just to say they’re just the same you have it in the more in the higher the spin the more indices, but it’s the same equation. And you can see it’s conformally invariant or
Eric Weinstein 2:02:52
just as a part of the problem that you’re going to get into with all these things is I would venture to argue that even the lowly Key identity, which is at the heart of how Einstein figured out how to do his equations, yes, to make sure that effectively his vectors pointed perpendicular to the orbits of the symmetries that he was considering that we don’t really even understand the things that are given to us for free fully. There’s an old paper of Jerry Kazdin, I believe, in which he actually reduces the Bianchi identity from much more fundamental principles. And the same thing is true with the sudden appearance of a version of the calculus due to levy Chavita from merely choosing rulers and protractors. Yeah, I really worry that we never actually grounded these fields properly. I don’t know if you’re familiar. I think it’s checkoff who said that if a if a gun is placed above the mantel place in the first act, it must be fired by seen for well for it example we have this thing called the torsion tensor of God that everybody is introduced to in the first day of Romani and geometry and then they properly are encouraged to forget about thereafter never really seems to show up in any meaningful way. Anyway, it’s always a puzzle I
Roger Penrose 2:04:15
know. And I’ve never quite made made up my mind about it. Let’s not go into that story that, yes, I don’t use it. I once wrote a paper, but that she
Eric Weinstein 2:04:25
asked you just in terms of the path forward. It strikes me that what we have learned about our physical world and what comes up in this book, is of a very frightening nature that Einstein’s equations when you really understand them, through Hilbert said insight, come from the simplest possible thing we could minimize. Oh, yes, same thing for Maxwell’s equations. They spread from the electromagnetic Isn’t the weak force into the strong force? Because it was the simplest possible thing that could be optimized? Isn’t the Lagrangian, the Lagrangian, I’m trying to avoid saying those words. And then those that know it and then derive Yes. Yes. third equation. To complete this triptych is the equation for matter, which generates all of something called k theory, 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 now that we found that are the simplest and best possible equations of their type not that we’ve found so far. But provably so.
Roger Penrose 2:05:48
Yes, I think the trouble with simplicity arguments which I agree with, is that it’s simple in one context and what simple exit maybe
Eric Weinstein 2:05:58
but nature is shown such I mean, the thing that I can’t get over is that her taste in mathematics. You know, I’ve analogize this to raiding a jewelry store with millions of pieces, and in under half a minute finding all the best stuff.
Roger Penrose 2:06:19
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 see, Dirac was the same college as I was St. John’s College in Cambridge, where I was a fellow. And I happened to be sitting opposite him at one point. And I had been working on these two spinner ways of looking at General Relativity. And so I said to him, I thought, you know, I thought something you might be interested in a good way would he have an opportunity to talk me about it, so, so he reserved a room and I had a little discussion with him and then I wrote down this equation, which is this wave equation, which you which represents the big identities, and I wrote this thing down Direct, I thought he would instantly recognize it because it’s basically the same equation that he had in his paper with all these different spins. And he asked me if I wrote down the equation is where does that equation come from? So I said, it comes from the big identities. And he said, what should it be? Enki identities Holy
Eric Weinstein 2:07:21
Roger Penrose 2:07:23
And I thought, well, he’s been writing all these papers in general relativity, and he must know perfectly what he simply rediscovered them himself. He just didn’t know they were called the bnk identities.
Eric Weinstein 2:07:34
I don’t know. It’s a very curious story. And this was in the form that the derivative of the curvature in terms of the natural derivative is equal to zero that’s
Roger Penrose 2:07:45
in vacuum, say, yeah, and you take the the viol curvature, which is all that’s left of every man curvature. And you write that in spinners and it’s a spinner with four indices, completely symmetrical.
Unknown Speaker 2:07:59
And then when you
Roger Penrose 2:08:00
write the derivative, it’s the derivative acting on those four things in one contraction, the derivative got two indices, and you can track one of those. And that’s your equation that’s vanishes. That’s the equation, same as the Maxwell equation the same as you train if you had one index and no mess. And it’s the way I think about these things in the conformal invariants is very crucial. That leads me to all sorts of ideas that I wouldn’t have thought of otherwise. And it was clearly the sort of thing durack would have played with himself because his equation all the high spin equations, although in excuse me in his paper, he did the Masters case a different way, which I never quite understood why. But anyway, it was there clearly, things that he understood completely and somehow maybe never connected. I don’t know what it was.
Eric Weinstein 2:08:50
Do you did you read his 1963 article in Scientific American where he makes a very interesting case against naive application of the scientific method.
Roger Penrose 2:09:03
No, I don’t. That’s the wreck sent in Saturday.
Unknown Speaker 2:09:05
Roger Penrose 2:09:06
his point should have seen that.
Eric Weinstein 2:09:09
He makes the point in the case of Schrodinger, yeah. And he says Schrodinger would not have been led into error if he had not been pressed for agreement with experiment. Because Schrodinger, then, after publishing, there was a period of time where it wasn’t understood that spin somehow entered the picture, and complicated the theoretical prediction with its experimental verification. But I think secretly, he was actually talking about himself where he had introduced the Dirac equation, there had to be positively and negatively charged particles. And at that time, the 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 of the same mass 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 particle is something
and I think that that 1963 paper from Scientific American is direct trying to give us a gift from Mount Olympus to say, stop with the incessant insistent on the naive scientific method. Give yourself more room to imagine more room to play more room to be wrong. I think that’s a crucial thing is 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 nothing rather than anything. So this is a big thing with him. And I think he was disturbed by
Roger Penrose 2:10:40
Yeah, you’re right. I mean, he could have predicted instantly. I think he needed more freedom. And he didn’t have it. And he tried to give that fade away into 10 minutes. Yes.
Unknown Speaker 2:10:48
What crashing? Yeah.
Eric Weinstein 2:10:52
Let me ask you a harder question.
Unknown Speaker 2:10:54
Right. Because we haven’t asked you any hard questions. I’ll be going
Eric Weinstein 2:11:00
You’re going to be in your 90 soon. If you weren’t working Yes, if you were to point to younger people, there’s There seems to be a failure to pass torches that I’ve noticed. And you don’t seem to be the sort of person I would imagine to have that problem. Who would you be pointing to? into a human being individuals who said tricky when I tell you not to push push anyone down, but who would you Who would you build up? And who’s young and vital who might be? You might say, look, if anyone’s got the sent, this might be a person to look at.
Roger Penrose 2:11:40
I think I’m not going to take you up on that one. I’ll decline gel declined to push further. Yes, it’s just it’s not so obvious. I mean, I’ve certainly had people clearly good in inferential ways and think of things I’d never thought of.
Eric Weinstein 2:11:57
But 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. Do you? Do you worry that the glory that is the Oxford School of geometry and physics may not continue? Without? do worry a bit about that? Yes. I mean, there was unbelievable nucleus of people.
Roger Penrose 2:12:18
You’re absolutely right. It’s very remarkable.
Eric Weinstein 2:12:21
And I worry that the UK doesn’t value itself enough. I think that you guys are so idiosyncratic. And so weird and badly behaved. I don’t know what to call it. But the UK is punching way above its weight by tolerant tolerating and encouraging personalities, idiosyncrasies
Roger Penrose 2:12:40
that I think that there is a point that I I wouldn’t know how to generalize across countries because maybe, but I think I think you’re right to some degree, there is tolerance of eccentricity which which is specifically kind of Kind of tolerance, which is specifically English or British, I should say British. I don’t know. I’m nervous about saying things like that. Because you find somebody springs up somewhere else.
Eric Weinstein 2:13:10
Yeah, somebody else somebody will hate you more, but quite honestly, what are they gonna do make you pay with your career? I don’t think it’s gonna happen.
Roger Penrose 2:13:15
Yeah, but I think
I think what you say about the geometry developed in Oxford is was pretty distinctive. Yes. And then the people moved out to I mean, Michael went back to Cambridge.
Eric Weinstein 2:13:29
Well, that’s what, but the Oxford system I mean, I don’t have to make it so peculiar talks for but you know, even if I think about, like a Nigel Hitchin or Mason, I guess, has been in that system.
Roger Penrose 2:13:45
Yes. Now that a group of very able people, it’s clear. Yeah, they’re very jealous. No doubt about that. Yes. Yeah. But it’s, I mean, you’re asking me to a bigger thing, then.
Eric Weinstein 2:13:57
Look, let me just know One final thing. Have you been to the courtyard of the Simon center for geometry and physics at Stony Brook, which is tiled with Penrose tiles?
Roger Penrose 2:14:09
I’ve not been there. I’ve seen photographs of the tiling. Yes,
Eric Weinstein 2:14:13
ma’am. recommend a pilgrimage. They have a wall there as well.
Roger Penrose 2:14:17
Eric Weinstein 2:14:18
The so called iconic wall, which because Jim Simons made so much money, he was able to chisel introduced to some of the world’s most important equations and principles that you and I probably think of as being the hallmarks of being alive, you know, just contact with these things. They’re actually in a place that can be visited with a key. And I always think about in a fan, fantastic world, unlocking that wall and seeing whether it’s in fact, a gateway to something else.
Roger Penrose 2:14:51
Yeah, it’s a long time since I’ve been there. And I haven’t been there since the wall over page pavings. Or I recommend
Eric Weinstein 2:14:57
it. Yeah. Now I’d like to do the ask one final question that was out.
We all worry
when we’ve gotten this far along your road to reality, if you will, that we’re not going to live to see the final chapter completion that this is a mystery like none other
probably in some sense does have an explanation and, and it kind of end. Is that something that that occupies you? I mean, I find you absolutely vital and sharp as a tech, but like 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. So there’s a huge amount of chance involved in these things. So it’s a gamble. I think you see a real end till this is too remote for that. But on the other hand,
Roger Penrose 2:15:57
you see, we didn’t really discuss Where Twister theory is stuck or has stuck for 40 years? And where I think it’s got somewhat unstuck,
Eric Weinstein 2:16:08
you think it will be the answer?
Roger Penrose 2:16:11
Well, I’m not sure I have friends and take CS that’s not a question. But the main problem, as I saw it in Twister theory, is sort of rather surprisingly, things which worked surprisingly well. And one of these is to construct solutions of unsigned equations or the Ricci flat four dimensional space times, which were completely generic, provided they were anti self deal. Now what that means is you’ve got a complex solution of answers vacuum equations, which are left handed, 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, as these are wave functions, because functions are naturally complex. So I thought well is a wavefunction. But it’s a nonlinear wave function. So I call it the nonlinear Graviton. And it seemed to me a big step forward and understanding how quantum mechanics and gravity fits together. But it got stuck. It got stuck with what I call the Google a problem. Now you have to, if you’re not a member of the former British Empire, you probably don’t know what a googly is. It’s a it’s a ball both in the game of cricket. You see, in cricket, unlike baseball, you like to spin the ball about its axis. The direction it spins about the direction which is moving because it bounces, that’s the key thing. So it bounces one way or the other. And to make it spin left handed, is has a certain action with your hand. And there’s a 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 one of these in it gets the batsman completely bamboozled. And that’s called the googly. So you Using the same action, the spins the ball, left hand and you spin it right handed. So I use that term because he very apt, you have the frame the Twister framework, which naturally gives you the left handed Graviton make it to the right handed one. And I struggled and struggled and struggled and have all sorts of wild ideas for how to do this. And I came up with one machine I was very proud of, but it needed a cosmological constant to be zero. And so I thought there is no cosmological constant. Then I had a discussion with Jerry Ostreicher, who was a very distinguished astrophysicist. And I was talking about the observations that there seemed to be the 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 or something. And he looked at me said, That’s not the point. There are so many things in cosmos. G, which works so much better if you put this cosmological constant in. 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 can do something that didn’t work without it. And this enables you to have a construction, which I think solves this googly problem. The trouble is, from my point of view, it translates into algebra rather than geometry or even get back to geometry by thinking of as a connection on the bundle. So that is a geometrical thing. It is a good thick connection. And then you talk about this algebra and then instead of patching spaces together to make a curved manifold, you patch the algebras together, then they have to be non commutative. point that made clear to me by Michael a tee at one point. And this is the proposal you just construct these algebras and they are connections on bundles. And this enables you, at least in principle, to find the generic solution of the ads then vacuum equations with cosmological constant. When I say find it’s
Eric Weinstein 2:20:03
so you mean what would be called an Einstein manifold? The Ricci? scalar. to Charleston to nonzero
Roger Penrose 2:20:08
constant and nonzero? That’s right. That’s right, exactly what people don’t understand Speight but this is lorentzian and not understood positive definite. But it’s not a construction hint that you sort of write me down. It’s, you construct this algebra and then you’ve looked for sub algebras. And the algebra, that’s not the thing I’m good at doing.
Eric Weinstein 2:20:29
But still, it needs something way to collaborate.
Roger Penrose 2:20:31
Oh, absolutely. And I got distracted by cosmology and other things and
Eric Weinstein 2:20:36
stay away from that consciousness stuff. It’ll suck all
Roger Penrose 2:20:39
your time. Well, that is a problem, actually. Yeah.
But you see, other people are doing that I’m not really doing that I can they get me to give lectures on it. And I give the same old lecture which I’ve given,
Eric Weinstein 2:20:50
many, many, well, I have to say that if, if you stick with what you’ve what you’ve done in physics, and keep trying to push that ball forward Can’t imagine a better use of your time. You’re invited anytime you want to come back and return to this program, this has been an extremely heavy load for our listeners. I know we don’t apologize. Don’t apologize for that 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 spoon fed prettified version? That’s like pre chewed as if it were baby food. I don’t think they want that anymore. No, I agree. And I think even if you don’t understand all the things that they get some feeling for some of the things people are trying to do is is really important. We as important as the details, or perhaps more. Part of it is just respecting our listeners, they know that we don’t know how to get this to them in exactly the right way. And so I think we have the best listenership of any program out there because they’ve been habituated to recognize that not every program and not every sentence is going to make sense. So Roger thanks you for coming through. We’ll come back anytime and we’d love to continue the conversation about twisters or anything else you’d
Roger Penrose 2:22:05
like to talk. I’ve really enjoyed it. Thank you very much. Yes.
Eric Weinstein 2:22:08
All right. You’ve been through the portal with sir Roger Penrose hope you’ve enjoyed it. Please subscribe to us wherever you listen to podcasts. And if you are the sort of person who views podcasts, navigate over to our YouTube channel. Make sure that you subscribe and click the bell so you’ll be informed the next time our next episode drops below.
The Portal podcast transcription series
- Peter Thiel
- What is The Portal?
- Werner Herzog
- Timur Kuran
- Rabbi David Wolpe
- Jocko Willink
- Bret Easton Ellis
- Andrew Yang
- Bryan Callen
- Julie Lindahl
- Sam Harris
- Vitalik Buterin
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