0:00:38 > 0:00:4220 years ago, Stephen Hawking, a young research student
0:00:42 > 0:00:44at Cambridge University, began to show the first symptoms
0:00:44 > 0:00:47of an incurable disease at he was told might kill him
0:00:47 > 0:00:48within a few years.
0:00:48 > 0:00:52Amyotrophic lateral sclerosis.
0:00:52 > 0:00:55Undeterred, he married, had three children,
0:00:55 > 0:01:00and became a great scientist.
0:01:00 > 0:01:08His subject is cosmology, the study of the universe.
0:02:00 > 0:02:08STUDENTS CHATTER.
0:02:16 > 0:02:19You could pull that down.
0:02:27 > 0:02:30Could you shut the door, please?
0:02:30 > 0:02:37This week's seminar is given by Paul Todd from Oxford.
0:02:39 > 0:02:43What I was going to talk about is some applications of Penrose's
0:02:43 > 0:02:47quasi-local mass construction.
0:02:47 > 0:02:51I'll remind you to begin with, what that construction is,
0:02:51 > 0:02:55because it's something of a novelty.
0:02:55 > 0:02:58It's been around for about a year, and the way the construction works,
0:02:58 > 0:03:00or the way the definition works is...
0:03:00 > 0:03:03The Monday seminar is more or less compulsory for all the relativity
0:03:03 > 0:03:05group, especially the students.
0:03:05 > 0:03:08Chris is in his third year.
0:03:08 > 0:03:11He's working on supersymmetric theories.
0:03:11 > 0:03:13Bruce is studying the early universe, and like Chris,
0:03:13 > 0:03:18he's writing up his Ph.D.
0:03:18 > 0:03:22Then you contract the...
0:03:22 > 0:03:25Wayne concentrates more on the mathematical side than the physics.
0:03:25 > 0:03:27He is a second-year like me, Julian.
0:03:27 > 0:03:35I'm working on quantum gravity.
0:03:35 > 0:03:37It's like picking out some specific bits of spherical harmonic.
0:03:37 > 0:03:38Whereas in special relativity...
0:03:38 > 0:03:42There are three more students, all first years.
0:03:42 > 0:03:45To get into this group, you need a good advanced degree,
0:03:45 > 0:03:51so most of us are in our early 20s, except for Simon, who's only 17.
0:03:51 > 0:03:53So you get the same answer integrating it
0:03:53 > 0:03:59over any hyper surface.
0:03:59 > 0:04:02So if we integrate it over a hyper surface, like so,
0:04:02 > 0:04:04that's a number which depends on which particular killing vector
0:04:04 > 0:04:07I picked and if I picked one of the translation killing vectors,
0:04:07 > 0:04:09that's a component of the total momentum.
0:04:09 > 0:04:13If I picked one of the rotational killing vectors, it's a component...
0:04:13 > 0:04:16Most of us students are under the charge of Stephen Hawking,
0:04:16 > 0:04:19who is the Lucasian Professor of Mathematics, and head
0:04:19 > 0:04:25of the relativity group as well.
0:04:25 > 0:04:26That's special relativity.
0:04:26 > 0:04:28Now if you consider linearised general relativity,
0:04:28 > 0:04:35if this is the source, it gives rise to a gravitational
0:04:35 > 0:04:37field, so you should be able to spot that momentum
0:04:37 > 0:04:38in the gravitational field.
0:04:38 > 0:04:39INAUDIBLE.
0:04:39 > 0:04:44Sorry?
0:04:44 > 0:04:48What do the self dual rotations correspond to?
0:04:48 > 0:04:54Oh, well I...
0:04:54 > 0:04:56The combination of boost and special rotation.
0:04:56 > 0:04:58Yes, that's right.
0:04:58 > 0:05:02If it is, if you think of it as a rotation of the X Y plane,
0:05:02 > 0:05:05plus I times a boost and the TZ plane, they are just one
0:05:05 > 0:05:12of the rotations, naturally.
0:05:12 > 0:05:15Are they real?
0:05:15 > 0:05:23They are real.
0:05:23 > 0:05:26So they are real in the Euclidian space, but they're not
0:05:26 > 0:05:28going to be real here.
0:05:28 > 0:05:36This is what one might refer to as old-fashioned relativity,
0:05:36 > 0:05:38with plus minus minus minus.
0:05:38 > 0:05:46LAUGHTER.
0:05:53 > 0:05:55We gave that up ten years ago.
0:05:55 > 0:06:03LAUGHTER.
0:06:13 > 0:06:18A guy called Stewart Lowther at Manchester...
0:06:18 > 0:06:21INAUDIBLE.
0:06:21 > 0:06:25There are two different...
0:06:25 > 0:06:30In equivalent?
0:06:30 > 0:06:36Ah-ha.
0:06:41 > 0:06:43That equal something of the form like this, then Chi.
0:06:43 > 0:06:49It's going to be...
0:06:49 > 0:06:53Self dual, then that's got to be true.
0:06:53 > 0:06:57Which if you stick that in, gives you...
0:06:57 > 0:07:01People tend to congregate from the relativity group, and,
0:07:01 > 0:07:06at the time, you find that you learn almost as much as you do sitting
0:07:06 > 0:07:14in your office working or reading.
0:07:16 > 0:07:20And that equals something of the form like this.
0:07:20 > 0:07:23Right, so that one just corresponds?
0:07:23 > 0:07:27That is what I was wondering.
0:07:27 > 0:07:32So it doesn't work with one or two.
0:07:32 > 0:07:35You can do a certain amount of research and creative thinking
0:07:35 > 0:07:38each day and then what's really helpful is discussing with other
0:07:38 > 0:07:46people, so that your ideas are clarified.
0:07:46 > 0:07:51Why doesn't it work with five, for example?
0:07:51 > 0:07:55The group is quite close.
0:07:55 > 0:08:00We get to talk to each other about problems and have
0:08:00 > 0:08:02discussions all the time, which is very good in a social
0:08:02 > 0:08:06sense, and also in the sense that there are people here who,
0:08:06 > 0:08:08if you asked them a question about any particular subject,
0:08:08 > 0:08:12there's bound to be someone who can find an answer to it,
0:08:12 > 0:08:19and so you don't have to wait for very long to find an answer!
0:08:19 > 0:08:25Because the one...
0:08:33 > 0:08:35Because you have much greater contact with
0:08:35 > 0:08:37Stephen as a supervisor, because he needs your help
0:08:37 > 0:08:40all the time, he's always available to answer questions and to help
0:08:40 > 0:08:42you with things you don't understand, and he's also very,
0:08:42 > 0:08:47very clear in the way he explains it.
0:08:47 > 0:08:51And since he knows all his research students as friends,
0:08:51 > 0:08:58he seems much more relaxed and much less an academic physicist.
0:08:58 > 0:09:03He most definitely is number one an academic physicist.
0:09:03 > 0:09:08The most famous of all academic physicists is Albert Einstein.
0:09:08 > 0:09:11The source of his fame, the general theory of relativity,
0:09:11 > 0:09:16burst on the world of physics in 1915.
0:09:16 > 0:09:19But after an initial rush of enthusiasm, few other academic
0:09:19 > 0:09:26physicists took up his theory, and developed further.
0:09:26 > 0:09:31General relativity passed out of fashion for about 40 years.
0:09:31 > 0:09:38The initial?
0:09:55 > 0:09:58Sorry?
0:09:58 > 0:10:02Stephen Hawking was one of a group of scientists who resurrected
0:10:02 > 0:10:04interest in Einstein's general theory of relativity
0:10:04 > 0:10:10during the 50s and 60s.
0:10:10 > 0:10:15Stephen worked on mathematical theorems in general relativity
0:10:15 > 0:10:17which proved the necessity for a big bang at the beginning
0:10:17 > 0:10:21of the universe.
0:10:21 > 0:10:23He also investigated many of the attributes of a bizarre
0:10:23 > 0:10:26class of objects whose properties are predicted by Einstein's theory.
0:10:26 > 0:10:32Black holes.
0:10:33 > 0:10:36Massive as they are, black holes are not things
0:10:36 > 0:10:38you can actually see, because a black hole
0:10:38 > 0:10:43doesn't emit any light.
0:10:43 > 0:10:46But if a black hole passes in front of a background of stars,
0:10:46 > 0:10:54the stars appear to move away from their real positions,
0:10:54 > 0:10:56just as if the black hole were a giant lens.
0:10:56 > 0:10:59In fact, the light from the background stars is bent
0:10:59 > 0:11:02round and round the black hole, by its intense gravitational field,
0:11:02 > 0:11:08so you can see several images of each star at once.
0:11:08 > 0:11:12If you are a long way away from a black hole,
0:11:12 > 0:11:16you are quite safe!
0:11:16 > 0:11:18If you're a long way away from a black hole,
0:11:18 > 0:11:26you are quite safe.
0:11:32 > 0:11:35If our sun were to become a black hole,
0:11:35 > 0:11:38we would continue to orbit around it just as we do
0:11:38 > 0:11:41at the moment.
0:11:41 > 0:11:49In fact, it wouldn't make any difference to our orbit.
0:11:50 > 0:11:58Of course, we would get rather cold!
0:12:02 > 0:12:08But if you go close up to a black hole,
0:12:08 > 0:12:15then the gravitational field becomes stronger.
0:12:15 > 0:12:21And at a certain point,
0:12:21 > 0:12:29the gravitational field reaches critical strength.
0:12:38 > 0:12:43And if you go beyond there, you can't get out at all again.
0:12:43 > 0:12:46Stephen says that a black hole is rather like a whirlpool.
0:12:46 > 0:12:53Imagine you have a whirlpool, and you have some little boats nearby.
0:12:53 > 0:12:56Far away, there are quite safe, but if they get within a certain
0:12:56 > 0:12:59critical distance of the world pool, then even if they try to motor
0:12:59 > 0:13:01directly away from it, they will get sucked
0:13:01 > 0:13:05in by the current which is much faster than they are.
0:13:05 > 0:13:08From within this critical radius, nothing, whether little boats,
0:13:08 > 0:13:15rays of light or spacecraft can ever return.
0:13:21 > 0:13:28If it was a black hole with the mass of the sun...
0:13:35 > 0:13:38Then you would be torn apart by tidal forces before you got
0:13:38 > 0:13:41inside the black hole.
0:13:41 > 0:13:49But if it was a very large black hole...
0:13:51 > 0:13:55Such as we believe may occur in the centre
0:13:55 > 0:14:03of our galaxy, or in quasis...
0:14:20 > 0:14:28Then you wouldn't see anything special
0:14:29 > 0:14:31if you passed inside the black hole.
0:14:31 > 0:14:39But once you pass a certain critical point...
0:14:39 > 0:14:41Then you would never be able to get out again,
0:14:41 > 0:14:49no matter how much rocket power you used.
0:14:58 > 0:15:06Moreover, we assume you would run into a singularity...
0:15:06 > 0:15:08You would be doomed to run into a singularity.
0:15:08 > 0:15:16In a fairly short time.
0:15:16 > 0:15:21Like a few hours.
0:15:21 > 0:15:24So far, even though astronomers have been busily looking for black holes,
0:15:24 > 0:15:26none have been definitely identified, although there
0:15:26 > 0:15:30are some strong candidates.
0:15:30 > 0:15:33So the properties of black holes have had to be entirely worked
0:15:33 > 0:15:35out using mathematics.
0:15:35 > 0:15:39If Einstein's general theory of relativity is true,
0:15:39 > 0:15:44then inside the radius from which nothing can escape,
0:15:44 > 0:15:47called the event horizon, and at the centre of the black hole
0:15:47 > 0:15:49is a singularity.
0:15:49 > 0:15:57A place where gravity is infinite, and space and time come to an end.
0:16:02 > 0:16:09It would be a very nice idea.
0:16:09 > 0:16:11If one could fall into a black hole and then come out
0:16:11 > 0:16:19of another universe.
0:16:27 > 0:16:30And there are some solutions to the Einstein field equations
0:16:30 > 0:16:33which have this property that you can come out
0:16:33 > 0:16:41in another universe.
0:16:44 > 0:16:52But all the evidence we have shows these solutions are very unstable.
0:17:06 > 0:17:09So that is, if you disturb them slightly, for example by falling
0:17:09 > 0:17:17into the black hole...
0:17:24 > 0:17:29Than a passage which takes you through to the other universe
0:17:29 > 0:17:32gets closed off and you run right into the singularity.
0:17:32 > 0:17:38We all came out of a singularity.
0:17:38 > 0:17:46The Big Bang singularity at the beginning of the universe.
0:17:58 > 0:18:00So it wouldn't be that unnatural if we ended up
0:18:00 > 0:18:04in another singularity.
0:18:04 > 0:18:07Either a singularity in a black hole or the collapse
0:18:07 > 0:18:15of the whole universe.
0:18:21 > 0:18:25You could say, dust to dust and ashes to ashes,
0:18:25 > 0:18:33and singularity to singularity.
0:18:55 > 0:18:58It can be very frustrating when you're working at something
0:18:58 > 0:19:02and banging your head against a wall and never
0:19:02 > 0:19:05getting anywhere day in, day out, but then suddenly it clicks
0:19:05 > 0:19:09and everything works fine for a few days.
0:19:09 > 0:19:12An answer comes out.
0:19:12 > 0:19:17Whether it's what you want or what you don't want,
0:19:17 > 0:19:19you have to work out later.
0:19:19 > 0:19:27Part of it's just a search for beauty and prettiness in physics.
0:19:28 > 0:19:32So what do you want it for?
0:19:32 > 0:19:38Just to check on how he did.
0:19:38 > 0:19:43I tend to be more on the mathematical side,
0:19:43 > 0:19:45if you are looking at equations for mathematical consistency rather,
0:19:45 > 0:19:48then a physical relevance.
0:19:48 > 0:19:51I certainly wouldn't mind doing relativity all day, or mathematics,
0:19:51 > 0:19:53or anything like that.
0:19:53 > 0:19:55It just interests you.
0:19:55 > 0:19:58I don't think you could explain it, you would have to ask
0:19:58 > 0:20:04a psychologist about that.
0:20:04 > 0:20:07And there's certainly no monetary reward.
0:20:07 > 0:20:10Well, there's a bit of monetary reward, but not much, I could get
0:20:10 > 0:20:11more on the outside.
0:20:11 > 0:20:12But it's very comfortable.
0:20:12 > 0:20:15You can do what you want to do all your life, if you get
0:20:15 > 0:20:18to do it all your life.
0:20:18 > 0:20:20You're playing games all your life.
0:20:20 > 0:20:23It's pretty good.
0:20:27 > 0:20:33All of theoretical physics is formulated in mathematical terms.
0:20:33 > 0:20:39The theory of physics is really a mathematical model of the world.
0:20:39 > 0:20:43But being good at mathematics isn't enough, one also needs what one
0:20:43 > 0:20:51calls physical intuition.
0:20:52 > 0:20:54You can't deduce physics purely deductibly from a set
0:20:54 > 0:20:57of basic principles, you have to make certain intuitive
0:20:57 > 0:21:05leaps to introduce new models.
0:21:05 > 0:21:08The ability to make these intuitive leaps is what characterises a good
0:21:08 > 0:21:15theoretical physicist.
0:21:27 > 0:21:30Stephen is lucky that he chose one of the few fields
0:21:30 > 0:21:36in which his disability is not a serious handicap.
0:21:36 > 0:21:43Because most of his work is really just thinking.
0:21:43 > 0:21:50And his disabilities don't stop him doing that.
0:21:50 > 0:21:57In a way, they give him more time to think.
0:22:14 > 0:22:16In 1973, Stephen started a new line of research
0:22:16 > 0:22:19that was eventually to make him famous, with the discovery
0:22:19 > 0:22:23of Hawking radiation.
0:22:23 > 0:22:26Up until then, his work on black holes was concerned
0:22:26 > 0:22:30only with large ones, with the mass of the sun or bigger.
0:22:30 > 0:22:36But then, he began to think that there might also be very
0:22:36 > 0:22:38very small black holes.
0:22:38 > 0:22:41Stephen realised, in order to an designed them,
0:22:41 > 0:22:43Einstein's general relativity would not be enough.
0:22:43 > 0:22:45He needed to use a completely different branch of physics
0:22:45 > 0:22:47called quantum mechanics.
0:22:47 > 0:22:49Quantum mechanics was formulated by Werner Heisenberg
0:22:49 > 0:22:53and Erwin Schrodinger in the mid-1920s.
0:22:53 > 0:22:58Theirs is a theory of very small things, like atoms.
0:22:58 > 0:23:01Quantum mechanics is the greatest achievement in physics this century,
0:23:01 > 0:23:06even greater than Einstein's general theory of relativity.
0:23:06 > 0:23:09It implies that what we normally think of as empty space isn't
0:23:09 > 0:23:11really empty at all, but is filled with pairs
0:23:11 > 0:23:15of particles and antiparticles.
0:23:15 > 0:23:18These appear together at some point in space, move apart,
0:23:18 > 0:23:22and then come together again, annihilating each other.
0:23:22 > 0:23:24They are called virtual particles because you can't directly measure
0:23:24 > 0:23:32them with a particle detector.
0:23:32 > 0:23:35According to Hawking, if there's a small black hole present,
0:23:35 > 0:23:38one of the members of these pairs might fall into it.
0:23:38 > 0:23:42Of course, the other one might fall in, too,
0:23:42 > 0:23:45but it's also possible for one of them to escape, and in that case,
0:23:45 > 0:23:53it would appear to be a particle emitted from the black hole.
0:24:00 > 0:24:04In fact, to an observer a long way away, it appears that the black
0:24:04 > 0:24:06hole is emitting particles and radiation as if
0:24:06 > 0:24:07it was a hot body.
0:24:07 > 0:24:09Very small black holes aren't black at all,
0:24:09 > 0:24:12they shine with Hawking radiation.
0:24:12 > 0:24:20If you have a black hole with the mass of the sun,
0:24:22 > 0:24:24then its temperature is only one 10,000,000th of a degree
0:24:24 > 0:24:31above absolute zero.
0:24:31 > 0:24:39And the amount of radiation would be absolutely insignificant.
0:24:44 > 0:24:48But if you have one of these small black holes, then the temperature
0:24:48 > 0:24:49would be much higher, and it would emit
0:24:49 > 0:24:57a lot of radiation.
0:25:01 > 0:25:05In fact, the most interesting mass of a black hole
0:25:05 > 0:25:08is about a thousand million tonnes, which is about the mass
0:25:08 > 0:25:16of a mountain.
0:25:23 > 0:25:27But the actual size of such a black hole would only be that
0:25:27 > 0:25:32of the nucleus of an atom.
0:25:32 > 0:25:40But it would emit a lot of radiation and energy.
0:25:43 > 0:25:51Equivalent to about six nuclear power stations.
0:25:59 > 0:26:04So if you could find such a small black hole,
0:26:04 > 0:26:07and if we could harness it properly, then we would really solve
0:26:07 > 0:26:15all our energy problems.
0:26:26 > 0:26:29However, we have been looking for radiation
0:26:29 > 0:26:37from the black holes like this, and we haven't found any so far.
0:26:42 > 0:26:50In a way, that's rather disappointing for Stephen.
0:27:00 > 0:27:03Because, had we found one, Stephen would have got a Nobel Prize!
0:27:04 > 0:27:04No biscuit?
0:27:04 > 0:27:12Er, yes, please.
0:27:33 > 0:27:37I should go and buy some coffee.
0:27:37 > 0:27:39Oh, that's right, it's quarter to 11.
0:27:39 > 0:27:40Should I buy some instant?
0:27:40 > 0:27:41Try eight ounces.
0:27:41 > 0:27:45Eight ounces.
0:27:45 > 0:27:46There'll be crowds pouring into Stephen's lecture.
0:27:46 > 0:27:49I mean, we didn't have enough last week, and it was getting
0:27:49 > 0:27:51a bit weak at the end.
0:27:51 > 0:27:52Hello.
0:27:52 > 0:27:54Tea?
0:27:57 > 0:27:59Some of us are mathematicians, and others physicists,
0:27:59 > 0:28:02and we're all working on different problems.
0:28:03 > 0:28:08Do you want the Omega for the embedding in the cylinder?
0:28:08 > 0:28:16These problems are usually either suggested or allocated by Stephen.
0:28:18 > 0:28:23These problems are very different from each other,
0:28:23 > 0:28:25but are basically connected, in that they are
0:28:25 > 0:28:28all trying to unearth the fundamentals of the universe.
0:28:28 > 0:28:29So that's supposed to have...
0:28:29 > 0:28:37Does it?
0:28:39 > 0:28:44No, it won't, will it?
0:28:44 > 0:28:47It is certainly an ambitious task.
0:28:47 > 0:28:54People have been working on it for, I'd say, 50 years or longer,
0:28:54 > 0:28:57so I guess it's even more ambitious, since we don't even know if
0:28:57 > 0:29:00the answer is that it can be done.
0:29:00 > 0:29:04A zero on the horizon, on the boundary?
0:29:04 > 0:29:11Yes, because r is half pi there.
0:29:11 > 0:29:13So it's not right?
0:29:13 > 0:29:15Yes.
0:29:15 > 0:29:18In that case...!
0:29:18 > 0:29:21OK.
0:29:49 > 0:29:52Morning, Chris.
0:29:52 > 0:29:58Right here!
0:30:07 > 0:30:15The boundary partitions...
0:30:25 > 0:30:29We are trying to unify many of the modern ideas of physics.
0:30:29 > 0:30:33I'm interested in the almost philosophical, or even religious,
0:30:33 > 0:30:41quest for what actually makes the universe work.
0:30:43 > 0:30:49I mean, certainly the conformal group corresponding to flat
0:30:49 > 0:30:57three space would be 041.
0:31:02 > 0:31:03There's an embarrassing inconsistency at the heart
0:31:03 > 0:31:04of modern physics.
0:31:04 > 0:31:06Einstein's general theory of relativity, which describes
0:31:06 > 0:31:09the nature of very big things, disagrees with the theory of very
0:31:09 > 0:31:11small things, quantum mechanics, in apparently unresolvable ways,
0:31:11 > 0:31:13even though no one has managed to prove either theory untrue.
0:31:13 > 0:31:16So perhaps the way out of this dilemma is to find
0:31:16 > 0:31:23a more profound theory, which incorporates both.
0:31:31 > 0:31:36Two outstanding partial theories have been discovered this century.
0:31:36 > 0:31:44They are general relativity and quantum mechanics.
0:31:57 > 0:32:01Ultimately we have to find one consistent theory,
0:32:01 > 0:32:09which will describe everything...
0:32:11 > 0:32:14Not only general relativity and quantum mechanics,
0:32:14 > 0:32:22but all the other interactions in physics, as well.
0:32:31 > 0:32:39We have had quite a success recently...
0:32:42 > 0:32:44In that we've developed a theory which unifies
0:32:44 > 0:32:52electromagnetism in the weak nuclear force.
0:33:00 > 0:33:03Now we want to go on to unify these interactions with gravity,
0:33:03 > 0:33:11and also unify gravity with quantum mechanics.
0:33:12 > 0:33:20Unfortunately, this is a very ambitious programme,
0:33:23 > 0:33:31but there's quite a reasonable chance of success.
0:33:35 > 0:33:43Stephen would put the chances at 50-50.
0:33:43 > 0:33:51In that you could succeed in this task by the end of the century.
0:33:56 > 0:34:04Now we have a definite candidate...
0:34:05 > 0:34:13For the complete unified theory, which will describe everything,
0:34:16 > 0:34:24and this candidate is called N=8 Supergravity.
0:34:30 > 0:34:38If it doesn't work, then we have no idea what will work.
0:34:52 > 0:35:00We're working very hard on this theory.
0:35:05 > 0:35:08But at the moment it doesn't seem to predict the kind of particles
0:35:08 > 0:35:16that we actually observe.
0:35:18 > 0:35:22But we're hoping that maybe when we understand the theory
0:35:22 > 0:35:30better...
0:35:43 > 0:35:45Then we could construct the particles we observe
0:35:45 > 0:35:47out of smaller pieces, which are the particles
0:35:47 > 0:35:55in the N=8 Supergravity theory.
0:36:10 > 0:36:13And, in that case, we could actually say that theoretical physics
0:36:13 > 0:36:21was over, we had a complete theory of the whole universe.
0:36:31 > 0:36:39If we had a complete theory of the universe, we could,
0:36:42 > 0:36:50in principle, predict everything.
0:37:21 > 0:37:23But in practice, the computations involved are very, very complicated,
0:37:23 > 0:37:25so in effect, we can't predict anything, apart from
0:37:25 > 0:37:33the most simple situations.
0:37:37 > 0:37:39In fact, we already know all the laws which govern all normal
0:37:39 > 0:37:47matter and all normal situations...
0:37:59 > 0:38:01So, in principle, we can predict everything that
0:38:01 > 0:38:09happens on the earth.
0:38:11 > 0:38:13But we haven't had much success in predicting human behaviour
0:38:13 > 0:38:21from mathematical equations.
0:38:31 > 0:38:34It's mostly complicated, a human being contains
0:38:34 > 0:38:41about a million million million million million particles.
0:39:46 > 0:39:48I don't think we really need a very big lunch,
0:39:48 > 0:39:50because we felt ourselves up with doughnuts this
0:39:50 > 0:39:56morning, haven't we, Timmy?
0:39:56 > 0:40:04She's gone out to lunch with Juliet, and she's gone swimming.
0:40:06 > 0:40:09Well, I can afford to buy myself a small black...
0:40:09 > 0:40:11And I can afford to buy Stephen half of one.
0:40:11 > 0:40:13Neither Mrs Hawking nor their son, Timmy, are particularly
0:40:13 > 0:40:15interested in mathematics, so that when they come
0:40:15 > 0:40:21to lunch we try not to talk too much about work.
0:40:21 > 0:40:23Oh, dear, look, Stephen, that's a bit much!
0:40:23 > 0:40:24White?
0:40:24 > 0:40:25Black.
0:40:25 > 0:40:29Two white...
0:40:29 > 0:40:36How's that?
0:40:55 > 0:40:59OK, what Stephen's going to say...
0:40:59 > 0:41:07So Stephen will basically be talking about infinity.
0:41:11 > 0:41:13LAUGHTER.
0:41:13 > 0:41:14Unfortunately, infinity's rather hard to talk about,
0:41:14 > 0:41:22because it's rather a long, long way away!
0:41:24 > 0:41:27So what Stephen's going to do is he's going to try
0:41:27 > 0:41:34and bring it a lot nearer.
0:41:34 > 0:41:36In other words, Stephen's going to conformally compactify
0:41:36 > 0:41:43anti-de Sitter space.
0:41:51 > 0:41:59The Einstein static universe is topologically S3 cross of one...
0:42:05 > 0:42:13Where S3 gives the spatial sections and R1 gives the time.
0:42:14 > 0:42:22So the Einstein static universe...
0:42:22 > 0:42:27So it's really a sort of cylinder.
0:42:27 > 0:42:34With the time being the axis.
0:42:34 > 0:42:37Now it just so happens that we happen to have the universe here.
0:42:37 > 0:42:44LAUGHTER.
0:42:44 > 0:42:45LAUGHTER.
0:42:45 > 0:42:53Sorry!
0:43:00 > 0:43:02Unfortunately, we were unable to get the full 4-dimensional
0:43:02 > 0:43:10universe in here today...
0:43:17 > 0:43:20But the anti-de Sitter space is a time-like hyper surface.
0:43:20 > 0:43:22And that leads to an important difference...
0:43:22 > 0:43:25Crystal clear.
0:43:25 > 0:43:29The way he thinks, he manages to cut away all the dross,
0:43:29 > 0:43:34cut away all the trees, and just see down to the base
0:43:34 > 0:43:37cut away all the trees, and just see down to the basic
0:43:37 > 0:43:39simple, central fact that is necessary to consider.
0:43:39 > 0:43:40And he makes everything so crystal clear, simple.
0:43:40 > 0:43:48It's quite astounding sometimes.
0:43:49 > 0:43:51And because he can't write, because he can't, he finds it
0:43:51 > 0:43:54hard to read papers, hard to read books, he tends to,
0:43:54 > 0:43:57he thinks in terms of diagrams all the time, he thinks very
0:43:57 > 0:44:04clearly, and manages to make everything very, very simple.
0:44:04 > 0:44:07That equation is conforming...
0:44:07 > 0:44:12It depends upon the taste of the person in a way,
0:44:12 > 0:44:17there is a certain taste people have, in which they appreciate
0:44:17 > 0:44:20mathematical beauty of the theory, and it's sort of hard to describe,
0:44:20 > 0:44:24but this is really one of the reasons for doing physics,
0:44:24 > 0:44:32that you find that there are just a certain number of laws,
0:44:32 > 0:44:35and they are very simple when written out, mathematically,
0:44:35 > 0:44:39and simplicity is quite beautiful, and the fact it describes
0:44:39 > 0:44:43what's happening around us is quite amazing, really.
0:44:43 > 0:44:48And the question is whether we can keep on simplifying our laws
0:44:48 > 0:44:56and postulates, and maybe derive an ultimate law like that.
0:44:58 > 0:45:00APPLAUSE.
0:45:00 > 0:45:07Are there any questions?
0:45:14 > 0:45:15Either everyone's understood everything, or no one's
0:45:15 > 0:45:18understood anything!
0:45:18 > 0:45:20Shall we have a vote?
0:45:20 > 0:45:23LAUGHTER.
0:45:28 > 0:45:32In the tearoom, we have a number of portraits of former
0:45:32 > 0:45:40professors of mathematics...
0:45:51 > 0:45:53And Stephen's not quite sure what the criterion
0:45:53 > 0:45:55are that should determine whether you get your
0:45:55 > 0:46:03portrait in the tearoom...
0:46:05 > 0:46:13But one of them seems to be that you've left the department.
0:46:16 > 0:46:24On the wall that this office is on...
0:46:31 > 0:46:35There are the portraits of Stephen's four immediate predecessors
0:46:35 > 0:46:41in the Lucasian chair...
0:46:41 > 0:46:49One of them was Paul Dirac...
0:46:54 > 0:46:56Who is in fact still alive...
0:46:56 > 0:47:03He was one of the founders of quantum mathematics.
0:47:03 > 0:47:11It was he who had the idea of antimatter.
0:47:17 > 0:47:25In the corner, there's Sir George Gabriel Stokes...
0:47:29 > 0:47:37Who was professor for about 54 years...
0:47:37 > 0:47:44Because in those days you didn't have any retirement age...
0:47:47 > 0:47:55And there's a space outside here...
0:48:06 > 0:48:08In which it's fairly obvious they'll put Stephen's
0:48:08 > 0:48:16portrait if he leaves...
0:48:19 > 0:48:25It gives him a rather creepy feeling...
0:48:25 > 0:48:33It's like seeing your own tombstone.