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Good evening.

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My name is and I go, really and I'm in charge of external relations for the Mathematical Institute tonight for the Oxford Mathematics public lectures.

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We have a very special event. But before we proceed.

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A special thanks to a sponsor market because markets are leading quantitative driven electronic market maker with offices in London,

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Singapore and New York. The ongoing support is crucial in providing you with quality content.

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No, it is usual to say that a particularly prestigious speaker does not need an introduction.

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This is especially true for Roger Penrose, code winner of the 2020 Nobel prise in physics, for his work on black holes.

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Tonight, we will join the celebration and explore its work and life in details.

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The event will have three parts revolving around Roger black holes and singularities.

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As Sherlock Holmes once said, Singularity is almost invariably a clue, and much of Roger's work follow that clue.

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First, we will hear from Dennis Lam from the University of Bonn.

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It will introduce the general concept of spacetime singularities and black holes and Chris Rogers work in a story called Context Segun.

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We will hear directly from Roger about his own work.

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As you probably know, Roger is also an extremely talented public speaker, and I've always enjoyed his lectures.

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Finally, the lectures will be followed by an interview with Roger by Melvyn Bragg men.

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Melvin Bright does not need an introduction, either. As you probably have listened to his wonderful BBC radio programme in old time.

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On a personal note, I've had the great pleasure and privilege to interact with Roger the Mathematical Institute.

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I would like to echo the voices of many in the institute and say that, of course,

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I've always been impressed by his brilliant intellect, but also by swarms as a human being.

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So one more time congratulation Roger, and a very much look forward to tonight's event.

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Denis, please start. No. Space, some similarities amongst the most fascinating ideas in the history of science.

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They are also amongst the most puzzling.

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What are they are they objects that could actually exist in nature, or are they artefacts of our mathematical reasoning?

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And how are they related to black holes?

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At different points in the history of general relativity, ideal for short, different answers to these questions have been given.

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Major milestone of this story was Roger Penrose, a singularity theorem of 1965,

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which changed our entire thinking about space, time singularities and indeed our thinking about air more generally.

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The purpose of this lecture will be to put this theorem into its historical context and to prepare you for selecting

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his own lecture on how he found the theorem and on how his thoughts on the topic have developed since then.

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Everything starts with three questions. The first question is, how does gravity work?

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And in 1915, Albert Einstein gave an entirely new answer to this question.

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In 1920, Arthur Eddington answered the question how to start work and the two questions together, as they developed over the next decades,

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brought about a third question which was answered and the work of Roger Penrose

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does the gravitational collapse of stars lead to singularities in spacetime?

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Now, how did all that happen? Here's a.

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Snapshot of Rogers paper from 1965, which bears the title gravitational collapse and space, something it urges.

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In the next half hour, I will try to show you how this phenomenon became related.

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And here are a few sentences from the introduction Do not worry, if not, everything becomes clear immediately.

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It's the purpose of this lecture to help with it. So it goes most exact calculations concerned with the implications of gravitational

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collapse have employed the simplifying assumption of spherical symmetry.

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The general situation with regard to factory symmetric body is well known when sufficient thermal energy has been radiated away.

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The body contracts and continues to contract until a physical singularity is encountered at the centre of the body.

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As measured by local court moving observers, the body passes within its transfer radius,

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the question has been raised whether this singularity is in fact simply a property of the high cemetery assumed

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it will be shown that deviations from Straker symmetry cannot prevent space time singularities from arising.

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And what we're going to do in the next half hour is to essentially introduce the core concepts of

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these claims and to make it visible how much of a game changer the result at the end really was.

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So we're going to talk about the notion of gravitational collapse and how it's related to spherical symmetry,

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which was a major assumption in earlier work on gravitational collapse by Oppenheimer and Snider,

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criticised by Wheeler and referred to by Penrose in this footnote number two.

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We're going to discuss about different notions of singularities, clarify what a sponsored radiuses connected to the so-called sponsored singularity.

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And we're going to put into a wider context why it was such a game changing result.

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A deviations from sorry symmetry cannot prevent spacetime singularities from arising.

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Now to start with here is the general structure of panels,

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this thing clarity here and indeed Penrose is theorem served as a blueprint for all later

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singularity theorems and completely changed how physics thinks of what a singularity actually is,

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and whether accepting G.R. means that you have to accept the existence of singularities in spacetime.

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He has the structure of the 1965 theorem in particular, and I'm going to argue that almost every part of it.

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What came before it on its head is the first assumption which says that local energy is not negative and

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we're going to see this if this is a far more general assumption than any assumption of collapsing matter,

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that it can be flat.

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We're going to talk in detail about the newly introduced concept of a track surface and why it really changed so much in the history of China.

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And even the conclusion. The conclusion that incomplete duties is.

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We'll follow from these conditions and bring about a singularity in space time was new because it was a new way of thinking,

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but what a singularity really is. Yes, we're going to see.

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But to appreciate how radical these changes were, how much of a game changer the first singularity theorem actually was.

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We have to understand what came before it.

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We have to understand how we got from Einstein's derivation of the perihelion of mercury to that of sponsored singularity.

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From there to had a mass catastrophe and ancient argument that the catastrophe would never, ever happen.

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And we have to understand Oppenheimer's and Snider's thoughts on the gravitational collapse of a star before

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we can understand the significance of Penrose as newly introduced concept of a trapped surface in spacetime.

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And what follows from it? Now we're going to structure the whole thing by looking at the three questions I mentioned at the beginning.

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First, how gravity works, how stars work and whether they might be able to collapse.

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And finally, this will point us to the question of what is space time singularity is and

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whether it's linked to gravitational collapse and the existence of black holes.

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OK, first, the question how does gravity work?

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The whole thing starts in 1915, when Albert Einstein introduced, what would you take while the Einstein fielded questions,

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the new gravitational law that was supposed to replace Newton's gravitational law from hundreds of years before.

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The equation links the gravitational field on the left hand side associated to the

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curvature of space time and the mass energy of matter on the right hand side.

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Essentially,

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the equation says that the more mass and energy you haven't given region of space time and depending on what form and shape that mass and energy has,

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will create a particular gravitational field, the particular curvature of time in that region.

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Now you have the two equations again. The full ancient equations with mass energy of matter as a source and the special case,

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when no matter is present and when you have a pure gravitation of fear, which is described by solutions to this equation.

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In fact, every solution to these equations represents a universe or a part of the universe that is possible, according to Jia.

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And in 1915, in the same month in which he found defeated questions,

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Einstein set out to describe a particularly important part of our universe, namely, he wanted to drive the path of Mercury around the Sun.

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That's a problem that has caused some trouble for Newtonian gravitational theory.

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And Einstein thought that his newly introduced theory of gravity should be able to do better.

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And in setting about to solve this problem,

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he took the linear sized vacuum equations the nearest because he knew that the gravitational field of the Sun was comparatively weak.

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And so he could use the linear equations. He was also only interested in the exterior gravitational field of the Sun, not in the Sun itself.

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And so he took a solution to the vacuum equations.

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The Sun itself did not need to be modelled in order to know how its gravitational field influences matter.

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This is going to be important. He further made three assumptions about the gravitational field that the Sun would produce.

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First, he assumed that the field would be strictly symmetric because the Sun itself is approximately spherical symmetry.

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Second, the gravitational field would be static because the sun is approximately static doesn't change very much,

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at least as far as Mercury is concerned. And third, that the gravitational field would be some trophic effect.

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But far away from the Sun, the curvature of space would tend towards flatness because the gravitational field becomes weak.

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Now, Einstein did not really expect that an exact solution to his complicated equations would be possible,

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and the approximate solution was good enough to give a precise calculation of Mercury's path.

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But only a few months later, co-sponsored astronomer. And the exact counterpart to Einstein's 1915 approximate solution.

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And you see the solution down here, every solution of the ancient equations gives an interval that is formed by the metric tensor,

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which gives the distance between any two points in spacetime. And transit solution had two surprising properties.

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Well, at least one surprising property, it had a single entry in the centre.

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And that Centro Singularity was not quite unexpected.

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This fairly symmetric solution to Newton's gravitation equations had a singularity at the centre to the point where the gravitational field,

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while the components of the metric tensor tend towards infinity.

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Schwartzman and Einstein interpreted this singularity as a placeholder for the Sun that had not been included in the model.

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But there was also a second singularity, and that came as a bit of a surprise.

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Plus, it had a ring like shape. So you see, here's is the centrist singularity.

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She has the ring shaped second singularity that has no counterpart in Newtonian gravitational theory.

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Both ancient and fashion were a bit puzzled about this,

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but I it eventually convinced the two of them that it wouldn't really be a problem because for any realistic star,

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that ring shaped singularity would be inside of the star, not really accessible to any possible measurements.

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So there was no real problem without what I would call the centrist energy.

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It was the so-called sponsored singularity ActionScript, but some by others so-called with a drink with its ring shape that puzzled everybody.

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And discussions about the nature of this structured singularity came to a head in April 1922,

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when Einstein gave a series of lecture at the collection of class in Paris.

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So you see him here discussing something that looks pretty similar to what I just said in the previous slide.

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Turing's that might well be one of them. The outer surface of the Sun and the second the swan should singularity with its ring shape.

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Now, at this conference on the 5th of April 1922, Jack Harman's great French mathematician asked Einstein what if a star were to be so massive

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that it sponsored Singularity ended up outside of the star announced and immediately answered.

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This would be a catastrophe for the theory.

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Now, only two days later, Einstein came back and said, well, had a mass catastrophe would never, ever happen.

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Calculated that before a star could accumulate sufficient mass to be entirely contained within its own

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structure to reduce the pressure at the centre of the star would become infinite under such conditions.

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He said clocks would not run and thus time would stop preventing the drama catastrophe from ever developing since nothing develops without time.

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Now, why would it have been a catastrophe in the first place? Einstein was fine with introducing singularities to stand in for matter.

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Some. As long as singularities could be interpreted as a placeholder for matter, rather than something that actually exists.

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Everything was fine, fine. That's why he did not worry about the central singularity in the transport solution.

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But singularities were not supposed to actually appear in nature, and that's what was at stake in the debate with Hatami Harriman.

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Asked if a star could be so heavy that its fractured singularity would be outside of the star and actually appear an empty space?

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Now, discussion during the 1920s kept focussing on the nature of the sponsored singularity and how it should be interpreted.

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Here's a quote from Arthur Eddington from 1920.

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He said about the structured singularity there is a magic circle which no measurement can bring us inside.

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It is not unnatural that we should picture something obstructing our close up post and say that a particle of matter is filling up the interior.

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So for Eddington, it seemed like a barrier and other names introduced in the 1920s,

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there was a real cottage industry introducing ever new names for this wretched singularity when in the same direction.

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Schwarzer himself called it the discontinuity caller called it the barrier while quoted sometimes the sphere,

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sometimes the gravitational reduced pricing pressure quarter to the hole in the world.

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Quite prophetic, given that as we would see, the structured singularity will eventually be related to the event horizons of black holes.

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Clearly encoded the singular frontier, the catastrophic frontier, the limits circle,

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and not one the person who took the notes at the Paris meeting simply quoted the death.

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Now, I have not seen anybody comment on this, but it's a bit surprising,

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it's a bit ironic that the person who introduced to discover the sponsored solution and the sponsored

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singularity that would eventually be called would eventually be related to the event horizon of black holes.

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Was cars fashioned who if you translate his name into English, the name would mean black shield.

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Accident of history. All right. So much for now about the development of the theory of gravity in the 1910s and the 1920s.

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Now let's turn to our second question. How do stars work? And first answer to this question.

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This promising answer to this question was given by Arthur Haddington.

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In 1920, Eddington suggested that stars shine because of the energy produced in the nuclear fusion of hydrogen.

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The resulting outward radiation. The resulting outward radiation pressure.

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Is what keeps the staff from gravitationally collapsing? Because if there was no pressure to the outside,

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then an object as heavy as a star would simply collapse under its own gravitational attraction under the gravitational attraction of its parts.

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But this immediately created the question What would happen when the star runs out of hydrogen

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to burn and thus out of the fuel that makes the gravity radiation pressure to the answer happen?

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Then only the inward gravitational attraction would remain. Would the star collapse?

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And if so, would he find a new equilibrium state become a smaller star, less bright but still stable?

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Well, in 1935, Chan Rasika calculated for the special case of a neutron star kind of star that in principle could become the smallest possible star.

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That's if a neutron star is heavier than a particular limit.

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There will be no new equilibrium state. This suggested that the star will just continue collapsing to ever smaller regions of space time.

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This line of thought was further strengthened by a calculation of Oppenheimer and Snider in 1939,

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who quote that paper on continued gravitational contraction. Oppenheim and Snider constructed an explicit it's symmetric model of a collapsing star.

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They predicted it collapsed collapse continuously without ever achieving a new equilibrium condition.

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Collapsed within the ring formed by its fractured singularity. They also predicted that once this happened,

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what lies within the boundary formed by the structured singularity would not be accessible to an outside observer anymore,

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and the outside would not be accessible to the observer. Within the boundary formed by the structured singularity ensured they predicted a

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collapsing star to turn into an object that would soon be called a black hole.

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And they predicted that as a result of this collapse, the central singularity of the Schwartzel solution would form.

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So if Oppenheimer and Stein are correct, then what Einstein and Rothschild thought of as a placeholder for matter could actually come about in nature?

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Now, did Oppenheimer and Snider falsify Einstein's reasoning of 1922?

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I think not, because Oppenheimer and Snider make idealising assumptions that the pressure inside the star vanishes.

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Westphal Einstein the assumption of a non vanishing pressure played a major role in his argument.

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Thus, Oppenheimer and status analysis rests on two very specific assumptions that the

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gravitation of fear of the collapsing star is exactly spherical asymmetric,

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and that the metal of the stars made off can be idealised as pressure less dust.

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Now, as we're going to see, Penrose would show that the major results of Oppenheimer and stator that of continuing

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collapse and that of a formation of a centre singularity do not depend on these assumptions.

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This brings us to our third topic where gravitational collapse and singularities come together.

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Relativists analysed the Swatch institution by using ever new coordinates systems,

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some of them got rid of the puzzling and now famous sponsored singularity.

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And in them, it looked like a completely normal part of spacetime. Such corporate systems were found by Eddington in the 1920s.

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The Matt and Robertson in the 1930s and by David Finkelstein in the 1950s.

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But the interpretation of the school and its systems remained controversial and knowledge of them did not really catch on,

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even when Finkelstein rediscovered arrangements for that system in 1956. Many people spoke of the structure of singularity.

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Shortly before Finkelstein had published on his governance system, John Wheeler had entered the study of GM.

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Remember that witness paper was sited next to that of Oppenheimer and state owned panels opening paragraphs?

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Wieder was a nuclear physicist and was lured into jihad by studying the work of Oppenheimer's group from the 1951 onwards.

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Willa Harrison and Marcano reconsidered.

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Oppenheimer started in 1957 using some of the earliest computers to model the gravitational collapse of a star.

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Way into the 1960s, when I was very sceptical of Oppenheimer's nineties prediction of continued collapse.

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He expected that general activity was not trustworthy beyond the shots at singularity and would need to be replaced by a quantum theory of gravity.

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Yet to be found. Still, it was Wheeler who made the term black hole stick for the type of object that Oppenheimer and

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Snider had described and who spent decades of his life researching the physics of black holes.

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Now, also in the early 1960s,

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the Russian School of Racket Activity took aim at the central singularity that Oppenheimer and Snider had claimed would form.

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They wrote a paper so salvage and in particular,

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Lifshitz and Kalashnikov wrote a paper that argued that Oppenheimer's and standards analysis of gravitational collapse

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is not generic and in particular that if you did not have perfect spherical symmetry of the collapsing matter.

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A central singularity would not fall.

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And that suggested that the fact that the centre singularity did form and Oppenheimer Cincinnatus analysis was an artefact,

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a mathematical artefact produced by the assumption of symmetry.

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Now, so far, everything I've said was mostly about theoretical G.R. and how gravitational collapse could in principle happen to stop.

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There was no so far no relationship to any heavenly bodies.

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This all changed in 1962 and became clear, especially in 1963, if the first Texas conference,

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which brought together mathematical service and astrophysicists because quasars had just been discovered.

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Here's a picture of the quasar 3C 273, the brightest quasar on the night sky.

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And a quasar. It's a fascinating object, Iguazu can emit more energy than our entire Milky Way galaxy.

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Now you might ask, how could it be that these objects were only discovered in 1962 if they're so energetic?

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The answer is because all that energy is met.

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It is admitted in the radio spectrum and we don't see radio waves with our bare eyes, nor with our optical telescopes.

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And so radio telescopes had to be developed before quasars could be observed.

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And this picture of a quasar was discussed at the 1963 Texas conference.

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Here's a picture of the same quasar the brightest one in the sky from 2013 from Hubble, but a pretty good picture.

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Now, how is all this related?

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The idea quickly came up that the source of all that energy put out by crisis could be the gravitational contraction of a star,

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the death of a star and produced an enormous outburst of energy.

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And well, so suddenly, all the calculations by mathematical relativists about gravitational collapse became immediately relevant to astrophysics.

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And everybody was happy.

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Tommy Gold, at the after dinner speech at the Texas conference, summarised up the spirit of the conference and said everyone is pleased.

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The relativists who fear they are being appreciated, who are suddenly experts in a field they hardly knew existed.

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The astrophysicists for having enlarged the domain, the empire by the annexation of another subject, general relativity.

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Roger Penrose was present at this conference and was inspired to revisit his thoughts

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on gravitational collapse and the formation of singularities from years before,

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especially in the light of new mathematical tools that he had developed in the meantime.

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Now, one can interpret Eddington Limit and Robertson as having understood that the structured singularity is not a real singularity,

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but a coordinated singularity, an artefact of the court and system chosen.

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But it took Finkelstein and Rentschler to fully realise that though the fractured singularity might not actually be a singularity,

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it is something else. In 1956, Greenblatt called it an event horizon defined an event horizon that's a boundary in space time,

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which divides all events into two non empty classes. Those that have been,

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are or will be observable by a given observer and those that are forever outside a given observe as possible power of observation.

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While the Schwartzman's solution, this meant that no observer outside of what was formerly called the sponsored singularity can observe what

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is going on inside and no observer inside this event horizon can ever observe what is going on outside.

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Penrose understood all this, and he would tell you himself how Finkelstein and Rentschler influence just work.

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But in a way, all this meant that those strange the structured singularity was not as big a problem as physicists had long thought it to be.

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In contrast, the centrist singularity of the structures solution that originally nobody was worried about had

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become more and more threatening with Oppenheimer Sunstein as omniscience of gravitational collapse.

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Well, there it looked as if such a singularity could actually arise in nature as the result of a physical process, namely gravitation.

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A contraction of a star wheeler, slovic,

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Lifshitz and Kalashnikov had argued that this was an artefact of the spherical symmetry assumed by Oppenheimer and.

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And this is where Penrose this theorem entered the fray.

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We're now in a position to understand the project the panel's outlines at the beginning of its 1965 paper.

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We understood what came before.

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What kind of gravitational collapse had been envisaged and how in the work of Oppenheimer and Snider and criticised by Wheeler,

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spherical symmetry played a major role. And especially how the spherical symmetry had been argued as being maybe

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responsible for a physical singularity being produced at the centre of the body,

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according to Oppenheimer and Snider, it was to speak spoken about the structured radios, which used to be called the Schwartz with singularity.

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But by now, when Penn Resort had been re conceptualised as an event horizon, especially by Rinella,

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even though the battery conceptualisation would only really catch on after the work of Penrose into the 19 late 1960s,

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and we can also now appreciate why it would have been such a big deal,

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why it was such a big deal that deviations from spherical symmetry cannot prevent space time singularities from arising

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because that went entirely against the development that had been going on in the previous 20 years when Willa Lifshitz,

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Kalashnikov, everybody expected that the formation of a centre singularity was only an artefact of produced by the stroke of symmetry.

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Assumption employed by Oppenheimer Stop.

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We are also now in a position to see that at least two of the premises and the concept used in the conclusion of Penrose as 1965,

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there were utterly game changing. Regarding the first assumption.

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If you think back to what I said, all previous treatments of gravitational collapse had assumed a very specific model for the collapsing,

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but Penrose only assumed that whatever the collapsing stars made of whatever symmetries the matter has,

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and no matter whether it is subject to pressure or not, the only assumption needed is that its local energy is everywhere, not negative.

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It's an incredibly minimal assumption about the matter concerned. Translated into a condition on the curvature tensor,

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this brings about a focussing of enthralling light rays, and Roger himself will talk more about this.

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Now, the concept of a chat service that is introduced in the third premise was truly revolutionary,

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or it was one of the first global concepts in GIA, and it managed to ship around all the previous problems involving code and systems and symmetries.

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I will say more about what it is in a moment. Finally, you've seen that previously, whenever anybody talked about a singularity,

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what they referred to was that the metric tensor or the curvature tensor would tend towards infinity.

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The problem was that you could never really be sure whether this behaviour was subject

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was because of the coordinated system chosen or whether it reflected something deeper.

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The idea of moving away from thinking about whether the metric of the curvature tensor becomes inverted and

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towards thinking instead about whether the path of a light rail is complete or instead suddenly stops,

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which is the incomplete GTC referred to here. And to take this as a sufficient criterion for that to be a singularity was another game changer.

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Now it is today hard to fully appreciate the ingenuity, but the concept of a chat surface demanded at the time.

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Note that it needed a coordinate system like that of Eddington and Finkelstein to be brought about.

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And yet the concept itself does not need any reference to a cornered system, and it does not rely on the space time having any symmetries.

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It boldly allows for a global property of space time. Why the consensus for half a century had been that only local concepts are to be trusted.

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That had been the whole push to once shy away from Newtonian theory.

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So here's the basic concept basic idea of a track surface after the stars collapsed within its transit radius,

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which has now been understood to not be a singularity.

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The sphere can be found in the empty regions surrounding the collapsing matter, and the sphere is an example of a trapped surface.

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Light rays, which means that light rays emitted from within that sphere, no matter in which direction they are shot.

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Will always converge in what's. And here is A. This conclusion from the 1965 film about how Jack surfaces and singularities are related.

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He says the existence of a trapped surface applies irrespective of symmetry that singularities necessarily develop.

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And the singular behaviour that he speaks of here is exactly at the path of light race cannot be extended further,

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but it suddenly stops and the case of the structured space time, this happens exactly at the centre.

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So if this is the track surface laden race, I might add somewhere here,

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they will all converge inwards towards the singularity where their path suddenly stops,

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and this is taken as a sufficient criterion for the presence of a singularity.

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In the case of the structured solution, the outermost track surface is located at the structured radius, i.e. at the event horizon.

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Thus, what I said and swatch of thought of as the swatch at Singularity is actually something entirely different.

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It's how been reconceptualize as an event horizon.

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Something very different from a singularity and a concept that had not been available to Einstein instruction.

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OK. So Einstein and Schwartz should have thought of the centre of the structured solution as harmless.

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Of the centrist and hilarity of this fractured solution as a placeholder for the start itself,

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but for general showed that four collapsing star and without making any assumptions about the symmetry of the style about what it consists of,

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a singularity like this will actually arise in nature.

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If it is right, then such a singularity is not just a mathematical placeholder, but something that could actually exist in nature.

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It would come into existence as a result of collapsing matter and the formation of a black hole.

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Now, and this was brought about by Richard Penrose, this would.

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But what about Einstein? A. Singularity argument his argument against the paramount catastrophe?

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Well, remember that Einstein's argument went against the possibility that the Schwartz should singularity could ever end up outside of Oppenheimer,

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and Snyder showed that this is possible and thus that black holds impossible.

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But Finkelstein and Penrose showed that the sponsored singularity is not a singularity, but an event horizon.

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Now, would Einstein be reconciled by this?

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I think not for the centrist singularity to to appear in nature would have been equally catastrophic for him.

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Now that it can't be interpreted as a placeholder for matter,

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but must be seen as the result of collapsing and something that actually appears in the universe.

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And what about wena scepticism, about space, time, singularity, superior nature?

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Does the existence of black holes necessitate the existence of space, some singularities?

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Well, yes. If she is trustworthy all the way down into a black hole, Penrose,

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a singularity theorem shows that singularities an inescapable consequence of G.R. and that they will inescapably form in gravitational collapse,

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as described by Gaia. But as structure would be the first to admit and indeed did admit already in the 1965 paper,

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Wheeler's dream of complementing classified air with a quantum theory of gravity that kicks in

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beyond the event horizon and might stop singularities from happening and coming into existence,

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remains an open and viable project. Now, I would like to finish with two quotes.

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The first is a quote by Griffith and Podolski on a textbook on the exact solutions of ancient equations.

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They wrote It appears that it is much easier to find a new solution of ancient equations than it is to understand it.

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Well, and given as we've seen that it took that it took structured only a few months to find the Schwartzman's solution.

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And yet it took more than half a century to properly understand sponsored solution,

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which is the simplest exact solution of the answer to any questions. I think Griffith and Polonetsky have a point.

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Here's a second quote, which is from pretty patient. He's writing about the history of quantum mechanics, but I think the case of Paciencia.

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He writes how difficult where these advances, if we now acquaint ourselves with some of the detours, errors and psychological blocks.

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It is not to console ourselves with the thought that even the great physicists do not always move in a straight line,

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but rather to grasp in some measure how difficult it really was.

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Well, this points us to the question,

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how did Roger Penrose actually come up with a singularity theme and all of the new concepts and ideas that went into the Singularity theme?

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If you think back to what's the last half hour, you'll see that haven't really told you how he came up with it.

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I only told you what was there before and showed you how all these concepts that he introduced put the entire state of the discipline on its head.

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Well, with that, I turn over to Sir Roger himself,

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who can tell you how he came up with this year and how his thoughts on the topic have developed since then.

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Thank you. With this talk is sort of my Nobel lecture, but a little bit different.

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This first slide shows. Four dimensional space, that is to say, I've got three space axes and a time axis.

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Now this space time is actually you two in Kosky rather than Einstein.

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But I didn't like the idea when he first heard of it, but nevertheless you got used to it,

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and then he it was crucial to his theory of general relativity.

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Now in the next slide, I'm going to show you what a light rail looks like.

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So imagine a photon which is whizzing along with speed of light.

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Now an order that shouldn't be just sort of in the special direction pretty well.

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I want to make the axes. So the speed of light is comparable to actually.

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So if I if the time is in seconds, then the space would be inspected in light seconds.

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If it's years, then it would be not years. So it's 45 degrees or some reasonable angle.

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Okay, so that's that's the photon. I'm really interested in the hope possible photon trajectories that gives us the nail cone.

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So the red there you see the can, and I'm more interested in the outcome.

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And in the particular light red, because it really represents all light rash.

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So that should move the light right, impacting into moving the axes.

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We don't need that. The crucial thing is the light that's the most important structure in spacetime.

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It's almost all of the structure I'll come to later. Well, completed to be more of a structure, but it's almost all the structure now.

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In general, relativity and special relativity light cones will be all uniformly arranged.

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But in general, relativity, where the spacetime is curved and now represents, represented it in this picture, where the looks like a surface.

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But you must imagine that the surface there is. Four dimensional and that the cones also have another dimension to them because the

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end of the cone looks like looks like a circle and looks like a circle flattened out,

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but it really should be a sphere. So you've got to imagine if you can beat the cone really has a sphere at each end of it.

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OK, well, let's go on to the next picture. Now, the important thing about space time is it represents the history of things.

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Now if you have a. Particle, which is moving the speed of light on the left hand side, you see a massive particle.

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Its trajectory is always within the cones. It's travelling less than the speed of light, if you like.

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That's what that means. Whereas a photo travels with the speed of light, it's always tangential to the curve.

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Now you see these little cones represent usually alcohol and are now cones, but the lichen,

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if you like you have imagined that a flash of light occurs at this point in the middle.

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Just note on the left, the suppose there's a flash of light there, and then the light worked its way out.

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And because the space-time is curved, it may do funny things later on.

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It starts out quite reasonably, but then it may start crossing itself.

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So you see at the top right hand side, you see the light rail start crossing over and we get what's called a cross section, the crossing region.

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And it's important to realise that these things happen because in the general space, time light cones can behave in this sort of way.

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OK, now let's move on now.

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I want to describe a little story here because I first got interested in general relativity, but my brother told me a few things about it.

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When I was young and when I was an undergraduate, I bought a copy of Schrodinger's little book Space-Time Structure.

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Very nice little book, where he described the ideas of general relativity.

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So I had some little bit of a feeling for the subject and also a little bit later.

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I think when I was an undergraduate, I was listening to a.

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Some lectures given by Fred Hoyle. I think there were five of them or something like this, and he was talking about it,

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first of all, he asked and they went out to Solar System and further and further out.

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And then he started talking about cosmology,

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and he was describing the particular view of cosmology known as the steady state model and the steady state model.

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You have the universe expanding all the time. The problem was at that time that there were two observations which seemed to contradict one.

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No one was certain clusters of stars called globular clusters, and they seem to be very, very ancient.

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And the age of the universe is calculated from the Sun.

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Certain stars called shifted variable stars seem to say that he was actually less than the age of these clusters, which is a contradiction.

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How could the globular clusters be older than the universe?

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It was ultimately resolved because there was an error and people had looked at two different kinds of these certainly variable stars.

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And actually, the universe was considerably older than people thought. But at the time, there was this apparent contradiction.

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So the point of view, known as the the steady state model was put forward by the gold boundary,

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and Hoyle and Hoyle was describing this model in this lecture.

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So what we have here in this picture are the light cones in this model in the central strip going upwards.

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That would be the part of the universe that we can see. This is us up here somewhere and we are looking back.

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And the way Hoyle described it was that the galaxies get further and further away.

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They expand away from us. There's always hydrogen being produced to sort of keep the the density of the universe constant.

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But the galaxies drift away, and when they get faster than light, then they disappear from view.

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That was what Hoyle said.

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And I find this very puzzling because I drew pictures like this one here, and I imagine us looking back and these cones sort of point outwards.

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Notley's and you see our past the light rail as it follows the cones.

391
00:43:12,050 --> 00:43:18,260
Will always intersect the the world lines of the galaxy, so let me go to here.

392
00:43:18,260 --> 00:43:24,290
Here we see some galaxies. The Wilsons are the galaxies are always within the light cones.

393
00:43:24,290 --> 00:43:29,810
They don't travel faster than light locally, but you see relative to us, they travel faster than light.

394
00:43:29,810 --> 00:43:33,080
And so it was arguing that they would disappear. And I don't know,

395
00:43:33,080 --> 00:43:40,340
they don't disappear because here's us at the top and we look back on our past like sort of creeps along inside

396
00:43:40,340 --> 00:43:49,760
this well horizon between collide and we would always see any galaxy which had crossed the cross you associate.

397
00:43:49,760 --> 00:43:57,080
It may fade out gradually and become stranger and stranger. Now I did believe, but I didn't believe I just vanished.

398
00:43:57,080 --> 00:44:02,210
So I happened. To be visiting my brother at that time was a graduate student in Cambridge,

399
00:44:02,210 --> 00:44:06,410
and I complained about this and said I didn't see how the galaxies disappeared.

400
00:44:06,410 --> 00:44:13,530
And he said, Well, I don't know much about cosmology, but over there is Dennis Sharma sitting at the table and [INAUDIBLE] explain it all to you.

401
00:44:13,530 --> 00:44:19,040
So I went and I talked to Dennis and I gave him this argument and he said, Well, I'm not sure about that.

402
00:44:19,040 --> 00:44:22,220
And he went and said, I'll talk to a friend about it.

403
00:44:22,220 --> 00:44:30,800
And that's the main point about this was that he realised that that he thought I would be good cosmology I was doing.

404
00:44:30,800 --> 00:44:35,150
When I went to Cambridge, I was actually studying mathematics.

405
00:44:35,150 --> 00:44:46,260
I'm studying geometry. But Dennis decided he would teach me physics, and he thought that maybe he'd get some input from talking to me.

406
00:44:46,260 --> 00:44:51,050
He was very good at bringing people together, and at one point he suggested this.

407
00:44:51,050 --> 00:44:55,540
I think this a little bit later on here we here we have the extended statement again.

408
00:44:55,540 --> 00:45:03,920
You can see our past like intersecting of the range, the whereabouts of all the galaxies.

409
00:45:03,920 --> 00:45:09,350
Anyway, when I went back to Cambridge later on as a research fellow,

410
00:45:09,350 --> 00:45:17,740
I think it was and I was at St John's College Cambridge and Dennis suggested that.

411
00:45:17,740 --> 00:45:27,820
I might accompany him to go to hear a lecture by David Finkelstein that was at King's College London in 1958.

412
00:45:27,820 --> 00:45:34,330
And David Finkelstein was describing basically what this picture here is the

413
00:45:34,330 --> 00:45:39,850
Oppenheimer Schneider picture of a collapse to a black hole at the bottom.

414
00:45:39,850 --> 00:45:45,280
We see material you have to see. Time is always going up the picture in my pictures here.

415
00:45:45,280 --> 00:45:56,050
So here we have the bottom. Some matter which is considered to be sort of impressionist fluid is the way Oppenheimer described it, and it's neither.

416
00:45:56,050 --> 00:45:59,920
It was what they call dust, which has no pressure anyway.

417
00:45:59,920 --> 00:46:01,870
Never mind, so collapses inwards.

418
00:46:01,870 --> 00:46:10,620
And then there you have this situation in the future where you have these light cones pointing in now because I wasn't describing this particular.

419
00:46:10,620 --> 00:46:17,410
But he was describing, look at the top part. This is a picture of the structural solution.

420
00:46:17,410 --> 00:46:24,050
Misfortunate solution was introduced shortly after Einstein introduced his general theory of relativity.

421
00:46:24,050 --> 00:46:33,220
Karl Schwarzschild solve the equations for historical body such as the Sun, something like that of star.

422
00:46:33,220 --> 00:46:42,610
And the way that the metric is based on metric, including the light cones would behave was given by his equations.

423
00:46:42,610 --> 00:46:50,350
But the way he wrote the formula down, you came into a problem just at this place, which is the boundary.

424
00:46:50,350 --> 00:46:58,900
This sort of synergy that you see going up was its boundary, where it becomes tangent to the light cones in the coordinates that Georgia was using.

425
00:46:58,900 --> 00:47:05,050
It looked as though it was singular, so you had a place where things go to infinity.

426
00:47:05,050 --> 00:47:12,680
Singular really means that something goes wrong. Your metric seems to go to infinity, and that doesn't make any sense when that happens.

427
00:47:12,680 --> 00:47:15,670
So. So you give up at that point.

428
00:47:15,670 --> 00:47:25,480
But so people thought that the structure of singularity, which is this boundary, was a place where things blew up and you got nonsense.

429
00:47:25,480 --> 00:47:37,220
However, various people showed that by a change of coordinates, you could actually see that it wasn't a singularity that you could.

430
00:47:37,220 --> 00:47:44,090
As long as you had a coordinate system which enables you to to describe these like crimes pointing inwards.

431
00:47:44,090 --> 00:47:47,960
And David Finkelstein in his store was describing, I think of the top part of this picture.

432
00:47:47,960 --> 00:47:53,210
Forget about the collapse at the bottom. That was the picture that Finkelstein was describing,

433
00:47:53,210 --> 00:48:01,700
and I was very impressed by this because I really was this most amazed by how you could get rid of this seeming singularity,

434
00:48:01,700 --> 00:48:06,980
and it wasn't there at all. Nevertheless, at the centre, there you have this squiggly line in the middle.

435
00:48:06,980 --> 00:48:12,590
You really do get a single act. This is where the space-time carriages become infinite.

436
00:48:12,590 --> 00:48:15,670
And I came away from this lecture thinking.

437
00:48:15,670 --> 00:48:21,550
But somehow you could manage to get rid of the same thing if it was a singularity, but you're still stuck with it.

438
00:48:21,550 --> 00:48:28,290
Maybe there's some general theorem which tells you whatever you do, you can't get rid of this nasty thing in the middle.

439
00:48:28,290 --> 00:48:38,530
That look quite wise. And you couldn't. But it seemed to me that somehow this is a problem that maybe you have generalisations of.

440
00:48:38,530 --> 00:48:46,270
This is not disparately symmetrical case with irregularities and maybe the stuff falling in the pressure or something like that,

441
00:48:46,270 --> 00:48:54,560
which might make a difference. A much more general situation, which is qualitatively similar, but not exactly the same.

442
00:48:54,560 --> 00:49:00,250
And do you still get the singularity or do things sort of squish around and come squirting out again?

443
00:49:00,250 --> 00:49:05,050
And then I thought to myself, Well, I don't know much about general relativity.

444
00:49:05,050 --> 00:49:10,300
If I was going to try and prove this, a theorem like this, this is about nineteen fifty eight.

445
00:49:10,300 --> 00:49:23,050
What do I do? Well, the only thing I knew that I thought might be unfamiliar to general relativity period of time was about two components spinners.

446
00:49:23,050 --> 00:49:30,400
I think a few months earlier, I'd been, of course, due to Paul Dirac great quantum physicist.

447
00:49:30,400 --> 00:49:38,230
And this was his second loss of his. He had an elementary course and a more advanced course, and this is in his more advanced course.

448
00:49:38,230 --> 00:49:43,180
And he deviated from his usual course, which was rather an unusual thing for him to do.

449
00:49:43,180 --> 00:49:49,270
And he described two components steps. I was trying to learn about them for other reasons.

450
00:49:49,270 --> 00:49:52,810
Previously, I just found a very puzzling and I didn't understand them at all.

451
00:49:52,810 --> 00:50:04,450
The direct lectures made them very clear. And this is the sort of picture which I sort of out of this imagined myself on the right hand side.

452
00:50:04,450 --> 00:50:14,440
We see this little flat there. It's we have the future cone and the flagpole is along the cone.

453
00:50:14,440 --> 00:50:18,940
So it really points out towards as a as a light rain would go.

454
00:50:18,940 --> 00:50:29,830
You can imagine also the pass pulling back on the light cone so that if you look out at the sky, we're looking at photons coming in from infinity.

455
00:50:29,830 --> 00:50:32,620
And these photons coming in would be a sphere.

456
00:50:32,620 --> 00:50:37,990
So this sphere on the left hand side, you can call the celestial sphere if it's if it's the passcode cone,

457
00:50:37,990 --> 00:50:46,600
that's the actual celestial sphere of light coming in. But we can still call the celestial sphere of a light going out to infinity.

458
00:50:46,600 --> 00:50:55,450
And the the little two component spinner describes a single point on this celestial sphere is also about a little flag on it.

459
00:50:55,450 --> 00:51:00,850
And this is the just characterises the description of the two components.

460
00:51:00,850 --> 00:51:06,140
There's a little problem about the sound of it, which I won't reach at the moment.

461
00:51:06,140 --> 00:51:18,080
OK, now what's that got to do with this? Well, not much, but I started thinking about this problem and seeing what I could do with general relativity,

462
00:51:18,080 --> 00:51:24,440
and I found that some things worked extraordinarily well. If you wrote them in terms of these two components finished.

463
00:51:24,440 --> 00:51:30,140
You take the curvature of space time and it automatically splits into these two parts.

464
00:51:30,140 --> 00:51:38,360
One of them is called the viral part and the other is the Ritchey part. And the Ritchie Pass is what Einstein's equations directly determine.

465
00:51:38,360 --> 00:51:45,220
So if you have a massive distribution, this massive distribution gives you the Ritchie curves.

466
00:51:45,220 --> 00:51:51,800
That is the Einstein equations. It just tells you that the richer curvature is given by the massive distribution stress-free.

467
00:51:51,800 --> 00:51:57,200
That really means you're looking at the light rays and not the whole thing, but never mind too much about that.

468
00:51:57,200 --> 00:52:09,300
But what the richer curvature does is to focus the light rays inwards and a sort of uniformly where it's like a positive lens, which magnifies things.

469
00:52:09,300 --> 00:52:13,910
So if you're the observer at the top you looked at, this was slightly magnified.

470
00:52:13,910 --> 00:52:21,050
What you're looking at now, what is the violent curvature do? It distorts. So it's purely stigmatic.

471
00:52:21,050 --> 00:52:29,510
It's a lens which is entirely asymmetric and it magnifies in one direction and magnifies in the other direction.

472
00:52:29,510 --> 00:52:35,090
Anyway, I got a good clear picture of how light rays were affected by the curvature,

473
00:52:35,090 --> 00:52:39,410
and at one point I remember thinking about the steady state model.

474
00:52:39,410 --> 00:52:51,350
I was thinking about it, I think at the time where it had lost some credence because people had in the meantime discovered the microwave background,

475
00:52:51,350 --> 00:53:00,920
which showed that the universe had only stage in which it was extremely hot so that this was more in accordance with the models of the universe,

476
00:53:00,920 --> 00:53:03,590
which expanded out from a Big Bang.

477
00:53:03,590 --> 00:53:11,390
Whereas the steady state model didn't really agree with this at all, Dennis, when he was convinced that these observations were correct.

478
00:53:11,390 --> 00:53:15,950
He changed his mind and he said, Look, I was wrong to promote the steady state model.

479
00:53:15,950 --> 00:53:22,700
And I thought about it a bit myself because various people were still going on trying to promote it.

480
00:53:22,700 --> 00:53:27,830
And I had a sort of thought, can you show that if the energy density is positive,

481
00:53:27,830 --> 00:53:33,410
even if you wiggle so, so steady state model, we wiggles in it with that.

482
00:53:33,410 --> 00:53:38,240
Can you have such a model? And I convinced myself using focussing arguments,

483
00:53:38,240 --> 00:53:45,890
you simply couldn't have one that would be an impossibility as long as the energy flux was not negative.

484
00:53:45,890 --> 00:53:49,100
So this is something I had in the back of my mind.

485
00:53:49,100 --> 00:53:59,240
And later on in the early 1960s, when quasars were observed, these are very, very bright things which initially people thought were stars.

486
00:53:59,240 --> 00:54:03,800
I think they were radio sources initially that they noticed which were extremely bright,

487
00:54:03,800 --> 00:54:07,610
something like a hundred or a thousand times brighter than an entire galaxy.

488
00:54:07,610 --> 00:54:13,280
Yet they seem to be pretty small because they're they're and sort of the order of a week or so,

489
00:54:13,280 --> 00:54:17,420
which said that they couldn't be really bigger than the Solar System.

490
00:54:17,420 --> 00:54:23,900
So how could it be that bright have that much energy in them and yet be so small?

491
00:54:23,900 --> 00:54:32,180
So various people did start wondering whether something like the Oppenheimer saga collapse might actually be involved

492
00:54:32,180 --> 00:54:39,260
and that you were looking at things maybe as matter gets smaller and smaller would produce a lot of energy,

493
00:54:39,260 --> 00:54:46,460
and this engine might. You be a product of these things.

494
00:54:46,460 --> 00:54:54,500
Probing their short shot radius, I, a friend home in particular, was keen on idea Is this the shot?

495
00:54:54,500 --> 00:55:05,280
And there's a strong possibility, but this made many people think what happens when that collapse and they were thinking again about the iPhone,

496
00:55:05,280 --> 00:55:10,320
and it's not a collapse which I just showed you before.

497
00:55:10,320 --> 00:55:17,790
Yeah. The Oppenheim, not a collapse. And here you get a singularity in the middle.

498
00:55:17,790 --> 00:55:21,480
But let's suppose that the matter falling in is very irregular.

499
00:55:21,480 --> 00:55:29,670
So it's a lot of irregular things swishing around in all directions, and maybe you just square swirls around and some switching out again.

500
00:55:29,670 --> 00:55:33,690
And I at this time, there were some papers.

501
00:55:33,690 --> 00:55:42,660
There was a paper by Lifshitz and classmate Kalashnikovs, two Russians who seemed to show that in a general situation, we would look at singularities.

502
00:55:42,660 --> 00:55:51,100
And so I remember John Wheeler worrying about this a lot, and he asked me whether.

503
00:55:51,100 --> 00:55:53,140
You know, it can give me insights into this,

504
00:55:53,140 --> 00:56:01,370
and I remember I looked at the decision that was planned across paper and I didn't find the arguments completely convincing.

505
00:56:01,370 --> 00:56:05,590
There actually was an error in the paper, which I didn't notice.

506
00:56:05,590 --> 00:56:12,730
I hadn't gone into deeply enough to see that. But nevertheless, I thought it was worth thinking about the collapse problem anyway.

507
00:56:12,730 --> 00:56:15,520
And I remember walking in the woods and seeing trying to think,

508
00:56:15,520 --> 00:56:25,240
Was there some way when I remember thinking that had to be a non-local description that you couldn't because of the way things scale,

509
00:56:25,240 --> 00:56:29,080
it couldn't be something that was local. And it just got too big.

510
00:56:29,080 --> 00:56:34,360
And then it sort of swelled out again, and it had to be some more global criterion.

511
00:56:34,360 --> 00:56:44,260
And at a certain point when I was talking to a colleague and I had this idea came to me how you could characterise it collapse,

512
00:56:44,260 --> 00:56:48,940
which had reached a point of no return. Now this is the opposite of collapse.

513
00:56:48,940 --> 00:56:54,730
Picture more or less. It's actually pay attention to the picture from a paper that I drew.

514
00:56:54,730 --> 00:57:02,110
I drew the picture, which describes the paper, which eventually got the Nobel prise, apparently.

515
00:57:02,110 --> 00:57:06,220
And here we have a collapsing material at the bottom of the picture.

516
00:57:06,220 --> 00:57:10,180
And as we go upwards, we see this little black ring going around it.

517
00:57:10,180 --> 00:57:13,510
You have to remember there's another dimension here, so that isn't really a ring.

518
00:57:13,510 --> 00:57:20,620
It's a surface. But you picture as this little ring going around, it's a surface going round the collapsing material.

519
00:57:20,620 --> 00:57:26,140
And what's funny about it is that if you imagine a flash of light going all over that surface,

520
00:57:26,140 --> 00:57:33,580
that the flash of light converges on both sides on the top right hand picture here you see a little bit of a surface and

521
00:57:33,580 --> 00:57:40,600
you imagine a flash of light over that surface on the concave side that will converge on the convex side and diverge.

522
00:57:40,600 --> 00:57:47,830
What we have in a trap surface is a situation where it converges on both sides that looks a little strange.

523
00:57:47,830 --> 00:57:50,920
It's not actually that all that strange in relativity.

524
00:57:50,920 --> 00:57:59,790
The bottom situation we have to pass light cones, and as they intersect, you find a little bit of surface which has this property.

525
00:57:59,790 --> 00:58:06,280
It converges on both sides. But the thing about that is it's not closed up, it's not fiscal compact.

526
00:58:06,280 --> 00:58:17,290
And what's funny about the picture here is that you have the surface which the light waves are converging all the way around and it is compact.

527
00:58:17,290 --> 00:58:24,760
And it was that contradiction between not being a compact surface will is the fact that you look at the future of that.

528
00:58:24,760 --> 00:58:32,590
So you remember I had this picture of me, the future of a point, now a future of a surface, something complicated than that.

529
00:58:32,590 --> 00:58:36,670
But the way that it behaves and the fact it has light rays on it,

530
00:58:36,670 --> 00:58:42,580
which finally close up, and you could show that this was the boundary of that region,

531
00:58:42,580 --> 00:58:47,710
which is the future that when I call the trapped surface, that's the little ring in the middle there.

532
00:58:47,710 --> 00:58:52,900
That track surface had to be a compact region.

533
00:58:52,900 --> 00:58:58,330
And then you sort of project that backwards. I had a rather clumsy argument at the time.

534
00:58:58,330 --> 00:59:03,110
Charles Misner had a better way of describing it, which I hadn't thought of at the time.

535
00:59:03,110 --> 00:59:08,440
But the argument was I was thinking of GDDR6 coming and hitting the initial surface.

536
00:59:08,440 --> 00:59:14,290
I should say the surface. The bottom is what's called a koshy surface. This is what people are doing in physics.

537
00:59:14,290 --> 00:59:22,210
You consider that one moment you say, well, what everything is doing and then your equations tell you what that stuff is doing later on.

538
00:59:22,210 --> 00:59:27,070
It's called a koshy surface. You have enough data on your initial surface to predict the future.

539
00:59:27,070 --> 00:59:33,040
Now, in this situation, I'm imagining a local thing. So the Kushi surface could be assumed to be non compact.

540
00:59:33,040 --> 00:59:42,190
It goes off to infinity in all directions. And when you project back to your compact region at the top, which is the future of the surface,

541
00:59:42,190 --> 00:59:47,320
the boundary of the future of the surface, you simply arrive at a contradiction in that contradiction.

542
00:59:47,320 --> 00:59:51,910
Something is wrong as long as the energy doesn't ever go negative.

543
00:59:51,910 --> 00:59:58,090
That would spoil the argument, but as long as it remains not negative, you have this problem and you get it.

544
00:59:58,090 --> 01:00:05,920
What was it? Whatever definition you have, a singularity makes a difference, but you have something goes wrong and this is the singular stage.

545
01:00:05,920 --> 01:00:15,280
So what it's telling you is that you can't have a general collapse of the Oppenheimer Schneider type of body,

546
01:00:15,280 --> 01:00:26,180
which is sort of reasonably, reasonably compact in itself and can be very, very irregular, actually can consist of a lot source.

547
01:00:26,180 --> 01:00:30,850
You see, a lot of people used to worry maybe a realistic situation.

548
01:00:30,850 --> 01:00:36,130
Could you could you avoid having a track surface? Do you necessarily have a track surface?

549
01:00:36,130 --> 01:00:41,260
Well, it's not so easy to see. So I used to often use a different argument.

550
01:00:41,260 --> 01:00:49,640
The same theorem applies. Suppose you have a point. The point at the bottom of the concert is its future lies.

551
01:00:49,640 --> 01:00:54,740
And as you can see it, following up on the boundary of its future.

552
01:00:54,740 --> 01:01:01,910
With this light rain start to converge again, none is necessarily going to be a contract region, and that's good enough.

553
01:01:01,910 --> 01:01:06,740
You don't have to have a truck surface as long as you can imagine that they have a

554
01:01:06,740 --> 01:01:13,010
point where the future light comes at a light rail start to converge at some point.

555
01:01:13,010 --> 01:01:18,680
And it's not so hard to see that if you have a large cluster of stars, let's say an individual star,

556
01:01:18,680 --> 01:01:23,870
there's probably most people worried that you'd have individual stars. The density might get so huge.

557
01:01:23,870 --> 01:01:27,320
And do you trust your equations when the density gets very large?

558
01:01:27,320 --> 01:01:34,460
But if you consider the collapsing collection of many, many stars, then it's very easy to see if you have enough of them.

559
01:01:34,460 --> 01:01:38,430
It's not hard. The density doesn't have to be the average density.

560
01:01:38,430 --> 01:01:43,370
It can be less than the density. Now, it's not much problem getting enough stars doing that.

561
01:01:43,370 --> 01:01:50,510
So it seemed to me that it was a very general phenomenon, and there's no problem about whether you can have a trapped surface.

562
01:01:50,510 --> 01:01:54,650
You could say that this condition is there just as the serum works just as well.

563
01:01:54,650 --> 01:01:59,510
OK, well, let's move forward a bit. Now we move on to the Big Bang.

564
01:01:59,510 --> 01:02:07,040
You see, that's another thing that actually and Stephen Hawking, I gave a talk at King's College where I describe my techniques.

565
01:02:07,040 --> 01:02:14,900
This was in 1964 and the paper was published, which got the Nobel Prises in 1965.

566
01:02:14,900 --> 01:02:23,540
It was published in 1965. I wrote it in 64, and then Sharma suggested I would give a repeat of this in Cambridge.

567
01:02:23,540 --> 01:02:28,910
The movie suggests that Stephen Hawking was present at my lecture in London, which is not true.

568
01:02:28,910 --> 01:02:36,020
He wasn't there. But however, he was there at the talks in Cambridge, and we had long discussions.

569
01:02:36,020 --> 01:02:40,670
He and George Ellis and I discussed the techniques I was using,

570
01:02:40,670 --> 01:02:48,980
and Stephen very quickly picked up on the issue and started to generalise the techniques and use them in reverse time directions.

571
01:02:48,980 --> 01:02:56,300
So you could ask whether if you have a Big Bang, which was not could be complicated and not not not nice and symmetrical,

572
01:02:56,300 --> 01:03:03,740
as they usually have pictures of the universe, then might you avoid the singularity?

573
01:03:03,740 --> 01:03:09,410
And the Big Bang could be the result of a previous collapsing phase which bounced and came out again.

574
01:03:09,410 --> 01:03:16,010
And he generalised these arguments very much and had several papers, three papers in the Royal Society.

575
01:03:16,010 --> 01:03:25,130
Then later on, we got together and proved a very general theorem, which which will encompass things that happened before.

576
01:03:25,130 --> 01:03:37,670
This is not a picture of the universe. I remember I was puzzled by the fact that people did not discuss in cosmology and serious cosmology.

577
01:03:37,670 --> 01:03:41,900
I'm talking about the cosmologists, not the people who worked on general symmetry theory.

578
01:03:41,900 --> 01:03:45,980
I'm talking about the people who actually don't observational cosmology.

579
01:03:45,980 --> 01:03:51,320
And they looked at universities and I asked them, I remember talking to James Peebles,

580
01:03:51,320 --> 01:03:58,520
who was sitting in the car about to go off to a meeting at Stevens Institute, and I went off on a different car before he drove off.

581
01:03:58,520 --> 01:04:06,410
I asked him, Why is it that cosmologists, you cosmologists don't ever study these other complicated singularities and loads and loads of them?

582
01:04:06,410 --> 01:04:11,900
You just concentrate on the one case where you have a very symmetrical initial state?

583
01:04:11,900 --> 01:04:16,820
Well, why don't you look at these other me? She looked at me and said, Because the universe is not like that.

584
01:04:16,820 --> 01:04:22,310
I thought, Oh my gosh, it isn't. This is his argument I think was based on the cosmic microwave.

585
01:04:22,310 --> 01:04:30,260
Background is very uniform, and in this picture, I've drawn it as this very symmetrical you'll notice at the back,

586
01:04:30,260 --> 01:04:35,900
there's some sort of irregularities that's just so that the universe could be closed or open.

587
01:04:35,900 --> 01:04:40,100
It's a bit hard to draw a picture of the universe if it's not closed,

588
01:04:40,100 --> 01:04:45,680
so I pretend that it's closed for a bit and then it goes off to infinity around the back.

589
01:04:45,680 --> 01:04:51,450
But I'm not really prejudicing the issue as to whether it's actually open up close.

590
01:04:51,450 --> 01:04:57,800
Now, one of the arguments that people use in cosmology is that right there,

591
01:04:57,800 --> 01:05:04,130
tucked in at the Big Bang in order to see it, we need a magnifying glass, a really powerful magnifying glass.

592
01:05:04,130 --> 01:05:12,170
Very, very powerful magnifying glass because it's way down in sort of the first 10 to the minus 32 of a second.

593
01:05:12,170 --> 01:05:20,210
And what you apparently see, according to the theory, is this thing called inflation that is another exponential expansion of the universe,

594
01:05:20,210 --> 01:05:27,210
which may be which moves the universe, and it does other things which are more technical about the cosmic microwave background.

595
01:05:27,210 --> 01:05:35,120
But one of the arguments we're trying to make is that that Big Bang, if it had this inflationary phase, it would smooth out.

596
01:05:35,120 --> 01:05:44,630
And that's why you don't see all these irregularities. Now, I was not very convinced by this for the following argument.

597
01:05:44,630 --> 01:05:48,860
Let's imagine that time is going the other way.

598
01:05:48,860 --> 01:05:53,680
And so you have a model which is collapsing. And in this model, you've got.

599
01:05:53,680 --> 01:05:58,450
All sorts of irregularities, including black holes and things forming.

600
01:05:58,450 --> 01:06:03,820
And they they will converge on some horrendous next event.

601
01:06:03,820 --> 01:06:09,040
Now that is the cause of arguments from Stephen Hawking and Beck and so on and so on,

602
01:06:09,040 --> 01:06:17,710
who show the entropy of a black hole was it shows that this is an extraordinarily special state not to have these

603
01:06:17,710 --> 01:06:24,970
black hole constituents in a collapsing model so that a very general situation wouldn't be anything like what we see.

604
01:06:24,970 --> 01:06:32,950
It would be much more like this. Yeah, we have black hole singularity or congealing in a great mess.

605
01:06:32,950 --> 01:06:40,330
It's much more like the sort of model that Russia in the costs and charts and came up with later on.

606
01:06:40,330 --> 01:06:45,280
When corrected, the mistake was corrected and they found very complicated solutions,

607
01:06:45,280 --> 01:06:50,500
which would be nothing like what machine in the Big Bang and I should say.

608
01:06:50,500 --> 01:06:58,330
One feature of solutions is the vile curvature becomes enormously large, absolutely huge.

609
01:06:58,330 --> 01:07:02,290
Now that is a much, much more likely initial stage.

610
01:07:02,290 --> 01:07:07,750
Why don't we have that rather than what we seem to see, namely this?

611
01:07:07,750 --> 01:07:17,530
Why do we have a very, very regular universe? This is the problem posed by Jim Peebles and previous Nobel prise winner last year,

612
01:07:17,530 --> 01:07:26,320
and he had very good reasons to believe that it was like this from observational signals.

613
01:07:26,320 --> 01:07:34,960
Now, I find it very strange that we seem to see a singularity in the bang.

614
01:07:34,960 --> 01:07:40,150
The arguments were sort of similar back in time and forward in time.

615
01:07:40,150 --> 01:07:41,740
So why do you get this very,

616
01:07:41,740 --> 01:07:48,520
very great difference when used to think that these singularities would be resolved by some wonderful theory of quantum gravity?

617
01:07:48,520 --> 01:07:55,720
Quantum mechanics modifying gravity a small scale small sizes coverage does get very large.

618
01:07:55,720 --> 01:08:03,460
But the trouble is, if that theory explains how to get rid of the singularities in the future, why doesn't it apply to the Big Bang?

619
01:08:03,460 --> 01:08:10,180
Why did we get this very, very peculiar situation? So I just formulated a theory wasn't much of a theory.

620
01:08:10,180 --> 01:08:15,160
It's just hand-waving to say that whatever quantum gravity it is must be a very tiny,

621
01:08:15,160 --> 01:08:21,460
symmetrical model where the violent curvature is somehow necessarily zero.

622
01:08:21,460 --> 01:08:29,530
In past such singularities like the Big Bang was future type singularities that one we've just seen they need to be zero at all.

623
01:08:29,530 --> 01:08:35,740
Very, very strange kind of quantum gravity. This is all tied up with a major problem in physics.

624
01:08:35,740 --> 01:08:44,800
Another man called the Second Law of Thermodynamics, which tells you that the entropy increases with time entropy as measured randomness.

625
01:08:44,800 --> 01:08:49,780
And here we have in the top three pictures the gas in the box we have on the left hand

626
01:08:49,780 --> 01:08:54,700
side of the gas in a little box and then we open the box up and the gas spreads out.

627
01:08:54,700 --> 01:08:59,140
So this is what you find with entropy increasing for gas in the box.

628
01:08:59,140 --> 01:09:07,870
But what about stars and a huge box? They behave the other way around that they would address if they are spread out.

629
01:09:07,870 --> 01:09:12,160
This represents a low entropy state and as time progresses,

630
01:09:12,160 --> 01:09:17,710
disaster to clump and then you got black holes and things like that where the entropy just goes shooting up.

631
01:09:17,710 --> 01:09:23,140
So in both pictures, the top three and the bottom three, we have entropy increasing from left to right.

632
01:09:23,140 --> 01:09:28,060
In the top pictures is ordinary matter and the bottom picture is gravity.

633
01:09:28,060 --> 01:09:36,940
So gravity behaves very differently. What we do see in the early universe indeed, is a situation like the top right and the bottom left.

634
01:09:36,940 --> 01:09:40,540
In other words, uniformity. What does that mean?

635
01:09:40,540 --> 01:09:47,710
That means high entropy in matter, and that's confirmed by the microwave background and low entropy in the gravity,

636
01:09:47,710 --> 01:09:52,120
which is also confirmed by the microwave background because you see that it's uniform.

637
01:09:52,120 --> 01:09:59,860
But it tells us that the Big Bang was a very strange thing because it seems to be no entropy in gravity.

638
01:09:59,860 --> 01:10:05,740
It's the single outgrow. It is something special. Now that way, I started thinking about this.

639
01:10:05,740 --> 01:10:13,510
Later was due to an argument or a suggestion due to Paul Todd, my graduate student.

640
01:10:13,510 --> 01:10:22,030
Then at the time, he became an instructor at Oxford, and he had this suggestion that maybe what was peculiar about the Big Bang,

641
01:10:22,030 --> 01:10:32,290
not just say that our curvature is zero, but to say that it's if you could formerly stretch it out, it becomes regular.

642
01:10:32,290 --> 01:10:39,400
And the fact that you can squash down infinity and make that regular was something I knew about before.

643
01:10:39,400 --> 01:10:46,100
This picture is an Escher picture. Why don't you set limits and it describes a geometrical, hyperbolic geometry?

644
01:10:46,100 --> 01:10:52,660
Don't worry too much about the geometry. What I'm trying to say is a conformal representation you can see in the eyes of the fish.

645
01:10:52,660 --> 01:10:54,000
They're all circles.

646
01:10:54,000 --> 01:11:03,120
And as you get towards the edge, they remain circles, the shapes or the small shapes or angles are preserved and this match of the fish at the edge.

647
01:11:03,120 --> 01:11:11,740
Don't think they're any different to the ones in the middle. But this conformal compression is what Asher has used in this model.

648
01:11:11,740 --> 01:11:19,530
It's a Beltrami representation of geometry, and I want to try and apply the same idea to cosmology.

649
01:11:19,530 --> 01:11:23,090
That's something I'm used to do a lot with this question and finish. It's very useful.

650
01:11:23,090 --> 01:11:30,600
I'm talking about gravitational radiation. But the idea is to use that same argument in the opposite way to talk about the Big Bang.

651
01:11:30,600 --> 01:11:36,390
Now what does control mean in general relativity when it really just means the light cones you see?

652
01:11:36,390 --> 01:11:41,520
Think about the light cones. That's not quite the whole of the metric.

653
01:11:41,520 --> 01:11:44,130
That's nine out of 10 components in the metric.

654
01:11:44,130 --> 01:11:50,310
If you want the tenth component, you have to think of these little pill shaped things or bow shaped surfaces.

655
01:11:50,310 --> 01:11:55,640
What do they represent? They represent the ticking of clocks.

656
01:11:55,640 --> 01:12:04,290
Yeah, I've got the two most famous equations of 20th century physics Einstein, Jacobs and C squared Max Planck new news frequency.

657
01:12:04,290 --> 01:12:10,530
First one tells you energy and mass are equivalent. That's Einstein. Planck tells you energy and frequency equivalent.

658
01:12:10,530 --> 01:12:14,970
Together, this tells you that frequency and mass are equivalent.

659
01:12:14,970 --> 01:12:21,180
So if you have a massive particle that has a very definite frequency given by these equations.

660
01:12:21,180 --> 01:12:30,400
Now, if you imagine now there were lines of massive particles, so here we have two two particles.

661
01:12:30,400 --> 01:12:38,380
Travelling with large speed, but not the speed of light, the red one intersects these bulkhead surfaces that stick number one, tick number two,

662
01:12:38,380 --> 01:12:46,150
tick number three, the blue one is six and pick number one pick number two three particles of fix of a definite stable particle size.

663
01:12:46,150 --> 01:12:53,290
Definite mass make wonderful clocks. So they are perfect clocks if they have definite masses.

664
01:12:53,290 --> 01:13:03,790
Now that's this. But if you don't have mass, then you have photons and photons don't even see these surfaces, so photons don't register time at all.

665
01:13:03,790 --> 01:13:12,550
From the origins of the photon to the where it gets finely absorbed, if it does is as far as the photons concerned, no time at all.

666
01:13:12,550 --> 01:13:19,020
So it gets right out. To infinity, these lichens in our conformal structure.

667
01:13:19,020 --> 01:13:29,250
They don't depend on the mass they don't scale. The Beltrami picture or picture we just showed you is a conformal picture in space time.

668
01:13:29,250 --> 01:13:34,980
It's the lichens that we're talking about now. OK, now let's think about the whole universe.

669
01:13:34,980 --> 01:13:39,120
On the left hand side, we see the model of the universe with the Big Bang,

670
01:13:39,120 --> 01:13:44,070
and then we see the exponential expansion, which is a feature of Jarod's again,

671
01:13:44,070 --> 01:13:53,310
another Nobel prise early in the 20th century 21st century where people discovered that there was a cosmological terminations equations or equivalent.

672
01:13:53,310 --> 01:13:59,590
And this seems to show that when you issue squashed this down, you get a finite boundary in the future.

673
01:13:59,590 --> 01:14:03,300
I can see my error in one screen and those in the other. Unfortunately, that's try that.

674
01:14:03,300 --> 01:14:07,620
Yeah, we have a remote future, a nice space like boundary.

675
01:14:07,620 --> 01:14:14,050
Despite the Big Bang, there's also space like so you get you can squash down infinite and stretch out the Big Bang.

676
01:14:14,050 --> 01:14:19,020
Now, I was very struck by the fact that when you do that, they look very similar to each other.

677
01:14:19,020 --> 01:14:24,930
You see, you might say they're very different topic. Well, what about the remote future's very cold, very rarefied?

678
01:14:24,930 --> 01:14:28,320
What about the Big Bang? So hot and very concentrated?

679
01:14:28,320 --> 01:14:36,030
But if you use this conformal squashing it not only just make things smaller, it makes things hotter.

680
01:14:36,030 --> 01:14:40,020
Next, the energies go up. What happens to the Big Bang when you stretch it out?

681
01:14:40,020 --> 01:14:47,940
It makes things colder as well as less dense. So you something which looks as though they're pretty similar in the remote future, in the remote past.

682
01:14:47,940 --> 01:14:55,950
And in fact, now here's the exotic model that I put forward a few years ago, which I call hot conformal cyclic cosmology.

683
01:14:55,950 --> 01:15:07,420
Is that our. Universe is only one aeons and calling it of infinite only extended can succession of these models

684
01:15:07,420 --> 01:15:12,460
where our Big Bang was the conformal continuation of the remote future of a previous aeon,

685
01:15:12,460 --> 01:15:16,600
our remote future will be the Big Bang of the next year.

686
01:15:16,600 --> 01:15:23,710
Now, I guess I gave lectures about this lot thinking nobody would ever disprove me because there was no observations,

687
01:15:23,710 --> 01:15:31,840
and then I started worrying about this because there were some observations. So let me go and see certain signals can get through.

688
01:15:31,840 --> 01:15:38,980
In fact, if you have something with no mash, then it can get through. You might argue, Well, how about in our actual universe?

689
01:15:38,980 --> 01:15:46,810
Why it doesn't mass for a picture with a remote future? It's partly because it's mainly photons running around, and they don't have any mass.

690
01:15:46,810 --> 01:15:51,490
You have to have some other condition that the mass gradually fades out from massive particles.

691
01:15:51,490 --> 01:15:54,460
But I don't want to go into that for the moment. What about the Big Bang?

692
01:15:54,460 --> 01:16:03,850
Well, there the argument is that things are moving around so fast that the energy in particles is almost entirely in motion and not in their mass.

693
01:16:03,850 --> 01:16:13,360
And so that therefore they are effectively mass us because they're so hot, so that mass things at both ends.

694
01:16:13,360 --> 01:16:17,290
And if it's like a photon, it can actually get through from one side to the other.

695
01:16:17,290 --> 01:16:20,350
What else could get through? Well, gravitational waves.

696
01:16:20,350 --> 01:16:31,110
And yeah, I have one of the ideas that I proposed that if you have black holes in the previous year and actually before this horizontal surface,

697
01:16:31,110 --> 01:16:37,020
the previous part, this is the previously on the red part is already on the top,

698
01:16:37,020 --> 01:16:44,710
opposes the previous year and I have a number of black holes in a galactic cluster, supermassive black holes running into each other.

699
01:16:44,710 --> 01:16:51,760
So there will be several of these, and that cluster eventually becomes one big black hole and that sits around for an awful long time.

700
01:16:51,760 --> 01:16:57,100
But in the process, it will emit these huge gravitational wave signals.

701
01:16:57,100 --> 01:17:06,230
And can you see them? Well, my colleague Vijay Guzelian, who actually did an analysis of this, I won't go into the details of it.

702
01:17:06,230 --> 01:17:11,620
I show you this one picture, which is an analysis where he looks for rings.

703
01:17:11,620 --> 01:17:16,340
You see, when you look back into the previous Ian intersection between our past,

704
01:17:16,340 --> 01:17:23,620
current and the future of the purple cones is really a ring because you need another dimension, of course, to get sense of that.

705
01:17:23,620 --> 01:17:29,140
And so what I did was to look at rings and look at rings, which had low variance.

706
01:17:29,140 --> 01:17:34,630
That's the sort of signal that you might get from these colliding black holes.

707
01:17:34,630 --> 01:17:42,610
Little variation as you go around, but that wasn't very strong signal. What you had to look was for at least three concentric such rings as you.

708
01:17:42,610 --> 01:17:45,790
As I said, you get several of them in these collisions.

709
01:17:45,790 --> 01:17:53,440
And this one I want to point out is a remarkable signal because he didn't look for whether the temperature was warmer cooler.

710
01:17:53,440 --> 01:18:01,420
But the the red ones are with warmer temperatures are actually the more distant ones and the blue ones are with coat cooler temperature,

711
01:18:01,420 --> 01:18:06,490
the closer ones they actually with. Well, we call on with a partial icon, the red ones.

712
01:18:06,490 --> 01:18:10,990
You wouldn't even see the galaxy because they're outside that partial like you can do that because

713
01:18:10,990 --> 01:18:17,170
you look into the period you see on and the current spreads out further than it does in us.

714
01:18:17,170 --> 01:18:21,760
So we see these very curious, very concentrated regions.

715
01:18:21,760 --> 01:18:29,440
That's what's so puzzling about this picture. Whatever it is, it's producing his signals is very, very, very non-uniform.

716
01:18:29,440 --> 01:18:34,350
And that's a great puzzle for cosmology because people think the universe is very, very uniform.

717
01:18:34,350 --> 01:18:43,030
This tells you, is on a very large scale. It's not all that uniform and you have this very, very super duper clusters of galaxies.

718
01:18:43,030 --> 01:18:49,100
Of course, that may be another explanation. Maybe that's not the real reason in the model I'm proposing in the previous year,

719
01:18:49,100 --> 01:18:54,010
and you have great clustering and that will undoubtedly come through to you.

720
01:18:54,010 --> 01:19:03,610
The second observational feature was more to do with my Polish colleagues Christoph Meisner,

721
01:19:03,610 --> 01:19:09,820
Pavel Nawrocki and Daniel, and who did some analysis on, well, another pole originally.

722
01:19:09,820 --> 01:19:15,310
But Daniel, and in the subsequent measurements, which I'm talking to you now,

723
01:19:15,310 --> 01:19:22,370
this is another thing that Hawking predicted is that black holes not only have entropy, but they have a temperature.

724
01:19:22,370 --> 01:19:27,490
And this temperature is very, very, very, very cold. So you don't see much of that.

725
01:19:27,490 --> 01:19:31,390
But in the very remote future, when the universe expands and expands and expand,

726
01:19:31,390 --> 01:19:38,200
the black hole becomes the hottest thing around and it gradually evaporates and finally evaporates away.

727
01:19:38,200 --> 01:19:44,050
And it just goes away, maybe with what I call a pot. But whatever happens, all that radiation,

728
01:19:44,050 --> 01:19:51,890
because you remember the fish getting so concentrated in the in the present in the picture, yeah, everything gets so squashed down.

729
01:19:51,890 --> 01:19:57,070
All the radiation in the in the final picture gets squashed into a single point.

730
01:19:57,070 --> 01:20:03,670
Now here we have a. A picture from our paper published in the Monthly Notices of the Royal Astronomical Society.

731
01:20:03,670 --> 01:20:08,620
Daniel Han did the analysis detail computer analysis?

732
01:20:08,620 --> 01:20:15,400
Kristof also has a particular criterion for the looking for the use of hawking points, she said.

733
01:20:15,400 --> 01:20:19,120
I'm calling you hawking points here in the bottom part of the picture.

734
01:20:19,120 --> 01:20:24,070
No, just the horizontal line at the bottom that is the cross over from one year to the next.

735
01:20:24,070 --> 01:20:32,800
I'm imagining that there is a black supermassive black hole finally evaporating way way just underneath that crossover surface.

736
01:20:32,800 --> 01:20:39,550
As we call the hawking point, the all that energy comes pouring through and that will come pouring through.

737
01:20:39,550 --> 01:20:46,600
You don't see it immediately because it takes 380000 years before the light can ever get out.

738
01:20:46,600 --> 01:20:54,550
That's standard stuff. James stable and his colleagues very good work that they've done on the universe 380000 years,

739
01:20:54,550 --> 01:21:03,640
and that spreads out to what is about eight times the diameter of the full moon so that all their energies spread out to eight times that.

740
01:21:03,640 --> 01:21:10,690
I mean, you see at the top the sort of distribution of temperatures that you have in the middle, larger,

741
01:21:10,690 --> 01:21:18,910
larger increase in the temperature and it stays off as you go to the outside of a size, which is eight times the names of the moon or slightly less.

742
01:21:18,910 --> 01:21:29,680
If you're not quite in, quite seeing it head on. But these we do seem to see with a confidence level of ninety nine point nine eight percent.

743
01:21:29,680 --> 01:21:35,830
This is in the Planck data. This is a satellite which we originally looked at.

744
01:21:35,830 --> 01:21:39,220
Then we compared it with the older satellite, the map data.

745
01:21:39,220 --> 01:21:48,880
And for the five strongest points in this Planck data, actually where they are is not such confidence level, but as you see them in both.

746
01:21:48,880 --> 01:21:53,050
That seems to be pretty strong evidence that there are genuine hawking points that the

747
01:21:53,050 --> 01:21:59,380
five strongest points are seen in exactly the same places in the map and the Planck data,

748
01:21:59,380 --> 01:22:06,610
so I think they're pretty reliable. There's another one in the map data, which you see also in the same place in the Planck data.

749
01:22:06,610 --> 01:22:11,380
So there does seem to be something there if somebody else has another explanation.

750
01:22:11,380 --> 01:22:20,800
Yes, I'd like to see it, but it's not. It seems to me this is a pretty strong indication of something like the model that I'm putting forward.

751
01:22:20,800 --> 01:22:25,390
It certainly is something I hope people will consider seriously.

752
01:22:25,390 --> 01:22:33,650
Thank you very much. Well, welcome to this final session.

753
01:22:33,650 --> 01:22:41,210
And welcome to Roger Penrose, who I'm going to talk to you for the next half hour or so.

754
01:22:41,210 --> 01:22:53,240
Roger, when you think of your background, your family, there were artists, there was a chess grandmaster as a geneticist mathematician.

755
01:22:53,240 --> 01:22:59,540
Do you feel you were fed by that multivariate academic atmosphere?

756
01:22:59,540 --> 01:23:05,810
I think that's undoubtedly true. I mean, my father worked in human genetics.

757
01:23:05,810 --> 01:23:14,900
Both my parents were medically trained and actually they assumed I was going to be asked of me and my two brothers.

758
01:23:14,900 --> 01:23:28,450
I was the one they decided was going to follow them in the medical profession, and I believe this myself right up until I think I was in my.

759
01:23:28,450 --> 01:23:32,860
Second year, I think at school, if you had to decide what in the last two years,

760
01:23:32,860 --> 01:23:37,840
what subjects we would do and each one had to walk up and talk to the headmaster.

761
01:23:37,840 --> 01:23:42,650
I remember as I was walking up to talk to the headmaster, I was going to be a doctor because that's,

762
01:23:42,650 --> 01:23:47,260
you know, it was sort of established I would follow my parents professions.

763
01:23:47,260 --> 01:23:51,880
And then he said, Well, what subjects you wants to do in your final two years?

764
01:23:51,880 --> 01:23:57,130
And I said, I'd like to do biology, chemistry and mathematics.

765
01:23:57,130 --> 01:24:00,220
And he said, No, you can't do that combination.

766
01:24:00,220 --> 01:24:06,790
If you want to do mathematics, you can't do biology, you want to do bios, you can't do mathematics, make your choice.

767
01:24:06,790 --> 01:24:14,890
So I said, well, mathematics, physics and chemistry. And that was because I didn't want to lose the maths.

768
01:24:14,890 --> 01:24:19,930
I realised there was my medical career going down the drain, and when I got home,

769
01:24:19,930 --> 01:24:26,440
both my parents were really annoyed with me because that was the end of my actually they one in the end

770
01:24:26,440 --> 01:24:32,620
because I had a little sister who was eventually became a doctor herself and married to one as well.

771
01:24:32,620 --> 01:24:37,180
So they really wanted me and not with me. Was this?

772
01:24:37,180 --> 01:24:42,700
Was this something that you've mathematic, which is the thing you had to keep a grip on?

773
01:24:42,700 --> 01:24:46,990
I think it was just I just fell in love with it. Hmm. No.

774
01:24:46,990 --> 01:24:52,270
I certainly had a great fondness for mathematics from quite early on.

775
01:24:52,270 --> 01:25:00,760
Certainly, when I was nine or something like that, I can't remember the exact age of the earlier,

776
01:25:00,760 --> 01:25:07,120
but I hadn't thought as a career that really came gradually.

777
01:25:07,120 --> 01:25:14,850
First of all, with this when my parents would be very disappointed, which I ditched biology.

778
01:25:14,850 --> 01:25:21,640
Of course, these days you could do biology and mathematics because in those days it was very much more restricted what was allowed to do.

779
01:25:21,640 --> 01:25:24,670
But later on, when I decided to do mathematics,

780
01:25:24,670 --> 01:25:36,670
just just mathematics at University College for my undergraduate degree, my father was again very angry about that.

781
01:25:36,670 --> 01:25:43,510
He considered that people who just did mathematics are rather strange characters, you see, and he thought I could do other things as well as maths.

782
01:25:43,510 --> 01:25:49,300
So I should be more broad in what I did. But I was very determined.

783
01:25:49,300 --> 01:25:56,380
And I think, yes, my father had one of the lecturers, a man by the name of Kesselman, who was very good.

784
01:25:56,380 --> 01:26:02,770
He was extremely good lecturer and I didn't know that at the time because I wasn't there yet.

785
01:26:02,770 --> 01:26:07,450
But he made up a special lot of test questions.

786
01:26:07,450 --> 01:26:14,770
I think there were six or 12. I can't remember quite. And they were very unusual and I would never come across before.

787
01:26:14,770 --> 01:26:18,640
I respect respected him a lot. So taking all this trouble.

788
01:26:18,640 --> 01:26:22,690
But anyway, he made these questions up and he gave them to me and said, Well,

789
01:26:22,690 --> 01:26:28,990
you can take as long as you like, and if you only do one or two, that's fine.

790
01:26:28,990 --> 01:26:34,390
But then he came back later in the day and I done all of them. He was quite impressed by that.

791
01:26:34,390 --> 01:26:38,410
So I think that results converge as my father, he allowed me to do mathematics.

792
01:26:38,410 --> 01:26:47,590
Yeah. Did the MLA wasn't actually extremely well ordered household amongst your relations than their friends?

793
01:26:47,590 --> 01:26:51,710
Well, that certainly worries me when you that it was a bit chaotic, but go on.

794
01:26:51,710 --> 01:26:58,330
Yes. I mean, did you did you get something from the artist side and from the other side of that side?

795
01:26:58,330 --> 01:27:06,760
Yes, I think definitely from the artist side to now because my father was a he was a very good artist and he was one of four brothers,

796
01:27:06,760 --> 01:27:10,570
all of whom but one of them particularly distinguished as an artist.

797
01:27:10,570 --> 01:27:13,810
That was Roland, who was a younger brother of his.

798
01:27:13,810 --> 01:27:24,220
And Roland became a big figure in the art world and surrealism, and he was familiar with Picasso and Maxence and various things like that.

799
01:27:24,220 --> 01:27:32,560
And he then became a big figure in surrealist art and in Britain.

800
01:27:32,560 --> 01:27:39,070
But there's a plaque to him. I pass most days. Oh yes.

801
01:27:39,070 --> 01:27:45,310
See? Well, yes, but you see my grandfather, my father's father was a professional artist.

802
01:27:45,310 --> 01:27:52,660
He was. He was very skilled, extremely skilled, but he sort of very religious pictures.

803
01:27:52,660 --> 01:27:57,430
He was a Quaker, and my father was also a Quaker, but also the religious Quaker.

804
01:27:57,430 --> 01:28:08,200
He was more moral Quaker, you might say. And he used to go sketching, and I sometimes went with him sketching.

805
01:28:08,200 --> 01:28:14,110
He was very good at sort of green pen and ink, I think was this particular scaly hand.

806
01:28:14,110 --> 01:28:19,940
But I did more wild things which were not necessarily realistic, and I don't think he approved of that very much.

807
01:28:19,940 --> 01:28:26,500
But the idea of drawing and drawing as part of the intellectual and the life you allowed was just that from the start, that was very much true.

808
01:28:26,500 --> 01:28:30,850
In my case, I. I don't think my brothers were too much on that side.

809
01:28:30,850 --> 01:28:36,400
My sister picked up on it rather. But certainly my father's side.

810
01:28:36,400 --> 01:28:40,270
Yes. And I got a lot from him on the artistic side.

811
01:28:40,270 --> 01:28:48,940
I think that's true when you are at school. You said that you, you realise your mind worked in an unusual way.

812
01:28:48,940 --> 01:28:56,320
You know, I thought maybe when I go to university, I'll find people who think like me, but it wasn't like that at all.

813
01:28:56,320 --> 01:29:02,560
When I would talk to someone about an idea, I found myself not understanding a word that they were saying.

814
01:29:02,560 --> 01:29:09,850
Gladstone remark, which was sort of that I could pick up what the gist of what they were saying without really understanding the words.

815
01:29:09,850 --> 01:29:14,380
It was quite strange in a way. Obviously, that thought processes were very different.

816
01:29:14,380 --> 01:29:19,630
So when I went to university, I found that in fact, people thought very differently from me.

817
01:29:19,630 --> 01:29:27,430
On the whole, I think it was mainly the visual on visual divide, which is quite a significant one.

818
01:29:27,430 --> 01:29:30,790
I mean, there are lots of other differences, but primarily that one.

819
01:29:30,790 --> 01:29:36,040
There are people who tend to think visually and those who tend not to think visually.

820
01:29:36,040 --> 01:29:39,340
And I was very much on the visual side.

821
01:29:39,340 --> 01:29:45,160
I seem to remember when I was at university, they were only one or two people who thought very much on the visual side.

822
01:29:45,160 --> 01:29:47,380
One of whom was me for two or three.

823
01:29:47,380 --> 01:29:56,260
I guess I can remember one other particularly, but I mean, other people could do it, but that wasn't their primary way of thinking.

824
01:29:56,260 --> 01:30:03,280
So it was a lot the variation in ways people thought about things where it was quite striking.

825
01:30:03,280 --> 01:30:13,390
And as I say, when somebody might be talking to me describe some idea, and I wouldn't really follow the actual words or sentences in any detail.

826
01:30:13,390 --> 01:30:19,120
I'd pick up the gist of what was being said and maybe come to the conclusion that was required at the end,

827
01:30:19,120 --> 01:30:25,690
but not exactly following the details of what was being said to me that stay with you.

828
01:30:25,690 --> 01:30:29,200
Did it resolve itself in some way? I think it stayed with me.

829
01:30:29,200 --> 01:30:33,490
I think. No, I think it's very true.

830
01:30:33,490 --> 01:30:42,190
But I think it was true in relativity. I think that was a distinctive feature that I thought about the subject very much in pictures and how

831
01:30:42,190 --> 01:30:49,180
light rays behave and things like that happened rather than the equations do the equations when needed.

832
01:30:49,180 --> 01:30:56,710
Although even then I would have a very different way of looking at equations often.

833
01:30:56,710 --> 01:31:05,920
And this came about when I was a graduate student, mainly, and I was just doing I was supposed to be doing algebra geometry under the Hodge.

834
01:31:05,920 --> 01:31:14,980
William Hodge was a very distinguished algebra geometry that he I don't think he was very visible in his thinking,

835
01:31:14,980 --> 01:31:23,260
but he gave lectures on differential geometry and he was sort of equations all over the board and disorganised lecturer.

836
01:31:23,260 --> 01:31:26,650
And I had a great deal of trouble following in detail what these things meant.

837
01:31:26,650 --> 01:31:35,140
And so I developed this notation where instead of having symbols you see in the subject of differential geometry or relativity theory,

838
01:31:35,140 --> 01:31:40,150
you have symbols with lots of indices and indices at the top and indices on the bottom.

839
01:31:40,150 --> 01:31:45,730
And then you have to see which letter here corresponds to which letter over there. And that was much too complicated for me.

840
01:31:45,730 --> 01:31:53,170
So I just draw a line connecting these things, and I developed this diagrammatic way of expressing these equations.

841
01:31:53,170 --> 01:32:03,640
And it wasn't the way anybody else, but it was very helpful to me in trying to sort out the problem that he'd sent me any work.

842
01:32:03,640 --> 01:32:12,100
Yes, it. I didn't solve the problem because the problem didn't have a solution in the form one expected this

843
01:32:12,100 --> 01:32:18,160
was a striking thing because I use this method to show that there was no solution to this problem.

844
01:32:18,160 --> 01:32:19,570
In the most obvious way,

845
01:32:19,570 --> 01:32:26,890
you'd expect you're trying to construct something you had to to object to and you had to combine together to make a third object.

846
01:32:26,890 --> 01:32:28,690
I want to go into the details of that.

847
01:32:28,690 --> 01:32:37,960
And these were very complicated algebraic expressions that Jim Jarmusch is simply looking for at the intersection of two two geometrical figures.

848
01:32:37,960 --> 01:32:44,830
And that was clear to visualise what you're trying to do, but to do it algebraic, it was very, very complicated.

849
01:32:44,830 --> 01:32:51,670
And in order to do this, I developed this notation and I had these pictures with lines all over the place,

850
01:32:51,670 --> 01:32:59,980
and I remember showing them to my supervisor and I don't think he he followed what I was doing.

851
01:32:59,980 --> 01:33:07,630
He thought about it very differently. So at that point, I didn't show anybody for a long time.

852
01:33:07,630 --> 01:33:09,820
So, but no,

853
01:33:09,820 --> 01:33:18,340
it helped me sorting out this problem and to see that there was no solution in the most direct way and you had to go in directly to find a solution.

854
01:33:18,340 --> 01:33:24,220
But when you were when you were still a graduate student, you developed the Penrose Triangle.

855
01:33:24,220 --> 01:33:29,950
What was that and why was it such a breakthrough? Not a breakthrough when it plays you so much?

856
01:33:29,950 --> 01:33:33,490
Well, this was a complete digression from what I was doing.

857
01:33:33,490 --> 01:33:35,740
You see, I was at Cambridge at the time.

858
01:33:35,740 --> 01:33:47,650
I think it was in my second year and there was a conference at the International Congress of Mathematicians was taking place in Amsterdam,

859
01:33:47,650 --> 01:33:53,710
in the Netherlands, and I and a colleague decided we'd go to this conference.

860
01:33:53,710 --> 01:34:01,060
And I remember finding a lot of it was very mysterious and difficult to understand,

861
01:34:01,060 --> 01:34:06,730
but lectures by him and violet remember, which was very impressive and so on.

862
01:34:06,730 --> 01:34:17,890
And I then I think I was getting on a tram at one point and one of my lecturers, Sean Wylie, told me about algebra, algebraic topology.

863
01:34:17,890 --> 01:34:28,840
And he had in his hand a catalogue. And this was a catalogue of the an exhibition that was being held in the.

864
01:34:28,840 --> 01:34:34,000
And one of the early the museums in Amsterdam.

865
01:34:34,000 --> 01:34:41,920
And he said, you might be interested in this. It had this strange picture on the catalogue of these now famous picture.

866
01:34:41,920 --> 01:34:49,330
One of these it's called night and day. One of the pictures with birds flying and their one went into the night and the other way

867
01:34:49,330 --> 01:34:53,590
it sits in the day and the gaps between the birds become the birds and the other side.

868
01:34:53,590 --> 01:34:57,820
And it's very clever. And I'd never seen anything like that before.

869
01:34:57,820 --> 01:35:06,730
And so I went to this exhibition that was in the Van Museum, and they had a special room full of these as your pictures,

870
01:35:06,730 --> 01:35:12,760
as they thought mathematicians would be interested in that. He wasn't, as she was not famous at all at that time.

871
01:35:12,760 --> 01:35:18,790
And I was absolutely stunned by these things, most particularly one called relativity,

872
01:35:18,790 --> 01:35:22,960
which is the picture where the force of gravity was in three different directions and

873
01:35:22,960 --> 01:35:27,730
people were walking upstairs and at right angles to each other and that sort of thing.

874
01:35:27,730 --> 01:35:30,580
And it was absolutely fascinating.

875
01:35:30,580 --> 01:35:40,720
And I went away thinking that I hadn't quite seen something of the nature which I had in mind, which is a picture which was locally consistent,

876
01:35:40,720 --> 01:35:49,030
but as a whole inconsistent because there is a sort of ambiguity in the local picture about how far away it was from there.

877
01:35:49,030 --> 01:35:53,980
And I drew pictures with bridges and rivers and roads going different ways,

878
01:35:53,980 --> 01:36:01,360
and then I simplified it to this thing that people refer to now as the tribal three rods, each at right angles to each other.

879
01:36:01,360 --> 01:36:05,530
But you you can't construct locally, you can.

880
01:36:05,530 --> 01:36:08,140
So you can have a local picture that makes sense locally.

881
01:36:08,140 --> 01:36:16,360
But since the distance away from you gets inconsistent at some point, then it's an impossible figure.

882
01:36:16,360 --> 01:36:23,140
And I remember showing my father and he showed it to his colleagues, and they were so ill looking at these things.

883
01:36:23,140 --> 01:36:27,850
And he then developed that into impossible buildings.

884
01:36:27,850 --> 01:36:30,160
He had when he called an impossible college, I remember.

885
01:36:30,160 --> 01:36:39,800
And then he produced a staircase which went round and round and round, and we then wrote a paper on this the.

886
01:36:39,800 --> 01:36:48,270
Sorry. You and your father? Yes. My father and I and we we wrote a paper on this and we couldn't decide what the subject was.

887
01:36:48,270 --> 01:36:49,400
Where do we send it, you see?

888
01:36:49,400 --> 01:36:55,790
Well, my father said, Well, I have to know the editor of the British Journal of Psychology, so I'm sure he will accept it.

889
01:36:55,790 --> 01:37:03,530
So we decided the subject was psychology. And he said this paper, the British psychologist, it was duly accepted.

890
01:37:03,530 --> 01:37:11,840
And then we sent a copy to Asia. We acknowledge the, I think, the catalogue to the museum so interested should have.

891
01:37:11,840 --> 01:37:20,300
In the meantime, assured produced a picture of Belvedere in which which does illustrate the same thing.

892
01:37:20,300 --> 01:37:30,320
But then he picked up on this, and he developed the staircase into the one called ascending and descending and the triangle into a vertical waterfall,

893
01:37:30,320 --> 01:37:36,710
you said of the triangle and its impossibility in its purest form.

894
01:37:36,710 --> 01:37:43,300
Why did that attract you and why did you use the word purist? Well, you see, it's really.

895
01:37:43,300 --> 01:37:48,820
It's not there's no kind of elaborations to it. I mean, it really is just just the impossibility.

896
01:37:48,820 --> 01:37:54,670
That's what I meant. What I didn't know was that there was this Swedish artist Oscar Rosfeld,

897
01:37:54,670 --> 01:38:00,730
who previously drawn a very similar thing with cubes going around, I guess, which I didn't know about.

898
01:38:00,730 --> 01:38:05,110
And there are old pictures you can find. There's a Broyhill picture with called the Gallows.

899
01:38:05,110 --> 01:38:12,280
I think it's called a jack on the gallows isn't so subjective, and it's joined up differently in the top of the box.

900
01:38:12,280 --> 01:38:16,480
So it's quite deliberately. I mean, some people thought, Oh, he's made a mistake. No, no, he didn't.

901
01:38:16,480 --> 01:38:18,970
It was absolutely deliberate. You can see that.

902
01:38:18,970 --> 01:38:24,910
Did this attract you partly because of your interest in drawing as well as you interested in in the pure impossibilities?

903
01:38:24,910 --> 01:38:31,660
I think so. Well, you see, we did other things together that wasn't actually the first thing we did together.

904
01:38:31,660 --> 01:38:40,840
The first thing, as far as I can recall. As we were on a train going to Switzerland, where my mother's mother,

905
01:38:40,840 --> 01:38:49,600
my grandmother on my mother's side lived and we were going to visit her and my father came up and he said,

906
01:38:49,600 --> 01:38:54,430
perhaps you could help me developing an idea because there was no.

907
01:38:54,430 --> 01:39:04,060
The question is whether you could build a machine which would reproduce itself. And the great mathematicians on the island had proved some theorem,

908
01:39:04,060 --> 01:39:11,860
but with some several thousands or millions of pieces, you could make this machine, which would copy itself.

909
01:39:11,860 --> 01:39:18,130
My father was he knew about this, but he wasn't very pleased. I thought, Well, you know, life has got kind of come about from something simple.

910
01:39:18,130 --> 01:39:27,800
So there must be some simple thing which will reproduce itself. He suggested using some something with gadgets, which would.

911
01:39:27,800 --> 01:39:34,040
Copy themselves and so that to solve on the train, on the way to Switzerland on the night, it was a night train, you see,

912
01:39:34,040 --> 01:39:40,920
and so we had bunk beds or something, and I remember to produce, I produced my solution and he produced this solution.

913
01:39:40,920 --> 01:39:46,430
This was better than mine. I think he appreciates his mind, but I think he got his respect.

914
01:39:46,430 --> 01:39:48,380
I think it was best.

915
01:39:48,380 --> 01:39:58,040
So he then wrote an article for Nature, which got published between us, which was called self produced, self reproducing analogue or something.

916
01:39:58,040 --> 01:40:03,740
And it's had these two little pieces and you haven't got a track and you shake the track.

917
01:40:03,740 --> 01:40:07,850
And then they just hit each other and they don't combine.

918
01:40:07,850 --> 01:40:15,950
But if you link two together and you can mix them two ways this way or this way, think this way, then two other pairs will make up the same way.

919
01:40:15,950 --> 01:40:24,570
If you let them this way, then other peoples will link up that way the same way. So it was a very simple, very simple example of something.

920
01:40:24,570 --> 01:40:32,010
Which you could imagine some molecules doing something similar, so his life could begin with something extremely simple,

921
01:40:32,010 --> 01:40:36,190
not these complicated, vastly complicated things that so moment would introduce.

922
01:40:36,190 --> 01:40:47,460
So I thought the idea was was a very good one, not in detail and seemed like chemistry or what life would be like.

923
01:40:47,460 --> 01:40:51,030
Then my father then went on to develop much more complicated things with.

924
01:40:51,030 --> 01:41:02,400
He was trying to model DNA, that sort of thing. So he got a little bit, I think, too far into making this workshop in the lab,

925
01:41:02,400 --> 01:41:12,450
in the back garden that he would plug away with his petals, jigsaw and death and make dozens and dozens of these machines.

926
01:41:12,450 --> 01:41:22,620
And in 1964, you were said to have, I'm quoting, revolutionised the mathematical tools that we used to analyse properties of Space-Time.

927
01:41:22,620 --> 01:41:28,800
That's quite a mouthful. It must have been quite a it's quite so unravelled for us.

928
01:41:28,800 --> 01:41:37,500
I think it is what you were saying earlier. I was thinking about the subject differently for most people who see most people at that time.

929
01:41:37,500 --> 01:41:40,680
When I said at that time, this was a is bit before 1964,

930
01:41:40,680 --> 01:41:48,510
it was when the quasars were being seen and they were suggested that they were gravitational collapse

931
01:41:48,510 --> 01:41:55,950
sort of bodies coming together and producing who knows what and producing these very bright signals,

932
01:41:55,950 --> 01:42:03,180
which became known as the quasars, which are extremely bright sources in the radio signals.

933
01:42:03,180 --> 01:42:09,900
And they were very puzzling to people. But you see. The two ways people might think about general relativity at a time,

934
01:42:09,900 --> 01:42:18,440
either the mathematicians who are just trying to solve the equations and you could only solve the equations of a very simple symmetrical,

935
01:42:18,440 --> 01:42:27,050
had some very simple characteristic which you could use as a as a gadget to allow you to to find exact solutions in the equations.

936
01:42:27,050 --> 01:42:31,130
I could do that sort of thing, but I wasn't a particular expert at it.

937
01:42:31,130 --> 01:42:35,010
The other thing people might do is put things on computers.

938
01:42:35,010 --> 01:42:43,280
At that time, they haven't got very far with with how modelling things that we know called black holes.

939
01:42:43,280 --> 01:42:47,660
But I was thinking about this in a different way, which is much more geometrical.

940
01:42:47,660 --> 01:42:56,930
So I had this way of trying to visualise what was going on all the time, how light behaved, and it was very much my style of thinking.

941
01:42:56,930 --> 01:43:03,020
Were you making drawings? Oh, absolutely is drawings all the time.

942
01:43:03,020 --> 01:43:07,640
And that was how how light rays focus. That was the main point.

943
01:43:07,640 --> 01:43:13,490
And there's a really close analogy on the edge of physics at school, because you see,

944
01:43:13,490 --> 01:43:16,940
one of the things you did at school was was blue with optical benches,

945
01:43:16,940 --> 01:43:23,390
and you have a logical bench and you have these lenses and have different distances and you see how they focus lies and all that.

946
01:43:23,390 --> 01:43:29,960
And then you could have pure lenses, which are another stigmatic. So the focussing is the same in all directions.

947
01:43:29,960 --> 01:43:36,770
Or you can have a stigmatism where the focussing in one direction is different from the focussing other direction,

948
01:43:36,770 --> 01:43:41,600
and a purely stigmatic lens is when is completely positive.

949
01:43:41,600 --> 01:43:49,550
One direction, the negative in the other direction and the curvature due to pure gravity is of that kind.

950
01:43:49,550 --> 01:43:59,300
So I could understand how the focussing of light rays behave from having this experience in doing physics at school.

951
01:43:59,300 --> 01:44:01,760
We're playing with optical benches, so that was useful to me.

952
01:44:01,760 --> 01:44:07,270
So that's not just drawing pictures that was having some idea of what physics was involved.

953
01:44:07,270 --> 01:44:12,970
Says You got lenses now that the kind of lens that gravity.

954
01:44:12,970 --> 01:44:24,310
That's how it acts, a light rays of a purely positive focussing lens convex lens, which is positive focussing is what matters.

955
01:44:24,310 --> 01:44:34,030
And I just come back to the quotation now that the summary of another child is said to be, the two words revolutionised the mathematical tools.

956
01:44:34,030 --> 01:44:39,130
Not. Well, on those two revolutionising tools for the minister, too.

957
01:44:39,130 --> 01:44:48,780
I'd be very grateful. It's a hard question to answer, it's just the people weren't thinking that way.

958
01:44:48,780 --> 01:44:55,740
As I say, they were either looking at partial solutions, which didn't tell you much about the general case.

959
01:44:55,740 --> 01:45:02,160
There was this model of collapse to a black hole, as we would not call it mutual Oppenheimer and Schneider,

960
01:45:02,160 --> 01:45:08,310
which was put forward in 1939, just before the Second World War.

961
01:45:08,310 --> 01:45:12,420
And that was extremely symmetrical. So you could actually solve the equations.

962
01:45:12,420 --> 01:45:16,140
You would write down the solution on a piece of paper.

963
01:45:16,140 --> 01:45:24,790
That's the actual solution for the empty space and the Friedman solution for where the matter was.

964
01:45:24,790 --> 01:45:30,480
So you could combine these two together and simply write it down on a piece of paper what the equations were.

965
01:45:30,480 --> 01:45:37,020
But that was only possible because you assumed exact spherical symmetry.

966
01:45:37,020 --> 01:45:40,470
So it's absolute the same all the way around a sphere.

967
01:45:40,470 --> 01:45:45,870
So the collapse was exactly symmetrical in the fact that it had no pressure, nothing to stop it.

968
01:45:45,870 --> 01:45:49,890
If you like the falling in matter and the fact that it was symmetrical, is it?

969
01:45:49,890 --> 01:45:53,790
What is it got to go? There's nothing to stop it. So bits in the centre.

970
01:45:53,790 --> 01:45:56,370
And so the density would become infinite centres.

971
01:45:56,370 --> 01:46:03,480
You get this infinite density singularity where you, your equations give up because things go to infinity.

972
01:46:03,480 --> 01:46:06,600
And what do you do? So that was the problem.

973
01:46:06,600 --> 01:46:11,400
But most people thought, Oh, well, that's not realistic because things will be swishing around in a complicated way.

974
01:46:11,400 --> 01:46:16,670
They won't be in the middle. They won't be aimed at the middle. So what do you do?

975
01:46:16,670 --> 01:46:26,060
But I didn't try to solve the equations that was hopeless. I didn't know much about how to programme computers, and so that was hopeless.

976
01:46:26,060 --> 01:46:35,330
But I had my way of thinking, but just to see how how light rays focus and how they behaved and what is actually you see.

977
01:46:35,330 --> 01:46:39,380
There were two problems I'd worked on before which were helpful to this.

978
01:46:39,380 --> 01:46:43,640
One is one I described in my lecture, which had to do with the steady state model,

979
01:46:43,640 --> 01:46:53,300
which is one of the things that got me interested in doing cosmology and my friendship within the show, which is important to me.

980
01:46:53,300 --> 01:47:05,270
The other was quite a different problem. I was working at the same time a little bit earlier in 1964 on the problem paper,

981
01:47:05,270 --> 01:47:13,430
which I submitted to the Royal Society, which had to do with the asymptotic property of gravitational field.

982
01:47:13,430 --> 01:47:21,290
So say you're looking at gravitational radiation. And how does it behave and what is the curvature look like in detail as you go to infinity?

983
01:47:21,290 --> 01:47:27,620
And I had a way of looking at this, which meant squashing down infinity to a finite boundary.

984
01:47:27,620 --> 01:47:34,700
So I have in my head took this picture of me. Yes, your picture of the situation that you've got this boundary.

985
01:47:34,700 --> 01:47:39,980
So limit boundary edge. But that's a particular instance of what I was doing.

986
01:47:39,980 --> 01:47:44,030
We squash infinity down to make it look like a nice boundary.

987
01:47:44,030 --> 01:47:55,850
And I was able to prove certain things and I had one of the problem was that I needed that infinity look like a sphere.

988
01:47:55,850 --> 01:48:01,970
So this means that as you look out in the sky, you see the celestial sphere now the opposite direction.

989
01:48:01,970 --> 01:48:10,400
When you're looking at the future, incidentally, does it necessarily have this structure of a sphere up there?

990
01:48:10,400 --> 01:48:12,860
Or could you have something more complicated?

991
01:48:12,860 --> 01:48:18,740
And so in the appendix to this, I don't think there's any sensible person would just assume it's just showing up.

992
01:48:18,740 --> 01:48:23,360
But I wasn't satisfied that. So I set about, Well, can you prove it, Sofia?

993
01:48:23,360 --> 01:48:28,820
So I thought about what the light rays do when they get out. And I had a sort of argument.

994
01:48:28,820 --> 01:48:33,890
I think it was reasonably good in the appendix. It wasn't part of the main paper I slaves as a way of thinking.

995
01:48:33,890 --> 01:48:36,170
I was wasting my time all the time.

996
01:48:36,170 --> 01:48:44,050
And I developed a lot of these techniques of looking like what is the boundary of the future of a particular point with its future?

997
01:48:44,050 --> 01:48:49,550
And what's the boundary look like and how do the rest cross over? And you look at that after they've crossed you.

998
01:48:49,550 --> 01:48:53,090
Just look at the outer boundary and what step ahead in life and so on.

999
01:48:53,090 --> 01:48:59,750
And I developed enough of an understanding there that when I looked shortly afterwards,

1000
01:48:59,750 --> 01:49:10,220
not very long afterwards at this problem of gravitational collapse and you knew about the solar in the paper,

1001
01:49:10,220 --> 01:49:16,640
which seemed to show that you didn't get singularities. And I wasn't totally persuaded by that.

1002
01:49:16,640 --> 01:49:25,130
Then I remember going walking in the woods and trying to think of what condition could you have to show that these singularities?

1003
01:49:25,130 --> 01:49:29,090
I don't know why. I pretty well thought those singularities were genetic.

1004
01:49:29,090 --> 01:49:30,830
I guess that was an intuition I have.

1005
01:49:30,830 --> 01:49:37,490
I don't quite know what I was toying with both ideas that it might bounce ideas or it might be generally singular.

1006
01:49:37,490 --> 01:49:43,670
But I think I thought it was probably generally singular in opposition to what the Russians seem to believe.

1007
01:49:43,670 --> 01:49:48,410
And then I realised you needed something non-local,

1008
01:49:48,410 --> 01:49:57,890
just a local condition that says things blow up because of the equations work just because because of the symmetry, you could blow everything up.

1009
01:49:57,890 --> 01:50:01,580
And there was nothing of the scale to tell you that it could be local.

1010
01:50:01,580 --> 01:50:07,820
So I was pretty persuaded it had to be something more global. The condition, which is sort of more global.

1011
01:50:07,820 --> 01:50:12,800
And then it was later on this story, I keep telling people.

1012
01:50:12,800 --> 01:50:20,630
About us, I think I was I had this lectureship at Birkbeck College in London,

1013
01:50:20,630 --> 01:50:27,590
and I think I was going to my office in the neighbourhoods and there there Euston

1014
01:50:27,590 --> 01:50:34,970
Square and I was talking to a colleague who is an Englishman pull over Robinson.

1015
01:50:34,970 --> 01:50:39,260
He actually was. His job was then in the US, but he was a very good person.

1016
01:50:39,260 --> 01:50:44,630
It was one of these people very skilled at producing exact solutions. He had a real skill doing that.

1017
01:50:44,630 --> 01:50:52,610
I don't know what he was talking to me about how there were very these also skilled with with verbal if if you talk to him,

1018
01:50:52,610 --> 01:50:58,520
he would tell them this wonderful way. The Americans loved him because he had this flowery way of talking in English.

1019
01:50:58,520 --> 01:51:03,590
It was a beautiful skill. So he was talking to me like this. He was doing most of the talking.

1020
01:51:03,590 --> 01:51:07,820
And then we got to this point. We were across the street, and as we crossed the road,

1021
01:51:07,820 --> 01:51:13,500
he stopped talking and we were looking at the traffic and then we got to the other side and he talked again.

1022
01:51:13,500 --> 01:51:19,460
And then after he left, I had this strange feeling in relation to it was,

1023
01:51:19,460 --> 01:51:25,970
this is this I must have had something during the course of the day visit to admit.

1024
01:51:25,970 --> 01:51:33,860
And so I'm rather fussy about this sort of thing. So I went right through starting from the beginning and wanted to have some breakfast.

1025
01:51:33,860 --> 01:51:39,920
And then what was going on during the day and then it came to me crossing the street.

1026
01:51:39,920 --> 01:51:41,570
I God, that was it.

1027
01:51:41,570 --> 01:51:50,900
I had this idea as we crossed the street of a characterisation of a point of no return, which was a sort of global characterisation.

1028
01:51:50,900 --> 01:51:58,940
This is the thing I call the track surface. And this was a surface which you see as the matter falls inwards, you surround it.

1029
01:51:58,940 --> 01:52:03,970
We're still now probably in the vacuum region outside the margins and collapses.

1030
01:52:03,970 --> 01:52:10,310
And you could draw the sphere around it. And it has a curious property that if you had a flash of light,

1031
01:52:10,310 --> 01:52:16,910
imagine instantaneous flash of light on that sphere that the light rays converge both ways.

1032
01:52:16,910 --> 01:52:22,010
So if you imagine this convex surface, the massive flash of light on that surface,

1033
01:52:22,010 --> 01:52:25,730
on the concave side, the light rays will converge on the convex side.

1034
01:52:25,730 --> 01:52:32,610
They will diverge on this track surface, they converge on both sides.

1035
01:52:32,610 --> 01:52:38,010
Now, actually, this sounds strange, but there's nothing wrong with that.

1036
01:52:38,010 --> 01:52:45,180
If it's only a local region, what's wrong with it is when it goes all the way around the sphere and it's converging all the way around.

1037
01:52:45,180 --> 01:52:52,510
And I call that a trap surface. And I realised from what I've been doing on this other problem that I knew,

1038
01:52:52,510 --> 01:52:59,670
what if you looked at the future of that region that it had to have a boundary that was what's called compact,

1039
01:52:59,670 --> 01:53:08,220
closed upon itself because of this focus? And then you could see that was inconsistent with the initial surface being vertical.

1040
01:53:08,220 --> 01:53:13,620
So that could you see there? I didn't have the best way of doing at that time.

1041
01:53:13,620 --> 01:53:16,110
There was a slightly better way that Charles Misner,

1042
01:53:16,110 --> 01:53:24,630
who and I read a lot from in Princeton and certainly a lot of things to do with the collapse issue here.

1043
01:53:24,630 --> 01:53:30,360
One thing that I remember him telling me about this again, this question of whether it's a local,

1044
01:53:30,360 --> 01:53:35,560
you see, one of the things that people worried about is when stars collapse.

1045
01:53:35,560 --> 01:53:37,680
See, there's a lot of there's a lot of work.

1046
01:53:37,680 --> 01:53:46,950
I think Dennis Lim Cohen and so talked about this, the history of the collapse to black holes and a lot of this work was on stars.

1047
01:53:46,950 --> 01:53:53,570
And when they collapse down to this what's called the short short radius, the density could be enormous.

1048
01:53:53,570 --> 01:54:00,480
And so you might say, well, we don't really know enough about densities. And so maybe that's the problem that you see.

1049
01:54:00,480 --> 01:54:04,800
But Charlie, isn't it? It's crazy, but it's not. There's nothing to do it.

1050
01:54:04,800 --> 01:54:09,060
You've got a big, big city with lots of stars coming together.

1051
01:54:09,060 --> 01:54:16,050
And the overall density of stars coming together can be very small, much less than density of air.

1052
01:54:16,050 --> 01:54:20,470
And it was still that this condition of a trapped surface.

1053
01:54:20,470 --> 01:54:25,420
It this take you to working with Stephen Hawking. It did.

1054
01:54:25,420 --> 01:54:29,720
And what happened in that collaboration when you see it was I.

1055
01:54:29,720 --> 01:54:37,030
Well, I think it was probably December six before I gave a talk on this.

1056
01:54:37,030 --> 01:54:43,600
I just I just thought of this idea with the track surface. I'm not sure where they'd actually written the paper on that point.

1057
01:54:43,600 --> 01:54:51,670
I think perhaps ahead had, but I gave a talk at King's College London at which the distinguished.

1058
01:54:51,670 --> 01:54:54,670
Well, it's A.J. Helsing, whom I had learnt a lot from,

1059
01:54:54,670 --> 01:55:00,070
he had a very geometrical way of thinking about relativity, and I learnt a lot from his books on that.

1060
01:55:00,070 --> 01:55:03,740
But he happened to be in the audience, which is I was so proud of.

1061
01:55:03,740 --> 01:55:09,970
I gave his talk on the singularity theorem, which was the one that eventually got the Nobel prise.

1062
01:55:09,970 --> 01:55:17,500
I have to talk about that. According to the film Stephen Hawking was in, there was sparks coming out of his head and being inspired by this talk.

1063
01:55:17,500 --> 01:55:27,700
He wasn't there at all. That was just a fabrication. But Sir Dennis Sharma, who is in Cambridge at the time and he heard about the stock and he said,

1064
01:55:27,700 --> 01:55:31,360
Well, would you like to come and give a talk or piece if you were to Cambridge?

1065
01:55:31,360 --> 01:55:37,450
And that was early, perhaps January, in 1965, and I gave a talk there.

1066
01:55:37,450 --> 01:55:42,580
And Stephen Hawking was in the audience, and Dennis was very keen that I would talk to Stephen.

1067
01:55:42,580 --> 01:55:48,250
So he organised a private session that I had with Steven and George Ellis,

1068
01:55:48,250 --> 01:55:55,390
who was collaborating with Steven on trying to find some sort of a theorem about the Big Bang.

1069
01:55:55,390 --> 01:56:00,310
But it was much more limited using techniques. It was I was using.

1070
01:56:00,310 --> 01:56:04,600
So I gave a little private talk to them on my techniques.

1071
01:56:04,600 --> 01:56:14,860
Stephen very quickly, quickly picked up on the techniques and used my theorem in the reverse time direction.

1072
01:56:14,860 --> 01:56:20,910
In the very distance it was, it wasn't quite so.

1073
01:56:20,910 --> 01:56:30,420
Well, the argument was to show that my theorem could be used in reverse time direction to show that the singularity of the Big Bang was generic too.

1074
01:56:30,420 --> 01:56:35,460
So you could imagine a situation where the Big Bang was not the beginning,

1075
01:56:35,460 --> 01:56:41,100
but there was a previous collapsing universe and this switched around and did something complicated,

1076
01:56:41,100 --> 01:56:48,630
then come swirling out again, and that's what the Big Bang was. So I think that was quite a picture that was presented by people.

1077
01:56:48,630 --> 01:56:54,040
I don't remember when that came out of you and Stephen Hawking working together it.

1078
01:56:54,040 --> 01:57:01,990
I can't remember whether that was the prevailing view that people have had, but you see that was what Steven worked on.

1079
01:57:01,990 --> 01:57:09,070
Yes. I mean, he was using the techniques which I'd use for the black hole collapse, but as applied to the whole universe.

1080
01:57:09,070 --> 01:57:18,130
But now in the reverse direction, he then developed these techniques much further than I had to use them and introduced other ideas,

1081
01:57:18,130 --> 01:57:25,360
which, yeah, I had a condition that I've tried to describe.

1082
01:57:25,360 --> 01:57:31,930
It probably would being a little technical, but it's more or less saying that you can have an initial.

1083
01:57:31,930 --> 01:57:39,040
This moment, if you like, where you know what's going on in space time and then you can evolve your creations into the future.

1084
01:57:39,040 --> 01:57:45,580
Now that's what's called the Koshy surface Kristie the famous.

1085
01:57:45,580 --> 01:57:52,930
Mathematician and philosopher Koshy had a hand the view that you could.

1086
01:57:52,930 --> 01:58:02,140
Rockets that were shot across the coast, she was using the idea of developing equations to into the future, when can you do that?

1087
01:58:02,140 --> 01:58:06,280
So we call this a koshy surface is very appropriate to consider these things.

1088
01:58:06,280 --> 01:58:09,010
So that's the surface that you start from.

1089
01:58:09,010 --> 01:58:15,730
When I say it's a surface of three dimensional space, surface in space science as a moment in time, if you like.

1090
01:58:15,730 --> 01:58:21,380
And that koshy surface evolution then gives you what happens in the universe now.

1091
01:58:21,380 --> 01:58:26,920
Might it be like that? But it might be. Some other thing comes and joins on to your universe.

1092
01:58:26,920 --> 01:58:29,560
So you have to consider those other possibilities.

1093
01:58:29,560 --> 01:58:40,180
And so Stephen develops ideas of what you call Koshie Horizons, which are a very important idea coming from extending the things I did by quite a lot.

1094
01:58:40,180 --> 01:58:47,770
And then later on, we got together as a curious story to go together and wrote a paper together which

1095
01:58:47,770 --> 01:58:52,270
generalise pretty well all the techniques we've had previously into one theory.

1096
01:58:52,270 --> 01:58:54,280
Can I take you back to the Big Bang?

1097
01:58:54,280 --> 01:59:06,300
The the saying that the Big Bang didn't start from nothing and it eased in previous universe, but that was an idea.

1098
01:59:06,300 --> 01:59:10,150
Can you developed that? Because that's fascinating said there was a previous universe before us.

1099
01:59:10,150 --> 01:59:16,690
Was there a previous universe before that previous universe? And I think we shouldn't take this as a theory at the moment.

1100
01:59:16,690 --> 01:59:26,110
I think it was more that people. I mean, yes, there were certainly people who discuss that kind of thing.

1101
01:59:26,110 --> 01:59:31,600
Evidence is the word. So what evidence is there for this previous universe?

1102
01:59:31,600 --> 01:59:39,360
None whatsoever. Oh. You see, it was more.

1103
01:59:39,360 --> 01:59:44,220
I mean, there is now, but that's that's jumping ahead at that time.

1104
01:59:44,220 --> 01:59:48,510
There was none whatsoever. It was just this wild speculations.

1105
01:59:48,510 --> 01:59:55,200
People were wildly speculating about all sorts of things you see. You see that Einstein had this wonderful theory.

1106
01:59:55,200 --> 02:00:04,950
And people, this was a wonderful playground for making cosmologists usable, and this was what people were doing.

1107
02:00:04,950 --> 02:00:10,170
When I say people love the mathematics mathematicians who maybe didn't know much cosmology or physics,

1108
02:00:10,170 --> 02:00:16,380
or that maybe they were cosmologists who were trying to see what the universe might be like?

1109
02:00:16,380 --> 02:00:25,740
I mean, this is a simple model. You see the chart, you produce this early solution, which is the thing which describe Oppenheimer.

1110
02:00:25,740 --> 02:00:31,550
It's not a use and so on. And the initial models are circles symmetrical black holes came from that.

1111
02:00:31,550 --> 02:00:37,440
But there are also people working on cosmology. Where was this Russian mathematical statistical?

1112
02:00:37,440 --> 02:00:43,200
Friedman and Friedman, who discussed various different kinds of global structures.

1113
02:00:43,200 --> 02:00:48,780
The universe might be especially close in, especially flat to much and spatially hyperbolic.

1114
02:00:48,780 --> 02:00:52,290
That's the kind of geometry in my picture I showed you.

1115
02:00:52,290 --> 02:00:59,010
So these are all possibilities that people considered, and they might be there was a Big Bang, or maybe you could have a solution, have a Big Bang.

1116
02:00:59,010 --> 02:01:02,970
And so maybe other things. There are all kinds of things in the steady state model.

1117
02:01:02,970 --> 02:01:11,440
You didn't have a Big Bang. So certainly there was a lot of discussion about different things that could happen.

1118
02:01:11,440 --> 02:01:18,420
And the point about the work that Steven was doing there was it narrowed these down that any of those models in

1119
02:01:18,420 --> 02:01:26,010
which you had an initial collapse which bounced to an expansion and suddenly you could have Friedman type models,

1120
02:01:26,010 --> 02:01:30,840
which which behave that way, whether people took them seriously.

1121
02:01:30,840 --> 02:01:36,480
I mean, it was one which was called the oscillating, especially close, and it bounced like, this is happening.

1122
02:01:36,480 --> 02:01:42,720
So the number of repetitions was quite a well known and studied model.

1123
02:01:42,720 --> 02:01:47,250
And so maybe something like that was true of the universe. So you are you.

1124
02:01:47,250 --> 02:01:49,550
Which where are you in your thinking about it?

1125
02:01:49,550 --> 02:01:57,240
Then do you think there was a previous universe of the one in which we let's go, let's go inhabit to inflation?

1126
02:01:57,240 --> 02:02:03,270
How to think of the history here? Because initially you see, when I went to Cambridge and I got involved,

1127
02:02:03,270 --> 02:02:08,040
the Danish German people, and they were all very keen on the steady state model.

1128
02:02:08,040 --> 02:02:13,490
And so I got quite keen on that. It was philosophically very nice because the universe was there all the time and it was there.

1129
02:02:13,490 --> 02:02:18,790
And then there, you see, and so it was philosophically satisfying.

1130
02:02:18,790 --> 02:02:22,990
And I thought so, too. But then when they,

1131
02:02:22,990 --> 02:02:32,440
Penzias and Wilson really discovered that there was this Big Bang and the evidence for the early stage of the universe in which it was extremely

1132
02:02:32,440 --> 02:02:42,580
hot in the microwave background was just discovered seem to indicate that there was this early stage and that really put paid to the steady state.

1133
02:02:42,580 --> 02:02:48,880
And I greatly respected Dennis because when he was convinced that this was true, he says, Look, I was wrong.

1134
02:02:48,880 --> 02:02:52,240
And he went around lecturing and saying, Look, now take the Big Bang seriously.

1135
02:02:52,240 --> 02:03:01,000
There it was this initial stage where you might have to consider quantum gravity and all these things over that, and that was all going on.

1136
02:03:01,000 --> 02:03:13,330
But you see, Stephen was really arguing against the possibility of a previous collapse bouncing into it into an expansion,

1137
02:03:13,330 --> 02:03:17,560
and that was that you could use the theorems in future directions and maybe

1138
02:03:17,560 --> 02:03:22,570
strengthening my black hole results by maybe getting rid of the Koshy surface condition.

1139
02:03:22,570 --> 02:03:30,370
And sure, you could do things like that. But I think he was primarily concerned with proving that there was a Big Bang.

1140
02:03:30,370 --> 02:03:35,470
Yes, I was going to write John, but they said it didn't matter.

1141
02:03:35,470 --> 02:03:39,130
I'm going to keep going on like they can and brilliantly later.

1142
02:03:39,130 --> 02:03:43,480
There's two or three questions. One is why are we talking about beginnings, Big Bang?

1143
02:03:43,480 --> 02:03:50,870
You've described yourself as an atheist, but you've also said I quote, I think I would say that the universe has a purpose.

1144
02:03:50,870 --> 02:03:56,000
It's not somehow by chance. Yes.

1145
02:03:56,000 --> 02:04:00,640
You know, it's difficult to interpret what I was saying that I certainly didn't believe that there

1146
02:04:00,640 --> 02:04:07,270
was no man with a beard who is one of them to this universe or anything like that,

1147
02:04:07,270 --> 02:04:11,980
a conscious being producing. And that didn't help at all. I mean, where does that come from?

1148
02:04:11,980 --> 02:04:20,590
I don't believe any of that, but there is something in its in the connexion with mathematics, which is so deep in physics.

1149
02:04:20,590 --> 02:04:28,330
The more one probes reality, the more one sees how it tied off properties with mathematics.

1150
02:04:28,330 --> 02:04:37,270
But it's not the kind of thing that you see. I guess it may have to do with my views on consciousness and that there is something in the

1151
02:04:37,270 --> 02:04:43,900
time of mathematics which involves we haven't really seen that yet in our physical theories.

1152
02:04:43,900 --> 02:04:50,410
But you have to prove that kind of mathematics to understand what it is that governs conscious

1153
02:04:50,410 --> 02:04:58,180
beings and things which go beyond computation and things like that when I call it a purpose.

1154
02:04:58,180 --> 02:05:03,190
I suppose I would say in order to be a self-respecting universe,

1155
02:05:03,190 --> 02:05:09,750
the thing which you might call a universe has to have beings in it that can perceive it,

1156
02:05:09,750 --> 02:05:15,010
that something like that if I can try to expand upon what I was saying.

1157
02:05:15,010 --> 02:05:20,950
So it's not that the purpose is to produce conscious beings, if you like.

1158
02:05:20,950 --> 02:05:29,260
Maybe I could say it that way, but it's in a certain sense that it wouldn't even be universal if they weren't conscious beings in it,

1159
02:05:29,260 --> 02:05:31,270
because otherwise there's been nobody to see it.

1160
02:05:31,270 --> 02:05:42,400
It's like, I don't know, it's a little bit contorted talking about coming to this and talking about it, about consciousness.

1161
02:05:42,400 --> 02:05:46,720
There's a discussion going on or disagreement going on about the connexion.

1162
02:05:46,720 --> 02:05:54,400
Excuse me, about the connexion between fundamental physics and the human consciousness going on.

1163
02:05:54,400 --> 02:06:03,200
Thinkers like Minsky believe that humans are machines, and there are a lot of people who gathered around his case You're in the minority.

1164
02:06:03,200 --> 02:06:11,410
And as I understand it, you say that physics are inadequate, inadequate to explain the problem of consciousness.

1165
02:06:11,410 --> 02:06:16,730
Could you give us some idea of the battle that's going on?

1166
02:06:16,730 --> 02:06:24,970
We see again, a lot of these things go back to when I was a graduate student and I saw an important thing was I think I was a graduate student.

1167
02:06:24,970 --> 02:06:34,720
I went to lectures and general about funding by Dirac on quantum mechanics and of course, by a man called Steam on Mathematical Logic, Steam Steam.

1168
02:06:34,720 --> 02:06:47,160
And he explained Girdles Theorem. And I found it completely stunning because what he said is if you have a system of proving results in mathematics,

1169
02:06:47,160 --> 02:06:51,070
it's called a formal system and you could put this in the language of computers.

1170
02:06:51,070 --> 02:06:57,490
So if you could put this formal procedure on a computer, and he told he talked about Turing machines and all that.

1171
02:06:57,490 --> 02:07:04,000
So I wrote about all that. If you could put it on a computer, then all the things you could do.

1172
02:07:04,000 --> 02:07:08,830
How do you know what's true in mathematics when you have a proof and what is a proof?

1173
02:07:08,830 --> 02:07:14,950
Will you follow certain rules, axioms and rules of procedure? Perhaps. And then if you follow them correctly,

1174
02:07:14,950 --> 02:07:23,500
that's a proof that what girls showed is that there are certain statements that you can't prove this way, but that's not so much.

1175
02:07:23,500 --> 02:07:33,130
What struck me, what struck me was that you could see, by the way, that girl constructed that particular statement reproduced is true.

1176
02:07:33,130 --> 02:07:42,370
Now how do you see it's true. You true? You see, it's true by virtue of your belief in the formal procedures that you're following.

1177
02:07:42,370 --> 02:07:49,160
If you're simply following these procedures, why do you trust them? Why do you know that gives you truths when you understand them?

1178
02:07:49,160 --> 02:07:54,700
Now, if you understand them, then you know, not just things that you can get using them,

1179
02:07:54,700 --> 02:07:58,780
but you have things that you can get using your knowledge that they're correct.

1180
02:07:58,780 --> 02:08:01,510
That was remarkable. That's what goes in does.

1181
02:08:01,510 --> 02:08:12,550
It uses your belief that these procedures give you truths and that gives you a truth beyond the procedures if you like faith?

1182
02:08:12,550 --> 02:08:17,920
I wouldn't say so. It's like understanding what they've done is a word.

1183
02:08:17,920 --> 02:08:25,060
You see, you sort of give them this thing and you and you follow. I dropped it, and it's a good question.

1184
02:08:25,060 --> 02:08:31,230
It's not. That's exactly what it's not like. You see, it's like, understand you understand something.

1185
02:08:31,230 --> 02:08:38,710
I thought, What does this tell us? It tells us that understanding is not computational is not a computation,

1186
02:08:38,710 --> 02:08:43,960
and understanding is something you do with your consciousness or consciousness is.

1187
02:08:43,960 --> 02:08:49,060
It's very it's part of consciousness, as I understand, and it's that part of consciousness,

1188
02:08:49,060 --> 02:08:58,490
which is a you enabling you to do something which transcends the computation, but the rest of your ego and it's nobody is really.

1189
02:08:58,490 --> 02:09:05,170
I the loss of complaints endlessly. But the argument which one can produce, it's not quite the argument,

1190
02:09:05,170 --> 02:09:11,920
which tends to concentrate on that because I got myself all wrapped up in complications as a much simpler argument.

1191
02:09:11,920 --> 02:09:19,990
But it's quite clear. I think it's quite clear to me and I don't know why people don't follow me very much.

1192
02:09:19,990 --> 02:09:30,070
The understanding that God was a this understanding is something which is not a computation, and that thing is what consciousness is doing.

1193
02:09:30,070 --> 02:09:36,730
OK, you can make these machines rich and go incredibly well at chess or something, but they don't understand a damn thing.

1194
02:09:36,730 --> 02:09:40,300
They don't understand anything. They've just either.

1195
02:09:40,300 --> 02:09:45,980
They played zillion played itself a zillion times, and that's made passive recognition.

1196
02:09:45,980 --> 02:09:50,710
And it says, well, it doesn't understand why such and such a thing works.

1197
02:09:50,710 --> 02:09:55,900
And it's that thing which is not encapsulated without understand.

1198
02:09:55,900 --> 02:10:00,220
Why do you think that the opposition is a minority position in this argument,

1199
02:10:00,220 --> 02:10:08,980
but the idea that that we can become we can be analysed like machines and provided we keep at it as it were,

1200
02:10:08,980 --> 02:10:12,220
has being accepted by an awful lot of people as I understand it.

1201
02:10:12,220 --> 02:10:18,910
I quite understand why it's a minority position because it means going beyond current physics.

1202
02:10:18,910 --> 02:10:25,870
You see, you could and I had this view already when I was a graduate student, and it goes above beyond Newtonian mechanics.

1203
02:10:25,870 --> 02:10:29,770
It goes about special relativity, it goes beyond generals that you can put it on the computer.

1204
02:10:29,770 --> 02:10:33,070
See these things like how you get these little simulations. Yes. Yes.

1205
02:10:33,070 --> 02:10:38,560
Yes, yes. What about quantum mechanics churning equations? That's computational.

1206
02:10:38,560 --> 02:10:46,000
But what about the amazing thing that I staring out of the window in Dirac came during this first lecture?

1207
02:10:46,000 --> 02:10:50,200
Why is it that you can't have a piece of chalk in two places at once?

1208
02:10:50,200 --> 02:10:56,740
I didn't follow his reasoning because I wasn't this long, and I realise it's probably I could because there isn't a reason.

1209
02:10:56,740 --> 02:11:02,620
That's where you have to go beyond quantum mechanics. So you see, it's a very outrageous thing I'm saying.

1210
02:11:02,620 --> 02:11:12,260
I'm saying that what is going on in our brains, which is making us conscious, is going beyond current physics.

1211
02:11:12,260 --> 02:11:16,460
It's not outside physics, it's outside currencies.

1212
02:11:16,460 --> 02:11:25,010
And it's what happens, this is the position I held then and still is that is what's involved in the collapse of the way function.

1213
02:11:25,010 --> 02:11:32,330
Now the collapse of the way function, is this something which people brush under the carpet when they do quantum mechanics shrouding

1214
02:11:32,330 --> 02:11:37,400
Delphine said Homer's homelessness by trying to understand how that can make sense.

1215
02:11:37,400 --> 02:11:45,020
And he was saying, You know, I wish they had nothing to do with quantum mechanics. If I hadn't understood what was jumping, that has to go on you.

1216
02:11:45,020 --> 02:11:48,740
The jumping is you follow the shortening equation. Suddenly, it jumps.

1217
02:11:48,740 --> 02:11:52,940
That's something because this or this or this, that's not following this equation.

1218
02:11:52,940 --> 02:11:58,790
That's what's called the collapse of the wave function. We need a theory of the collapse of the wave function.

1219
02:11:58,790 --> 02:12:05,540
When we have this theory and when we know how to harness theory, then maybe we can make a conscious thing.

1220
02:12:05,540 --> 02:12:11,510
I hope I'm not alive when this happens, and I'm not sure I'm in any danger of that being the case.

1221
02:12:11,510 --> 02:12:16,340
But is this? Sure, it's part of physics. It's not part of current says.

1222
02:12:16,340 --> 02:12:23,920
It's not part of computational physics. Why don't you have, you know, the low? I do not think it's something rather also about away.

1223
02:12:23,920 --> 02:12:29,020
I think if it was there, I've changed my mind. So yes, I would shake his hand and say, Must you?

1224
02:12:29,020 --> 02:12:32,900
Sure. But there is something rather rather frightening about this.

1225
02:12:32,900 --> 02:12:38,470
I think, given that this machine, the idea of human beings actually being because.

1226
02:12:38,470 --> 02:12:42,220
You see, I don't think any of these machines have any consciousness whatsoever.

1227
02:12:42,220 --> 02:12:51,880
It's not even the tiny bits, it's just muscle because they don't incorporate this thing, which they need to know if they built a device.

1228
02:12:51,880 --> 02:12:53,320
There's no code in the machine.

1229
02:12:53,320 --> 02:13:02,890
A device which could take advantage of you can harness the collapse of the wave function or what really is going on in the collapse of the.

1230
02:13:02,890 --> 02:13:07,390
Then there is the potential for it to make a device, which is conscious.

1231
02:13:07,390 --> 02:13:13,000
And I certainly would accept that they're not going to do it with with computers.

1232
02:13:13,000 --> 02:13:19,840
They're not going to do with quantum computers. Quantum computer doesn't harness the collapse of the wave function.

1233
02:13:19,840 --> 02:13:23,680
So sure, it's got to be something else.

1234
02:13:23,680 --> 02:13:32,110
But people who will be around when these things come along, we'll be quite happy to say shake its hands and say, yes, OK, you take over your business.

1235
02:13:32,110 --> 02:13:36,400
That's all right. No, I don't mind things being better than I am.

1236
02:13:36,400 --> 02:13:42,620
I don't want to. The claim to be conscious when they're not at all.

1237
02:13:42,620 --> 02:13:46,490
That's a wonderful place to stop. Thank you very much, Roger, that. And I was terrific.

1238
02:13:46,490 --> 02:13:51,350
Thank you very much indeed. Very much and generous and your explanation?

1239
02:13:51,350 --> 02:14:14,002
Thank you. Thank you.