2020 Nobel Prize Winner Sir Roger Penrose in Conversation with Janna Levin

oh my god well I thought I had a plan and now it's all just gone I'm so excited to have roger penrose here roger penrose I know I was gonna give a semi-formal introduction but I'm not going to Roger as many of you know is one of the most creative mathematical minds of our time and has taught us so many things and is really just an exemplar of the idea of mathematical originality and we're going to talk about that creativity and originality in mathematics when I was a student I don't know if I ever told you this before I discovered physics and math I thought physicists memorized things oh look he's laughing good good because physicists have the worst memories in Roger know tonight we're talking about biology and how I couldn't keep track of all of those names and the nomenclature and the like physicists notoriously have terrible memories it's all about being able to derive something from the simplest original sentence right and I say Roger has taught us a lot of those original sentences things from which everything else seems to stem and and it's just an extraordinary honor to have you here and I've always enjoyed our conversations and I just want to give the audience a chance to welcome you here tonight thank you you look like you had something to say well I was going to thank you very much introduction and it's a great pleasure I gather there's some people out there but as a light shine I can see nothing it could all just be in our minds I can talk about what's in our minds later yeah so you have been knighted which is very unusual I was going to originally introduced you as Sir Roger Penrose and I know you're a little shy about the title sometimes but we were discussing earlier how it's inappropriate to say sir Penrose that's Sir Roger absolutely yes yes yes right yes I'm just wondering when Queen Elizabeth knighted you did she actually use a sword I have actually a very poor memory of it but yes there was a sword yes were you and um Stephen Hawking knighted at the same time no completely different yeah so it's really interesting okay we'll talk about that sir so one of the things I wanted to begin with is the impact you have had on the general theory of relativity so here we just have this as a bit of a cartoon of a black hole forming and it's a very interesting history because in 1915 Einstein first correctly writes down the theory of relativity general theory of relativity which he struggles with for many years and of course is you know he gets a letter in the post in just a few months later in 1916 from Karl Schwarzschild who is a German infantry soldier serving on the Russian front and in the context of Einstein's theory of general relativity by the way do you want to have a one-sentence shot at general relativity good I'm one sentence show you have forces give you as many as you want well the basic principle is what's called the principle of equivalence that's Galileo's principle you drop a big rock and a little rock from the Leaning Tower or whatever you like and they fall together I'm just gonna coax you to do rock star a microphone you said yes I don't I'm not experienced so let me know when I when I drift yes no the thing is so there's a little insect sitting on one of the rocks looking at the other it looks as though there's no gravity yeah so you get rid of gravity by falling freely and now we know astronauts you know you see them and the earth is right there and they seem to be feeling falling freely as though the astronauts in the International Space Station are weightless because they're too far away from the earth to experience gravity well that's completely wrong yes yes well that's the basic principle but you see it had been known since skeletal there was time but to make it into a theory that was something different so the equivalence principle just to cuz you know part of my job is I have to translate yes so Einstein called it the happiest thought of his life and he he thought you know right now I feel heavy in my chair you feel heavy in your chair and we think that that's gravity but there's something wrong with that description because what does the chair I have to do with gravity right say he imagines if I were up in an elevator and I felt heavy on my feet what does the elevator have to do with gravity so he imagine cutting the cable and falling freely in this elevator cab and what you would experience would be exactly what the astronauts experience on the International Space Station he would experience weightlessness if if I you know if I held my phone in front of me and I was falling that elevator cab it would look like it was floating in front of me just like it is for the astronauts in the space station see I always though there's a huge irony because science really started through the study of the planets and so on and then Kepler just you know found they were really a lipstick lip shakes and then Newton showed that they were that came from an inverse-square law and the force and all that stuff and then people use the idea force for other things and so science sort of started with gravity and then suddenly ice thing comes along says no it's not a force you get really bit by falling so it sort of pulls the rug from right under the right it's a beautiful idea that what's happened is the earth has inscribed historically behind its formation archaeologically in space-time the curves along which the International Space Station Falls freely so the the astronauts an International Space Station are like they are like falling in an elevator but they're just they're just doing it smartly so they never crash into the earth they don't experience the unhappy ending to that thought experiment exactly so here it is 1916 and Einstein gets this letter from his friend he says you know I've the war it's World War one the war has treated me kindly I have had the opportunity to wander through the land of your ideas and he presents him with the mathematical solution that we now call a black hole now when you were a young physicist starting out where black holes considered to be a mathematical oddity or real well you see they weren't black holes in those days because people didn't you see the what's called the Schwarzschild solution a pearl structural didn't live much longer after that was great shame he died within the years yeah yeah no you see the idea was that I mean he wrote down this equation which describes the space-time the curved space-time which represents a spherically symmetrical body yes no like like a an idealized planet the exact fear but the thing is that the body itself is way outside this thing called the Schwarzschild radius if you could squash it down smaller and smaller and smaller it gets to the place where well it's the easiest way to think of it just think of the scape velocity you see from the surface of the earth if you imagine there wasn't an atmosphere you could throw a ball at a certain speed and there's a critical speed where it will escape from the earth because normally it comes down you think everything goes up falls down isn't quite because you that's right fast enough you can escape so there's a certain velocity I think I forget what it is now 25 from the earth yeah anyway so there is a certain speed which which is the escape velocity now you imagine the earth 211 Jesus sorry yes anyway so the thing is if you imagine squeezing years down keeping the same mass but if it's squashed now smaller then the escape velocity bigger and the smaller you squeeze it down even the same mass there comes a point where the escape velocity is the speed of light and that's where this horizon occurs so you have a point that if you had a light signal shining away from the light from from the earth if the earth was squashed down to that size it wouldn't escape right and this is what you call the event horizon no black hole is something much more massive than the earth because you couldn't imagine actually squeezing the earth down like that but if you have a original thoughts were with stars I think the original thing came with these things called white dwarfs when Chandra Sekhar he was a very distinguished Indian physicist and I think he was only 19 or something yes the Cambridge and he worked out that there was a limit to the size at which white dwarfs to the mass of a white dwarf and if it was bigger than that limit there was no way of holding it apart he wasn't using the what's the thing called electron degeneracy pressure we didn't worry about that it's a certain force we can talk about into the pie yes and that has a limit that he squashed down below that limit then well sir here's here's the dilemma so Einstein gets this letter in 1916 and he thinks this is you for mathematics but it's not reality Heath because of the reasons you're describing he does not believe that there's a way I mean after all I can't crush this microphone down to a black hole because it resists the crushing as you're describing yeah and so he says well it's a it's a beautiful piece of mathematics but it's not reality when you started working on black holes do you think they were just a beautiful piece of math math and they did not have the name yet black holes as you know certainly they were just called short short singularity metric they were Misco of a yes yes so it was very confusing because there is what's called as thinking out in the middle yes and that's where the curvatures we haven't talked about so I want to talk about there cuz your work on the singularity theorems was probably your first big break out but but I just am curious before you did that work did you think these this mathematical solution was just this Platonic ideal in our minds or did you think it was real I think it was pretty real by they believe it yes well you see there was a story was in 1939 there was a paper written by Oppenheimer yes Oppenheimer's atomic bomb fame yes and a student of his cross Snyder and they had this model of a collapsing dust cloud and that model would describe what we now call a black hole but the thing about that is people thought well it's artificial because first of all it's this stuff called dust well that's just a material which doesn't have any pressure and so there's nothing to hold it apart that's the one problem the other problem was it exactly spherically symmetrical same all the way around so some to idealize yes everything falls towards the center and so the fact that you get in the middle this point where the densities become infinite and becomes what you call singularity is an artifact and is this real or not and I I was worked for some time with John Wheeler in Princeton 39-year child wrote this paper as you said it was published in 1939 on the date in my understanding that the Nazis advanced on Poland so you know people weren't paying too much time to the physics journals and so it sort of fell into obscurity but it was a big paper because the same people who later came to work on the nuclear physics and the bomb came to understand the nuclear physics and stars came to understand that the pressure from the nuclear physics was not sufficient to resist catastrophic gravitational collapse yes to a black hole well you see the story sort of came back again because of quasars these were these were originally there were radio objects and then people had observation visual and these were very very bright objects and they were so bright they were brighter than entire galaxies and people were very puzzled by this and they didn't know whether they were really were that bright and whether they were much closer and the redshift which told you how far away maybe there was some other reason for that and there was a lot of argument about it and it was very puzzling because not only they were there producing this much energy but they also varied very rapidly within a period of a there has to be small and spatially small but necessarily they could be heavy heavy small so people were trying never very good puzzled about these things it wasn't completely clear what they were at that time but people realized that you had to have something which was down to the sort of scale you see the Schwarzschild radius which is this thing we talked about for the Sun is what it's three it's three kilometers if the Sun were to be a black hole it would be six kilometers across so imagine taking the Sun is crushing it into Central Perk basically yes but sure but you see the big deal the more massive it is the less the density see the the point is that the Sun if you squashed it down to that scale it would be pretty dense okay there are some stars which are that sort of density but if you get bigger then the density goes less and it's the way things scale so the things that they were like a whole galaxy squash down to that size the density wouldn't be big at all would be less than air so it's the way that scales thing if it's big enough then these this horizon as we call it the Schwarzschild radius is not so puzzling saying that these quasars - so we just want to emphasize that this went on for decades that people did not believe that these objects were real they thought they were just mathematical so when you were talking about quasars what year are we talking about this is before your this is around about 1962 or something like so right before like really on the cusp of when you did yeah very well you see that the confusion is a wheeler was very interested are this is the singularity that you got in there the Oppenheimer Sailaja collapse an artifact of the symmetry and the fact you've got dust or is it a general general phenomenon it was a question arose and at that time there was a paper written by two Russians licious and clinical acne cough seemed to have proved that in general you did not get singularities said that it was an artifact and I I had a look at this paper and I didn't see quite how you could prove anything like this with by those methods so tell us what a singularity is first so super think of it as a solution light cannot escape it means these objects are dark because if light can't escape there by definition dark you see that you haven't earned the name black holes yet yeah that used to be what was called a singularity but we don't call our distinct because you could be there and it might be unpleasant you but you could but you wouldn't be depends how big it is but you see the singularity imagine something where the density say goes to infinity I'm the density of that glasses whatever it is and you can have things much denser than that and then you have these white dwarfs which are extremely dense on the neutron stars which are the density of a nucleus which is enormous but we're talking about densities which are infinite and that's this thing that this model that Oppenheimer and Schneider put forward the density weren't infinite in the middle and your physics goes crazy so this well how do you describe a thing when the density is infinite so I actually have this figure from year 1964 paper which is one of the most beautiful scientific papers ever written it's two pages long Roger it's do you know what it would take you know you know the Mark Twain quote I wanted to write you a short letter but I didn't have time so I wrote you a long letter instead it is a two-page letter and it has this beautiful diagram in it which I should explain that time is going up the time as part and there's two spatial dimensions yes you can't draw the third throwaway to mention them draw the picture yes yes sorry I should be doing this we're not gonna go into detail into this picture but it is it is so iconic this is this was drawn by you yeah in 1964 showing what you're describing which is the idea that when a star collapses it first forms an event horizon which is the region where the escape velocity as you put it would be greater than the speed of light that's the cylinder that you see that's the cylinder that you see and then after that it just keeps falling and this is something people don't understand so many people said to me isn't a black hole that's really dense Crusher matter when I get to the event horizon shouldn't I be like banging on some really dense crush of matter and this diagram is is so iconic and that it shows that the matter itself cannot help but to keep falling it cannot stay there at the event horizon any more than it can travel at the speed of light yeah but the point about the course was in this picture it's this very symmetrical picture Lampley oppenheimer that's not a picture and what I had to show was that you still get a singularity even if it's irregular so the singularity is what forms when the star keeps collapsing catastrophic ly even inside what we now call the black hole and then what's the singularity exactly what is it well we don't know what is its where the physics goes wrong all it tells you is that the physics goes wrong you the current theory can't explain what happens you get infinite densities or something infinite curvatures and something that goes wrong so you are credited with proving that no matter what in the general theory of relativity you will create a singularity it's not about the special circumstances it's not you know whether it's symmetric it's not whether it's dust it is an absolutely generic and and unavoidable prediction of general relativity that you form a singularity and so a lot of people have misinterpreted that as saying singularities are inevitable but I've always said what you did was you proved what we've never been able to measure which is that relativity fails at some point yeah well you see you have to have a condition which says there's a point of no return and this was the problem and I there was a sort of strange story about this because I have I develop certain techniques of how you might prove things like this using topological ideas and but I didn't have a criterion which tells you the collapse has reached the point of no return and I was puzzling over this and a friend of mine IVA Robinson who was an Englishman who had a job in Dallas Texas yes anyway so he would know the Americans all loved him because he had such a way of speaking he really did he had a wonderful way of using words and he was using these words on me we were walking on the street you see he was describing things I like to listen to and then we came to us a street in Road and we crossed the road and as we had to watch out for the traffic he stopped talking and then we got to the other side and he talks talked again you see and then when he left I had this strange feeling of elation and I couldn't think why am I feeling happy okay that's interesting conversation but I mean that's not it so I went through the day and I said well was it what I had for breakfast no I don't think that was it so all the way through the day and then I reconstructed the crossing of the road and then I remembered that I had an idea crossing the road which is this side you've just rubbed it off now yes we'll get there I'm gonna step behind yes the trapped surface is the trap set it's actually in the picture don't worry about it there's a trap surface in the picture and the idea is that this surface is something it's the thing it's a little ring in the middle yeah you have to throw away to mention it looks like a ring it's really a surface like a sphere and the point about it is if you imagine that a flash of light occurs all over that surface you see you're usually if you imagine a curved surface then if there's a flash bladder on that surface then it's convex one-way and concave the other way and the concave part the flash gets smaller and that convex part it gets bigger the thing about a trap surface is it gets smaller both ways and that was the criteria and I realized that if you go inside this region which is what we call the horizon it doesn't have to be symmetrical it's all but if you get this criterion where the surface is trapped in the sense that the flash of light goes in both ways then you're in trouble and that was the condition and by in trouble you mean you formed a singularity yeah so the theorem was to show if you have a trap surface and it can be quite completely irregular then you have a singular now this is an absolutely stunning mathematical theorem it really is because of the generality it's it's exactly what you're describing it's not the specifics a specific star but these specific conditions can make a singularity it was an absolutely general swatch it said any collapsing object will form a singularity it's it's a huge result did you immediately get a response I mean general this is 1964 that was 64 there was 96 before well and by then relativity is already 50 almost 50 45 years old and nobody has really taken it seriously black holes are not believed to be real nobody's actually seen a black hole where people do people ignore it it was it was using tech you see that sort of techniques people used was either to look at the exact solutions like schwartzman or they use computers which we're not very good back then they weren't that good at that time and you really couldn't tell you see and even now you wouldn't be able to tell if it's genuinely a singularity yeah because you have to go beyond what the computer can do so this was using techniques which were not used in this area so can we just discuss for a second again so people understand the impact why is a singularity so bad well because the physics gives up and because we do it's I mean it's bad because I should sort of qualify that a little bit because general relativity is a classical theory it doesn't use quantum mechanics and so on but but if you follow the physics you've got equations which tell you what happens you know what what happens now and these equations really what happens a little bit later predictability we'd like to be able to say what the consequence is yeah but as long as the what the trouble with the singularity is you get to a point where the equations go wrong they say oh you get to infinity and once you've got infinity there's no way it was almost like matter was blotted out of existence yes sir you were the stuff of the star in your drive that fell into the singularity it was like it fell out of the universe yes it's really bad for physicists yes sure so we don't like that we don't like that idea and other people don't like it no so do you like it now do you think singularities are real yes you said there was a bit of a discussion between Stephen Hawking and me see I proved this thing don't believe what you saw in the film because in that film they were Saturday with twenty means every wonderful theory of everything okay and in that film there was somebody was supposed to be me know there's an actor who played you I didn't look like me look like you and the lecture didn't resemble in the information man and in that audience was Stephen Hawking with sparks coming out of his head or something and he was he was being inspired by the legend they say okay well I did give a lecture in London about that it's true but Stephen Hawking wasn't there can you share celebrity over the singularity theorems because he thought about it in the context not of black holes but in the context of cosmology yeah well let me slightly if the film was completely wrong on that point the fact that the fell not could not so utterly wrong because Denis Sharma who was a great friend of mine and I learned a lot from him about physics and know he was a great man but he was at Cambridge I've listened lecture in London and he invited me to give a repeat of this lecture in Cambridge which I did and Stephen Hawking was present and that and he but the main thing was that he talked to me afterwards he and George Ellis had been working on the singularity but I did much more specific it wasn't it wasn't as general as this at all so they were told they'd been working on a different method of looking at these things and then I described the techniques I was using and Steven picked up on this very quickly and was able to use the same mathematical results as I had but applied not in a sort of reasonably local way like it but going out to large distances and talking about cosmology so he uses the result in a kind of reverse time way to apply it to cosmology which was a very ingenious thing to do but then later on he generalized the arguments and spent a lot of time doing more using more general arguments than I'd used to prove that you get singularities in the Big Bang Susie you can imagine go back in time now you think about the universe the universe was expanding so back in time it's collapsing and does the same sort of results apply there and do you still get synced Irishness in cosmology and this was this is what he was doing then and then later on we got together and proved two theorem which sort of encompasses pretty well things with singularity theorems are huge in the history of general relativity and they're they were incredibly important in terms of challenging everyone to understand that even relativity as sacred as even now all these years later has been confirmed by every observation every time very much stronger than we believe relativity is absolutely correct in the range in which it's valid but you and Hawking back in the 60s and on proved that it's never going to be valid forever basically so it's really I often say you didn't prove that singularities exist in physics you proved that relativity fails at some point yes well the usual argument was you've got to bring in quantum mechanics you see yes oh yeah I mean in my paper I never said actually that this theorem proves its singular as it maybe this is wrong that that that this and one of them is that the physics becomes or the space-time becomes quantum mechanical or something it's still a few years before even the term black hole is playing oh yeah it was a job the other coins the term black hole in 1967 so I'm told I never was quite sure that we went using that term before but I don't know yes I think it was a good weren't you tired of saying complete gravitational collapse before I don't think I use that term so I want to talk about the Penrose diagrams which you do next and I just want to say people don't necessarily always appreciate that there's different branches of mathematics and there's different talents and abilities that go into different branches of mathematics there's so many it's like it's like languages it's like a proliferation of branches you are a particularly extraordinary spatial thinker visualizer you know you're incredibly creative in that space it's just it's it's it's really probably I would say unparalleled it's it's I think it's the biggest division you see when I was in school at school not University and I you know I seem to be able to do mathematics pretty well and weren't so good so I thought well when I went to university I had found people who thought like me you see well I didn't expect says I think I found more different ways of thinking about things and mathematics than that ever experienced before and it was quite strange you know if two people would talk to each other I find it's often and I didn't understand would but the other person was saying what I was saying but somehow we realize we were groping for the same thing and yes and how one get this understanding without really in detail understanding the thought processes was a mystery to me but I think the main division and I certainly noticed this in thinking was whether you thought geometrically or in terms of equations and things like that and I was very much on the geometrical side there was only one other in the class I think who was derided was that considered I think there's a selection effects this is this is my theory you see I think the trouble is it's very hard to examine you see when I did my final exams see it or you don't see it when you see it you explain to the University College London where I did my undergraduate work we did the met the general papers in the first two years and then your special papers he won't be specialized it was the last two papers in the end of three years and I specialized in geometrical things it was super geometry now to write geometry and I thought yeah these will mean things I can do it you see easily the trouble was I could see how to do the problem but how do you write down the solution which any you should have to translate that into words so there are lot of words and the translation from how to do the problem is in the words and I was always slow at the writing and I didn't do it it turned out those were not my best papers my best paper was in algebra and see what I'm trying to say is that I think that there's a selective advantage disadvantage in being geometrical thinking in mathematics that people don't do so well in the exams if that's the way they think oh my god when I was okay just don't just between you and I when I was saying your visualizations like you're leaning on visualizations is your weakness and I remember thinking well I thought that was my strength is an example of one of the things you taught all of us which is what we now universally know as Penn roads diagrams you there there are Penrose diagrams for any possible number of space times but just like there's a map of the earth you take a sphere which is the earth but you project it onto a flat sheet of paper and you know that you're doing a projection you're making some map and some set of rules for how to do that the Penrose diagram is map and a set of rules for taking an infinite space into a finite region yeah it does that it does this is this is a we don't need to go into this structure of it but this is makowsky space which is basically flat space-time yes it's the infinite flat space and time mapped onto a beautiful little diamond it's special special relativity that is special relativity yeah that's makovski and why did you do this what motivated you to do cuz I can tell you how to be incredibly powerful I was teaching general relativity this also just between you and I this semester and the idea of using Penrose diagrams is such a wonderful way of teaching students how to visualize something in its entirety in like one scoop of the eye when you see I'll tell you I was in Syracuse where a lot of this was in 1961 would that be I was in Syracuse New York State and there were quite a lot of relativity people gathered together Peter Bergmann who'd was Einstein's last student and he collected this group of people together there and one of those was an J Trotman who was a very distinguished Polish relativists and he was giving a lecture on gravitational radiation and what the field looked like when it was far away very good talk but he was absolutely full of equations and I were not very good at following all those equations and I thought well there must be another way of doing this which saves one writing down all those equations now you see I was familiar with the idea of conformal geometry can forward you have an Escher picture here I do because I'm yeah this is a great example we're gonna come to all these things it's here wait yes now that's a wonderful illustration now that's illustrate it's a conformal picture you see you see it's a picture of an infinite universe the universe is two-dimensional and it's inhabited entirely by angels and devils and angels are in white I don't know yes but I don't think there was any racial no I was thinking more like I don't know bats are not shoot I don't like bats are cool so I'm gonna highlight the bats okay but anyway in this picture you see it's what's called a conformal representation of this geometry and you have to imagine that all the angels are really the same wherever they are no matter how close to the edge they are they they think they're just the same as the ones in the middle right mostly looks like the figures on the periphery are smaller that's actually that's just like a Mercator projection of the earth you're not reading distances properly yes they're they're as big as the ones in the middle that's right but you have to think in this projection or whatever you call it the angles if you look at the angles on the devil's wings or something and you see they're always the same or if you look at the shape of the eye it's just smaller and small chips exactly the similar shapes there could be smaller but they're the same shape you have to learn how to read them out yeah you can't take a map at face value they say they did anyway so it's it's a useful mathematical way of describing a geometry is this a conformal representation it's kind of geometry called hyperbolic geometry don't worry about that but in this picture infinity is represented as a finite boundary right so that's infinity that's infinitely far away infinity is that fine art circle around the edge when did you first see this image this is a sure when was this I don't know when this was drawn but when did you first discover a sure because I I just want to throw out a quote that you said which is though when you first saw him an exhibition of his you said I had no idea what role I would play in his life or he and mine I don't remember saying that but I could have said that I'm telling you Roger it was recorded by the BBC for well anyway yes I went to the it was what 1950 1954 in Amsterdam that's it okay it's my second year as a graduate student and I just stumble on this show well there is one of one of my lectures that he was just getting off a bus or tram or something and I saw he had had this catalog and what is that it was one issue picture night and day with the birds and I said is that he said oh there's an exhibition going on you probably be interested it and this was in the van Gogh Museum and this was a show I've never heard of Escher before this picture was not there it's an interesting story there too because the geometry coxeter had also been at this exhibition he was the same International Congress of mathematicians which was in Amsterdam at that time and he had suggested to a show to represent this kind of representation of hyperbolic geometry and actually learnt it beautifully and extremely accurately it's amazing without he claimed he was no good at math which is completely false clearly but maybe he wasn't so good at arithmetic or something but he well maybe he didn't understand math could also be visual because one of the points is to make that we skipped past because we got away we said the drawings that you make are are mathematically formal objects yes there are formal mathematical objects that can be calculated with their very dimensional visual geometric visual but not just cartoons you can calculate with them that's right you can sum them you can you know add them you can and then you can read at the end of the day a quantitative result off of the drawing and so that is just Dantas an ingenuity that I just think only you and Fineman really had which was that you can calculate with drawings but he had obviously made a great I mean the Fineman diagrams but no I mean a lot of other people who thought that way geometrical way I'm not talking about I mean I don't think it's a majority but that's a breakthrough it really is but anyway so you're seeing Asher doesn't see himself as mathematical because maybe he doesn't understand he doesn't acknowledge the math you just know you you just stumble on his exhibition yes and then you are motivated by that to think about some things yes I don't know this is a paper you wrote after you saw Asher's exhibition with your father LS Penrose and our Penrose are the authors of this paper that's right and you reference and you did not know Asher at the time of writing this no we had been to the Escher I don't know you've got that picture of what he called relativity with but you see had seen that one in the exhibition it was a big room yeah it was a big room with all these Escher yes that's the one yes and I remember being particularly struck by this one but there were all sorts of amateur which I found completely and so I went away and I thought I'd like to try and do something I'm not at that sort of level but I'd like to do something impossible that I hadn't seen in the exhibition who doesn't want to do something impossible yeah I'd like to do something impossible yes any possible picture well you see I started drawing things with rivers and bridges and roads going and then I whittled it down to this what I thought was kind of the most this is the impossible you're famous you drew this one actually this is and I drew this picture and exact one but I drew one of those pictures and I showed my father and then he started drawing in possible buildings in possible college I remember he drew a picture then it sort of developed this into this staircase and we hadn't seen anything quite like that in exactly inertia in the meantime Asha had produced what the one he calls Belvedere this is from your paper with your father staircase yes yeah and then sure does this watch is based on there we sent a copy of the paper you see the wood we written this paper and we couldn't think what the subject was she said wouldn't know this is a subject and then my father said well I happen to know the editor of the British Journal of Psychology so let's make let's say psychology so he's pretty sure I could get his exception so he sent it to the British general psychology and indeed and then we sent a copy to Escher and it was some friend of my father's I think were forwarded to Asia I don't know got to have it but anyway so he had developed these two prints the waterfall which I think but he sends them to you directly personally doesn't he he the original drawings oh yeah well I I had the when my father got the original of the staircase which has a dedication in the corner it's lovely and it's about ash Mallya now it is actually I don't I've actually got nine ashes I don't know how I've got Justin yellen's that's how that's how this works well he directly gave me one when I visited him you see in no I I've had this phone number because my father communicated with him and that just out of the blue phoned him up and he said just come round and I also understand that somebody gave and I just happened to have found this just accidentally that somebody can we turn the volume off of this sorry volume off volume of this was Picasso being handed a picture of one of your impossible drawings that's quite amazing and he said something he was so wowed about what you were doing in geometry and do you remember that hearing though I don't know what he said I think he said something like you should have been a cubist but and by the way I disagreed he should have been a physicist keeping you in physics but he think he said something like you and your father should have been cubist no I didn't actually know you seen any of these things innocence yeah it's quite amazing so that's allegedly if we have a history right Picasso looking at your impossible triangle toe because it's a picture and then this is also just to quickly talk about drawing one of your notebooks which I love which is just full of drawings in math and so I just wanted to ask you about your notions of creativity in math and physics you know when I when I first started studying though subjects I thought they were on creative fields that's thank you for laughing yeah all right and and I thought you know it was just you just followed rules then we're going to talk about algorithms in mind in a second yes and and I don't know exactly when the transition happened when I realized this was an outrageously creative field and this idea of you know drawing in your notebook it's not that you're trying to make something pretty if you're trying to solve a problem and you're trying to use incredibly creative solutions anything you have it's almost scrappy like anything you have at your disposal just solve these incredibly hard problems and I was so influenced by your work because it was so original the idea the approach that the ingenuity of thinking oh I could draw this diagram and then I can see it immediately when the calculation would take me 15 pages if I simply draw one of these diagrams I can see right away where the trap surfaces are where the event horizon is where the singularity is and it was it was really powerful and I'm wondering if you had a similar experience of realizing oh this is a creative field goodness well I mean I can slightly digress from that because you said that it's very hard to say when am I being creative or not I'm not going to find something which somebody found years and years earlier and you don't even know that but you're still being creative I suppose yeah so yes searching for tools to find solutions the way we do with language like we think language is creative when we make original sentences why don't we think we see it of C where math is creative when we make original sentences I think it's awfully difficult since to know about creativeness and so on they say my my take on this is a little bit different i when I was a undergraduate I had a good friend in percival who we used to talk a lot about mathematics and things and we talked about mathematical logic we didn't know much about it but we talked a lot about it well I'd heard vaguely about girdle's theorem which seemed to say as I understood it that there were things in mathematics that you couldn't prove but you're true and you couldn't prove and I didn't like that idea and so when I went to Cambridge as a graduate student I went to three courses which were nothing to do with what I was supposed to be doing maybe that's to be crazy I'm going to course is just nothing to do you're supposed to be doing so I went to three hours doing algebraic geometry and I went to a course by Hermann Bondi on generality not bad so that was amazing amazing course of lectures I went to a course by Paul Dirac on quantity and I went to a course by man Christine on mathematical logic and I learned about Turing machines you know basic idea of computation and that sort of thing and I learned about kernels theorem and I learned it wasn't well I was afraid of that there were things in mathematics that you couldn't see that were true that were true and you couldn't see because it wasn't like that it was like if you've got some restricted way of proving results that you could put on a computer so you want a system of rules that you could put on a computer and you can put the theorem on the computer and say ask the computer can you prove that say and it has a long string of this and maybe it would say yes and if it says yes and then you have to believe it's true now why do you believe it's true because you've looked at those rules you said yeah that one's okay oh I see that one too and you've gone all the way through and you say okay all those rules if you follow those those rules and it says yes it's true then it is true okay what does kurtal do he produces a statements which you can see the way it's constructed that it is true if you believe that those rules only give you truth yet it cannot be proved using those rules no that was absolutely stunning it was absolutely stunning and you know and in my role as translator may I just interject for a second before you continue I know nobody else except for Jim Simon knows what we're talking about so girdle proved that there were facts among the numbers that could never be proven to be true in the context of a particular axiomatic set of mathematics so for instance one plus one equals two can be proven to be true but he proved that there were statements like this statement is unprovable which could not be proved to be true which therefore made it true it's caused the meaning of it you understand that's right because you have to step outside of mathematics to recognize that it's correct true but it was not a theorem it did not lie among the infinite list of possible I mean I'm I'm a super huge good ol theorem fan I'm obsessing about this and it is chilling because it was chilling because Hilbert he was the greatest mathematician of that era Jim didn't demand but he he made a call out to all of the mathematicians to prove that all correct facts amongst the numbers could be proven to be true I mean who wouldn't believe that that was the case Hobart was conveying completely sensible all facts among numbers that are true could be proven to be true and here comes gold only says no invoices there's infinite he says in fact there's an infinite list of facts but the key thing is that what you mean by proof you see yeah because if you fix your certain set of rules and that is what you mean by proof then you're too limited and what he is showing that there are always other matters no matter how it's always one step out it can't be self-contained it's always one step outside of whatever system you still see by the way it's constructed it's just as true as anything you prove using the rules so what but he goes further and Turing goes further to say that most numbers are numbers about which we know nothing of numbers or numbers about which we don't we will never prove the facts about those numbers so there's levels of infinity and the biggest infinity are the uncomputable numbers where you get a lot bigger than that so this is okay so this is a segue into what I want to ask you about there's a segue into you're asking about creativity and all that yes yeah what I was going to say is that but what I'm trying to say is that you always you could always break out of a system and um you could say that's being creative because you well I'm good or what certainly being creative and using this type of argument which nobody perceived up before but I guess my it has to do with whether we I guess maybe you're coming to this whether our brains work as computers that was the question you were interested in go dolls so so let me just paraphrase it so I can prep for where we're going to go with your other theories which is that you were interested in the fact that there are certain things that can't be computed in an ordinary way and that there are numbers for instance that the relationships amongst numbers facts among numbers and numbers themselves that cannot come out of conventional mathematical algorithmic thinking may just make the convention bigger you see right we did it even then the convention gets infinitely so you see you you were thinking about Turing and Alan Turing of course is the great genius who gave us the idea of a mathematical computer a digital computer a mechanical computer electronic computer and an instrument that computed things by following rules and gödel's theorem suggested well if you follow those rules you're still going to miss a larger infinity effects we're carrying with what we're well aware of the girdle which is where you know a lot of people are like yeah Roger well I'm in contentment you see the geotag no I mean the idea more or less came when I was a graduate student and it was these three courses and I heard the deans course and it tells me it's not quite creativity because you can take girls creativity and it's the understanding then it gives you that was more the point so I trying to say understanding if what girl was telling me that mathematical understanding is not a computable process it's not a computation because the I mean there is all the arguments gets a bit more complicated than that but the basic thing is that you can always once you see how to do the computation you can see how to go beyond it but that's the basic argument and so I came to the view being I was certainly a physicalist and thinking that what's going on inside our heads is this a new agey which is which is where they think you get thrown yeah let me explain yes I certainly believe it's physics going on inside our heads and it's the same physics is going on in that class it's just organized differently but and different things about that physics are being made use of in different ways but you see I'd been to this course by Bundy and I thought about general relativity and they couldn't you what I knew about Newtonian mechanics can you put that on a computer well people do okay you have some little problem of what continuous numbers as opposed to approximations that's that's not a trivial problem but I thought that's was not the issue okay you could put it on a computer you can put Newtonian mechanics on you could for general activity on a computer and people know with LIGO they see these signals and they know well that's because of computations that people know what black holes knew when they spiral into each other and they produce signals like that sure you can put that on the computer what about quantum mechanics when I went to Dirac's lecture well what about quantum mechanics well the first lecture the Dirac gave he was talking about the principle of superposition so he's saying kind of a particle here and it could be the here or it could be here you have states of the world where it's here and here at the same time in two places at once and he saw that Illustrated this is there well why not this piece of chalk he had this piece of chalk I think he broke it in two and imagined it was here and here at the same time and my mind wandered at that point I didn't quite hear what he was saying and he went on to the next topic and I sort of remembered him saying something about energy but I didn't quite see what that had to do with it so I worried about that ever since so I thought ok well here in quantum mechanics you've got this problem which really is a problem which is what we call the collapse of the wave function the wave function says you can have the thing here and here once but you don't see it yet once you see the other here oh yeah that's because well it's Schrodinger's Schrodinger's cat you see he he gave this example of a cat which could be dead and alive at the same time and he was really using this as an illustration of his own equation he's saying if you follow my equation that's his equation then you could have a cat and it's dead in the light at the same time well that's absurd that's more or less as argument well many physicists say oh no extruding it says you could have a cat that's dead and alive at the same time Schrodinger was really trying to say there's something wrong right and I mean Einstein is famous for having to try to say something's wrong the quantum mechanics and it turns out to be true well you see often these things aren't true but this doesn't mean this particular thing is wrong I just want to take a step back say there's a strong AI attitude which you're reacting to so can we just establish the strong AI attitude which you are objecting to which is that computers which are algorithmic yeah are going to create conscious Minds yes would that be fair to say yes I mean that's that's fair that's the presentation of that particular view right but you are saying because gödel proved that algorithms cannot reveal all truths and that human beings are even step out of those algorithms and say well that that's a true fact among the numbers that's not algorithmically provable does that mean that human beings are doing something that algorithms can't would that be fair yeah well it sort of the I mean you have to be a little bit more careful about the argument but basically it is if some people say well you know we've got such complicated algorithm as I heard you can't know what the algorithm is so how can you use I guess that doesn't work what else where that argument because how did this complicated algorithm come about and it's natural selection sure I agree with that but their natural selection did not select against I mean you need this a complicated algorithm we can do girlís theorem it's not selected right so this is what I was gonna challenge you on it's like okay clearly gödel serum says that this particular algorithm can't yield things but I can but clearly what gödel did is algorithmic you could say and then you know it's just met it maybe it's like you're tilings which we are looking at here which we did not get to discuss nobody's ingenious but they take more than one algorithm they take more than one shape it's not possible to do them with only one algorithm the point is whether you understand what they are growth amines I mean you can you can you can put you can here take any other theorem you see which is true and you can to make an algorithm says this particular theorem is true but why do you believe it you've got to understand why that gives you truths you're after something with consciousness sure consciousness is many things it's appreciation of the color blue it's love it's its kindness its pain it's all sorts of things I only concentrate on one little thing sometimes you say why don't you talk because I don't have anything to say about them but this one little thing is the understanding which I'm claiming the quality of understanding is not computation that was my argument and I go to girl or for that okay and it's okay and I think that's indisputable I think you're that's absolutely well they're not invited to the after party okay well that may well be yes quantum mechanics yes shushing me where he's quieting me or a soothing me no no no no no you were so you were soothing my anxiety about quantum mechanics yes no I'm trying to say I'm gonna go through these three lectures I'm sure nothing to do was doing you see maybe it's a to go to courses which are nothing to do with what you're trying to do but you see a particularly the Dracula was this question about why you don't see chalk piece of chalk in two places at once and since I didn't hear his argument which would have calmed me down probably you see I I worried about that ever since so I'm worried about this thing called the collapse of the wavefunction it's something see people talk about quantum mechanics and say it's the most wonderful theorem of the most wonderful theory who ever had in physics what I don't know maybe what is it precisely tested theory in the paradigm and the history of it depends how you see it's very very limited quantum mechanics tests are over a huge range and that's certainly true but the trouble quantum mechanics itself inconsistent theory it's got one procedure which is the Schrodinger equation or unitary evolution or whatever you like to call it which tells you how the state evolves continuously smoothly in time it's got the other part which is what's called making a measurement you look at the damn thing and it does this all that it doesn't do a superposition of this and at the same time that's called the collapse of the wavefunction or the measurement problem was something and it's inconsistent with the Schrodinger equation lots of people struggle to make it consistent they if you do that you're led into what's called the many-worlds view all these things do take place in different worlds so essentially we absolutely all agree quantum mechanics is incomplete in Kinsella buddy and inconsistent people worth much to write in those old days I thought it was much too polite he said and Schrodinger they were a terribly polite they said quantum mechanics is incomplete okay I'm being rude I say quantum mechanics is inconsistent but that's a well accepted fact across all physics it's a well accept the fact that quantum mechanics is inconsistent so but that's fascinating but what does that have to do with consciousness why are you plugging it's agreed so I mean I know that you have been chastised for this and I really think it's a low-level criticism and I really don't want to advocate it but let's put them together and I know that's about what you're doing so you want to ask you to say why that's not what you're doing well because if I mean computational systems I'm trying to say can't do understanding and that's that's the girl business now you see is physics and computational system well if it's Newtonian mechanics it's pretty well a computational system if it's general relativity it's pretty real my computations if it's quantum mechanics in the sense of following the Schrodinger equation it's pretty well at the computational system so we have to look for something in physics which is has a chance of being not a computational system where do we see in physics something like that the only place I could see is in the collapse of the wavefunction because that is you're cheating you're going outside the computational system I mean it's not saying here we have a problem here we have a problem maybe they're the same it's nothing at all that's what you're saying you're essentially saying you believe you're physicalist yeah you believe that the mind is physical obviously and that the structures that we've inherited to understand the mind come from the structure of the mind itself yeah and so it's sort of this loop and then you can say well where where are the things that could possibly give us a hope of understanding something and you're just you're just doing your best guess basically because you're physics but you're essentially you're essentially known for really hardcore on ambiguous calculations like I just also want to point out just before because we're about to break for questions but okay Hawking's very faint Stephen Hawking is very famous for for Hawking radiation which is completely counterintuitive and if Hawking had come out and said black holes radiate I can't really explain it people would have freaked out nobody would have believed it and you also simultaneously concurrently concurrently were proving that spinning black holes had a very similar process in what we now call the Penrose process which which was these are basically ways that things that have no right to generate energy are making energy by exploiting the fact that energy is relative and and it's a very surreal phenomenon that you can spin down a black hole by creating Penrose radiation that a black hole can evaporate by creating Hawking radiation you and Hawking we're really in there man but if you had I guess the point I'm trying to get to is that if you had not formally mathematically proven it nobody would have taken you seriously and here you are mathematically not proving it really going out on a limb for you being really kind of a maverick you know just saying I'm just conjecturing I don't think I can't prove it I think that's I'm giving you an opportunity to respond now you see it's just you know I'm looking for a place where the picture that we have of the world is is fundamentally incomplete or inconsistent in fact and that's the only place that I can see clearly this case and so if you're trying to find somewhere where a process could be non computable before questions I really do want to ask why can't non computable processes be non quantum why do they have to be quantum well I mean what theory are you having I mean whether arc I can give you an example of a non computable approach well I'm not sure it's a good will there is one which is actually due to Dirac which is quite interesting it's non computable I think it probably is direct it's rather amazing because he had the equation of the electron which is the Dirac equation which is one of the most beautiful and exact eriously as we know which describes how electrons behave but he also toyed with ideas classical models of particles which could really charge particles moving around to each other and radiating in in order to make this work there's a little problem with making because they act on themselves that's the trouble the charge particle so the problem because the charge has to move into his own field as well and so you have to have ways of getting rid of that and his he had ways of getting rid of that and he produced this scheme where particles the trouble was that the there were too many solutions to the equations rather than being second order they were third order that's the technical point but there was the thing and what you found is that these charged particles running around every night again and they would start accelerating just by themselves and they go shooting off faster and faster and that's not something you want so you had to restrict the solutions so they never did that and then that was the kind of model but the trouble is how do you know they're never going to do that because they might wait a hundred years and then suddenly one of them does that so you have you it's it's basically a sort of a non computable problem because you don't know simply by a computation if ultimately something is go shooting off self accelerated I think it's an example of a non computable classical I sometimes I wonder if the entire universe is a non computable classical problem but before we open up to questions I just want to work him back to the time that you are working on Bower calls yeah and you probably weren't sure they were real at the time you were working on them and here you are you know 2019 working on consciousness and there's got to be a part of you that's not sure this is real if that's what yes yes honestly I'm pretty sure I'm just imagining all you up so are you I see how comfortable are you with the ideas of consciousness that you're I think we're less further away again I think we're much further away from an understanding you see the black holes was pretty good idea I mean a lot of things which you know people had to work out complicated calculations about what they actually do in detail but the general idea was pretty clear there whereas the issue of consciousness first of all it depends on a physics that we don't know yet which is what really happens with the collapse of the wavefunction and there are experiments the longest-standing one that I know of is by Derek Baumeister who is a Dutchman who I known for about 15 20 I'm not quite sure when I've met him first but he has designed an experiment where you put a little tiny mirror is a mirror which is about a tenth of the thickness of a human hair a little cube actually and it's just too small to see but you hit it with a photon which is being split now what does that mean you have a photon and it goes through a half-silvered mirror which means part of the photon goes this way and part of it goes that way you've got to believe that the photon is in two places at once quantum mechanics says yes it is so you have to believe that okay that's fine may not seem fine but it's fine okay now the photon is doing these two things at once now one of these beams this this part of the photons existence you keep using what's called a cavity so you flicked it backwards and forwards and it just keeps there the other one you have a funny kind of cavity which consists of a mirror which is a sort of Hemisphere and it hits this little tiny cube about a million times backwards and forwards and it pushes it in there just I mean the whole time kind of show criticism so that because the photon is here and here at the same time it's pushing the little mirror and not pushing the middle so the so time that's not there it's pushing in the mirror yes for the one that's not hitting the mirror isn't moving it so the mirror is moved and not moved at the same time so it's a shoulder Schrodinger's cat it's in two places at once now according to the scheme which I put forward some while ago you can because of gravity effects on quantum mechanics you can estimate a time scale for that for it to become one or the other and that time scale you'd like to say something like seconds to minutes so I think that's the sort of I'm not quite sure what where the experiment is now but it's it's pretty close to being done and the thing is that you could tell whether of this little mirror has become in one place or the other in seconds two minutes or whatever the criterion is depends on what its mass is and this distribution of particles in it and so on but it's a pretty clear experiment now according to standard quantum mechanics it would never become one of the other it would remain in two places at once but according to the type of scheme which I'm putting forward which is where gravity has to be taken into consideration and this is the gravitational field of a little mirror so it's a very tiny gravitational field when you take that into consideration you see there's a conflict with quantum mechanics the very basis of general relativity the principle of equivalence which we talked about before that principle is in conflict with the superposition principle of quantum mechanics and so is this conflict really being shown up by the fact that this little tiny mirror becomes in one place or the other and it's really exciting because when I saw him last which isn't in Vancouver at a conference he was pretty well indicating that within two or three years he will have an answer to this which is pretty consistent with his predictions because I was in I was in Leiden where his base one of his bases his Leiden and Santa Barbara in California and he at one point quite spontaneously without prompting said in ten years we'll have an answer I saw him two years later and he said seven or eight years we'll have an answer then I saw him in Marseilles and then I saw in Vancouver and he's pretty consistent he was saying he dropped a year or two but not much he was saying in two or three years we'll have an answer so I think he's probably right and does this remain the central focus of your interest what an issue of consciousness no mechanic's consciousness I don't think we're gonna have an ounce the consciousness for a long time so just like anacs you were just describing do you see the core bitch's widget like if you're a betting man another you got quantum mechanics and one stuff yes what are you betting on the cyclic cosmology first because we already have pretty good evidence for that people don't believe me but that's because they haven't looked at the data don't know there's really good evidence there that's that one I think is number one number two is the quantum experiment maybe with their other experiments there I have a colleague Evette Forte's who has an idea using bose-einstein that maybe it works and if so it might be done quicker I don't know but anyway in a few years we might see that so so that's number two consciousness way off I don't think we're going to know for a long time yeah but the ingredients that I consider to be necessary would be in this mystic experiment or something similar to see whether quantum mechanics really does break down at that level so essentially the underlying theory that you're looking for for consciousness would also be the underlying theory for all the other things well it could be shown wrong you say yes but if it works for consciousness it works for everything I'm not sure about that on that note on the note of uncertainty I really want to open this up to questions because we're pushing our audience to really late but please before we open it up to questions let's take a moment to thank Sir Roger you

Channel: Pioneer Works

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Keywords: sir roger penrose, roger penrose, nobel prize, janna levin, science studios, pioneer works, theory of relativity, penrose tiles, scientific controversies, stephen hawking, nobel prize physics, event horizon, Andrea Ghez, supermassive black hole, gravitational waves, nobel prize winner roger penrose, roger penrose talk, roger penrose janna levin, impossible triangle, singularity explained, black holes explained, black hole explainer, physics explainer, physics explained

Id: xi_auG9R-Wo

Length: 78min 55sec (4735 seconds)

Published: Tue Oct 06 2020