0:00:03 > 0:00:06- Royal Society. - Royal Society. OK.- Thank you.
0:00:06 > 0:00:09Anything in particular you're doing there tonight, or is it just...?
0:00:09 > 0:00:14I've got to attend some presentation of, you know the scientist, Stephen Hawking?
0:00:14 > 0:00:16Oh, yeah. Yeah, I know who he is.
0:00:16 > 0:00:19Well, I'm doing this programme about equations
0:00:19 > 0:00:24- and he deals with the enormity of the universe...- OK.- ..and his tool
0:00:24 > 0:00:28for scientific research is the equation, the mathematical equation.
0:00:28 > 0:00:29Oh, OK.
0:00:33 > 0:00:35My name's Matthew Collings.
0:00:35 > 0:00:38I'm an artist and art critic.
0:00:38 > 0:00:40That's what I know and understand,
0:00:40 > 0:00:43but I'm about to enter an alien world.
0:00:46 > 0:00:51To me, equations have always been incomprehensible hieroglyphs.
0:00:52 > 0:00:54What do they describe?
0:00:54 > 0:00:57Are they just a mathematical game?
0:01:01 > 0:01:06In this film, I'll learn about some of the most important equations in science.
0:01:06 > 0:01:10They're actually masterpieces that explain the universe we live in.
0:01:18 > 0:01:21APPLAUSE
0:01:24 > 0:01:28I would like to thank Dame Stephanie Shirley
0:01:28 > 0:01:31for commissioning this magnificent portrait.
0:01:31 > 0:01:33It will be an honour to have my picture
0:01:33 > 0:01:39join the Royal Society's collection of the greats of British science.
0:01:39 > 0:01:43I only wish I could remain looking as good as this picture!
0:01:43 > 0:01:44LAUGHTER
0:01:53 > 0:01:56With art, I think beauty is very important
0:01:56 > 0:02:00and I'm always trying to define it, and work out what it is.
0:02:00 > 0:02:05Now I want to apply that knowledge to mathematics and maybe understand why scientists talk
0:02:05 > 0:02:07of "beautiful" equations.
0:02:08 > 0:02:12Hello, Stephen. I'm Matthew Collings.
0:02:12 > 0:02:16I'm doing this BBC programme about equations and beauty.
0:02:16 > 0:02:20Hello. That sounds an interesting idea.
0:02:20 > 0:02:22Thank you. I look forward to speaking...
0:02:22 > 0:02:27I'm glad the most respected living scientist thinks I'm on to something.
0:02:27 > 0:02:32It's a busy night for Stephen, so I've arranged to meet him again in a week's time.
0:02:33 > 0:02:35Now, you yourself must work with equations?
0:02:35 > 0:02:38I do, I do, I'm...
0:02:38 > 0:02:41I mean, technically I'm an astrophysicist.
0:02:41 > 0:02:45I'm really what we call a theorist. What I like to do is noodle around
0:02:45 > 0:02:49with equations and work things out and make predictions.
0:02:49 > 0:02:52Equations is what I do every day. I mean, my colleagues who do astronomy
0:02:52 > 0:02:56like to show pretty pictures and beautiful pictures of the cosmos.
0:02:56 > 0:02:58I like to show equations. Very much so.
0:02:58 > 0:03:02Come and visit me in Oxford and I will tell you all about this. We can't do this here,
0:03:02 > 0:03:06but in Oxford we've got blackboards and I can explain the beauty of equations.
0:03:06 > 0:03:09Fantastic, thank you very much, Pedro.
0:03:20 > 0:03:24I've come to the University of Oxford to take up Pedro's invitation.
0:03:25 > 0:03:30And he's going to tell me about the most famous equation of all,
0:03:30 > 0:03:32the one that everyone's heard of,
0:03:32 > 0:03:35E = mc2.
0:03:38 > 0:03:41This equation conjures up a whole load of thoughts in my mind,
0:03:41 > 0:03:46but the main ones are that it's got something to do with the atomic bomb
0:03:46 > 0:03:49and of course, it's by Einstein.
0:03:50 > 0:03:54But there's cultural knowledge and then there's maths.
0:03:54 > 0:03:59I don't know anything at all about how E = mc2 works.
0:04:00 > 0:04:03When Einstein first published the equation in 1905,
0:04:03 > 0:04:06it started a scientific revolution.
0:04:16 > 0:04:17- Hey!- Hello.- Hello, Pedro.
0:04:17 > 0:04:19- How are you? - Very nice to see you again.
0:04:19 > 0:04:22- Thanks for coming. - Well, it's a pleasure.
0:04:22 > 0:04:25Thank you very much for having me. Now you've got this tall order
0:04:25 > 0:04:29to explain to me so that I can totally understand it.
0:04:29 > 0:04:33We'll give it a go, we'll give it a go. Let me just clear this up.
0:04:33 > 0:04:36'Uh-oh, what am I doing?
0:04:36 > 0:04:39'Pedro lives and breathes abstract numbers.
0:04:39 > 0:04:42- 'I'm an art guy who left school when I was 13.'
0:04:43 > 0:04:48- So what maths do you know? - Well, I must confess that I don't know any maths, any geometry,
0:04:48 > 0:04:51or any algebra or anything in that realm of experience.
0:04:51 > 0:04:54- I'm completely ignorant about all that.- OK.
0:04:54 > 0:04:57I know about art and that's about it.
0:04:57 > 0:05:00Ok, that's a good starting point. Let me get a pen.
0:05:00 > 0:05:02It seems a very bad starting point to me, but...!
0:05:02 > 0:05:07So, you know nothing about what an equation is?
0:05:07 > 0:05:10Only, uh, I think it's a sort of...
0:05:10 > 0:05:14code or some kind of metaphor for the natural world.
0:05:14 > 0:05:17It's the natural world reduced to a formula.
0:05:17 > 0:05:21That's pretty good. Let's start with a really famous one.
0:05:21 > 0:05:23Have you ever seen this equation?
0:05:23 > 0:05:28- Well, I've certainly heard of it. I know it's E = mc2.- Very good.
0:05:28 > 0:05:29E...
0:05:29 > 0:05:31E stands for energy. Do you know what energy is?
0:05:31 > 0:05:34It's a difficult question, so...
0:05:34 > 0:05:37- You're having energy as you talk to me.- Yes.
0:05:37 > 0:05:41A certain amount of energy is keeping me alive so I don't die and decay.
0:05:41 > 0:05:43Very good, very good.
0:05:43 > 0:05:45That's the limit. That's what I think energy is.
0:05:45 > 0:05:50Energy, I mean, energy is kind of a funny thing to try to define.
0:05:50 > 0:05:53The best way I can think of it is, it's the capacity to do things.
0:05:53 > 0:05:58- It's the capacity to lift something up, to heat something up.- All right.
0:05:58 > 0:06:01Then you've got this thing here. Do you know what the m stands for?
0:06:01 > 0:06:03I think it stands for mass.
0:06:03 > 0:06:08Exactly. Mass, and mass is basically the amount of stuff in a thing.
0:06:08 > 0:06:14So when you pick up a book, it's the amount of stuff that that book is made of. Mass is kind of interesting.
0:06:14 > 0:06:18For example, suppose you've got a nail and you weigh it, all right?
0:06:18 > 0:06:24And then you leave it out in the air and you weigh it three weeks later, it will have rusted and so...
0:06:24 > 0:06:28- Its mass has changed. More particle things.- It's gone up, exactly.
0:06:28 > 0:06:33Stuff has stuck onto it, there have been chemical reactions so the mass of it really does have to do
0:06:33 > 0:06:38with what it's made of and how it changes. And then we've got this thing over here, the c.
0:06:38 > 0:06:43- Do you know what the c is?- No. - There's no reason for you to know, it's the speed of light. OK?
0:06:43 > 0:06:49C is incredibly important because c is the speed at which light rays propagate through empty space.
0:06:50 > 0:06:54- I know what squared is, that means a thing multiplied by itself.- Exactly.
0:06:54 > 0:06:57So this is a kind of fascinating statement.
0:06:57 > 0:07:00This is saying suppose you have some mass, right,
0:07:00 > 0:07:04it's possible to convert that mass into a certain amount of energy.
0:07:08 > 0:07:11I can see that E = mc2, like all equations,
0:07:11 > 0:07:14is about balancing two sides.
0:07:14 > 0:07:17That's what the equals sign is all about.
0:07:17 > 0:07:21So this equation allows us to calculate how much energy
0:07:21 > 0:07:23is contained in any given mass.
0:07:23 > 0:07:26It's a surprise to me that it applies to everything.
0:07:26 > 0:07:30Toothpaste, a book, a nail, or uranium for that matter.
0:07:30 > 0:07:36This equation is universal. And since "c2" is such a big number
0:07:36 > 0:07:40a tiny lump of matter contains an enormous amount of energy.
0:07:40 > 0:07:44What this equation doesn't tell you is how to unlock that energy.
0:07:47 > 0:07:50The most dramatic proof that the equation was true
0:07:50 > 0:07:53came 40 years after Einstein first worked it out,
0:07:53 > 0:07:57when the atomic bomb was dropped on Hiroshima.
0:07:57 > 0:08:00Pedro walked me through the chilling sums.
0:08:06 > 0:08:10You have a mass which is something like half a gramme,
0:08:10 > 0:08:12I write it as a kilogramme.
0:08:12 > 0:08:16You need the speed of light and the speed of light looks like this -
0:08:16 > 0:08:20- it's about 300 million metres per second.- OK.
0:08:20 > 0:08:25OK. And we can work out how much energy there is, OK?
0:08:25 > 0:08:29All we've got to do we say that energy is going to be that mass
0:08:29 > 0:08:33times the speed of light, squared, and what you get is this.
0:08:38 > 0:08:40Joules. This is the unit of energy.
0:08:40 > 0:08:43So you get a phenomenal amount of energy.
0:08:43 > 0:08:48Now, if I told you this was something like 15 kilotons of TNT from,
0:08:48 > 0:08:50something the size of a pill,
0:08:50 > 0:08:53- giving enough energy...- Producing an explosion of 15 kilotons...
0:08:53 > 0:08:56Which is equivalent tons of TNT.
0:08:56 > 0:09:01I want to throw you, I don't know if this is a stupid question and you might have nothing to say about it,
0:09:01 > 0:09:04but supposing the sign for squared was changed to a three.
0:09:04 > 0:09:07- Would that just be nonsense, or...? - It would be nonsense,
0:09:07 > 0:09:12and the reason it would be nonsense is because we've tested it.
0:09:12 > 0:09:18We've gone into a lab and tested this relationship. We've weighed something, done something to it,
0:09:18 > 0:09:22weighed it again, worked out the amount of energy that came out and it was on balance
0:09:22 > 0:09:25so the left side was balanced with the right side.
0:09:39 > 0:09:44I'm impressed that E = mc2 was created before it was shown to be true.
0:09:44 > 0:09:47The equation was a prophecy.
0:09:49 > 0:09:54The five symbols explain the link between energy and all matter across the cosmos.
0:09:56 > 0:09:59This universality is part of its power.
0:10:00 > 0:10:06Einstein once claimed "the only physical theories that we're willing to accept are the beautiful ones".
0:10:06 > 0:10:09But what do scientists mean by "beautiful"?
0:10:09 > 0:10:13They talk about equations being testable, being universal.
0:10:13 > 0:10:16Is that what they think beauty is?
0:10:21 > 0:10:25I'm going to take you to the Rhodes building...
0:10:26 > 0:10:32..because Einstein actually came here in, I think 1933,
0:10:32 > 0:10:37to give the Herbert Spencer lecture. And it's an interesting lecture because it's a lecture
0:10:37 > 0:10:41where he basically discusses his philosophy.
0:10:41 > 0:10:47- Right.- Why he does science the way he does, and his craft, what he does as a theoretical physicist.
0:10:47 > 0:10:48And he basically said two things.
0:10:48 > 0:10:53The first is that the endgame of what he does is experience.
0:10:53 > 0:10:56It's experiment. It's the natural world.
0:10:56 > 0:11:01It's not theory for theory's sake. It's always relating to reality.
0:11:01 > 0:11:03Exactly.
0:11:03 > 0:11:05But the bulk of what he says is that what guides him
0:11:05 > 0:11:08is mathematical beauty, or mathematical simplicity.
0:11:08 > 0:11:13That's what guides his research. He says, "It is essential from our point of view that we can arrive
0:11:13 > 0:11:17"at these constructions and the laws relating them, one with another, by adhering
0:11:17 > 0:11:21"to the principle of searching for the mathematically simplest concepts and their connections".
0:11:21 > 0:11:26So go for simplicity, go for the simplest relationships which are mathematically true,
0:11:26 > 0:11:30and that underpins the way that he thought about what he did.
0:11:30 > 0:11:36- So he was telling people this in a lecture that was really about the philosophy of what he did.- Exactly.
0:11:36 > 0:11:40What his ultimate aims were, and what the use of what he did was to the world.
0:11:40 > 0:11:46It's a practical philosophy, it's what he actually did on an everyday basis. That's how he worked.
0:11:46 > 0:11:48So it gives us an insight into...
0:11:48 > 0:11:51what science at that level is about.
0:11:51 > 0:11:52- Exactly.- Yeah.
0:12:04 > 0:12:09Einstein believed that the laws which govern the universe would have an elegant simplicity
0:12:09 > 0:12:13and this would be shared by their equations.
0:12:14 > 0:12:17I paint abstracts in collaboration with my partner, Emma.
0:12:17 > 0:12:23It occurs to me that when we intuitively put shapes and colours together in a visual order,
0:12:23 > 0:12:25we too, like people who come up with equations,
0:12:25 > 0:12:29try to arrive at a convincing metaphor for nature.
0:12:30 > 0:12:34For us, art tells you something important about the world.
0:12:50 > 0:12:54This is a coloured engraving of Isaac Newton by William Blake.
0:12:58 > 0:13:01It shows Newton studying a tiny corner of the world
0:13:01 > 0:13:03with a pair of dividers.
0:13:04 > 0:13:07Blake despised Newton, who he felt reduced
0:13:07 > 0:13:11the magnificence of existence to cold and mechanistic equations.
0:13:17 > 0:13:20So today I'm coming to a place...
0:13:21 > 0:13:26..where I'm actually going to find out a bit more about what Newton actually did.
0:13:30 > 0:13:35This is Newton's house, where he developed his ideas on gravity.
0:13:35 > 0:13:39I'm going back to the 17th century because it's when scientists
0:13:39 > 0:13:42first used equations to try to explain the natural order.
0:13:48 > 0:13:50- Hello. - Hello, welcome to Woolsthorpe.
0:13:50 > 0:13:54I'm Margaret Winn, the house steward. Pleased to meet you.
0:13:54 > 0:13:56- Likewise.- Hi, I'm Ruth.
0:13:56 > 0:13:59I'm professor of theoretical physics from Durham.
0:13:59 > 0:14:02Thank you both very much for seeing me.
0:14:02 > 0:14:04It's nice to meet you. Have you been here before?
0:14:04 > 0:14:06No, never. This is my first time.
0:14:06 > 0:14:12Right, well, this is the house Newton was born in, Christmas Day, 1642.
0:14:12 > 0:14:17Yes. Ruth, the only thing I know about Newton is an image of him observing apples falling off a tree.
0:14:17 > 0:14:21- Falling from a tree!- And he suddenly works out that that means gravity.
0:14:21 > 0:14:26Well, we call him the father of modern science, and that is not an understatement.
0:14:26 > 0:14:28We can date our modern way
0:14:28 > 0:14:34of doing physics or science as trying to write down equations
0:14:34 > 0:14:35as coming from Newton.
0:14:35 > 0:14:39That's very clear, that equations come from beginning of equations.
0:14:39 > 0:14:44Yes, I think equations as a method, as a means of encapsulating,
0:14:44 > 0:14:48of modelling, of saying what physics is and what the world around us is.
0:15:05 > 0:15:09Why do you think the image of the apples falling
0:15:09 > 0:15:11is needed in the mythology of Newton?
0:15:11 > 0:15:16I think it's the link more than anything else. If we take an apple
0:15:16 > 0:15:19and just look at what happens
0:15:19 > 0:15:22as it goes up and down under gravity...
0:15:24 > 0:15:28Gravity is something that I think we often take for granted.
0:15:28 > 0:15:35And the apple falling, he realised that the same thing that made that apple fall down to the ground was
0:15:35 > 0:15:41the same thing that kept the Moon going round the Earth, or indeed the Earth going round the Sun.
0:15:41 > 0:15:47- Begs a lot of questions. How does he go from that to realising something about that?- A lot of hard work!
0:15:47 > 0:15:51Is it assuming that perhaps there's some kind of force
0:15:51 > 0:15:54connected to the moon that's similar to the thing that makes...?
0:15:54 > 0:16:00That's right, so as soon as you start thinking about planetary bodies or things moving round,
0:16:00 > 0:16:07round other objects... I think people at the time, they would have felt, "ell that's a mystery of God,
0:16:07 > 0:16:13"and we're not supposed to understand that," but by using this apple
0:16:13 > 0:16:16as this sort of metaphor for the moon or the sun,
0:16:16 > 0:16:22Newton managed to say, "No, actually man can start plumbing those mysteries."
0:16:22 > 0:16:28I'm absorbing everything you've told and as I'm starting to freeze a bit, maybe we could go in the house!
0:16:28 > 0:16:31- Shall we go up to the house? - You talked about he didn't want
0:16:31 > 0:16:34his theories to be thought of as the final word...
0:16:40 > 0:16:46Newton realised that mathematics could provide a precise and universal language to describe
0:16:46 > 0:16:51things as diverse as the fall of an apple and the orbit of the moon.
0:16:56 > 0:17:00He put his ideas in a revolutionary book, Principia Mathematica.
0:17:06 > 0:17:08I can barely tear my eyes away from this!
0:17:08 > 0:17:10THEY ALL LAUGH
0:17:10 > 0:17:12That is our very prized possession,
0:17:12 > 0:17:16a third edition copy of the Principia Mathematica.
0:17:16 > 0:17:22- If we turn to the relevant page, I'm going to leave you to our book. - Thank you very much. Wonderful.
0:17:22 > 0:17:25The first things that we notice here is not a single equation,
0:17:25 > 0:17:29having talked about Newton as being the father of modern science.
0:17:29 > 0:17:33The other thing is of course it's in Latin, which the language of...
0:17:33 > 0:17:35It's hard enough...!
0:17:35 > 0:17:39- The universal language at the time. - Propositio eight, theorema eight.
0:17:39 > 0:17:44Essentially, he is giving us his equation for gravity in words.
0:17:44 > 0:17:50So he starts off, "Si globorum duroum in se mutuo gravitantium materia undique in regionibus..."
0:17:54 > 0:17:59Newton's written version eventually formed the basis for the equation for gravity.
0:17:59 > 0:18:03So I want Ruth to unpick the different elements,
0:18:03 > 0:18:05a mathematical version of the words.
0:18:05 > 0:18:09I've noticed you've got a book, so we could try and translate
0:18:09 > 0:18:13what he said into one of these beautiful equations.
0:18:13 > 0:18:15Absolutely, find a blank page.
0:18:15 > 0:18:17- Anywhere will do.- Right.
0:18:17 > 0:18:21So we write both of these objects as M1 and M2.
0:18:21 > 0:18:25So these are just the masses. But then Newton talked about
0:18:25 > 0:18:28the force between the two spheres,
0:18:28 > 0:18:32these two bodies, is inversely proportional,
0:18:32 > 0:18:36which means we divide, to the distance squared.
0:18:36 > 0:18:39The two bodies or spheres could be any size -
0:18:39 > 0:18:43the Earth, the Moon, or even an apple.
0:18:43 > 0:18:46And this is G, for gravity.
0:18:46 > 0:18:48It's actually called Newton's constant.
0:18:48 > 0:18:52- You've written out an equation for me there.- Yes.
0:18:52 > 0:18:56And earlier you threw an apple in the air and it fell to the ground.
0:18:56 > 0:18:58Can you give me some numbers...
0:18:58 > 0:19:01- Certainly.- ..that will show me what the apple is doing?
0:19:01 > 0:19:04Let's talk about the apple.
0:19:05 > 0:19:08- OK, so one of the Ms is an apple? - An apple. What does an apple weigh?
0:19:08 > 0:19:15- Half... ?- You get a pound of apples so I guess that's about four apples, so that's a quarter of a pound.
0:19:15 > 0:19:17- We work in kilograms! - SHE LAUGHS
0:19:19 > 0:19:22Let's just say it's 200 grams.
0:19:22 > 0:19:27- But is the other M the Earth? - You don't need explaining, do you? You know this already.- I'm guessing!
0:19:27 > 0:19:32But I don't know how much the Earth weighs, I very rarely buy one from the grocer!
0:19:32 > 0:19:34Well, I can give you a rough idea.
0:19:34 > 0:19:38- Five times ten to the 24 kilograms.- Got it.
0:19:38 > 0:19:41So it's ten to the power of 24.
0:19:41 > 0:19:43Which is a trillion trillion.
0:19:43 > 0:19:45OK, good.
0:19:45 > 0:19:51Now the radius of the Earth is 6,000 kilometres.
0:19:51 > 0:19:54We've got a 200 gram apple,
0:19:54 > 0:19:58several trillion kilograms Earth
0:19:58 > 0:20:00and radius of Earth 6,000.
0:20:00 > 0:20:05Now, what I'm going to do is cancel all those off to make it easy.
0:20:05 > 0:20:08Then what I end up with is a simple ten on the top
0:20:08 > 0:20:12times the 0.2 of the apple.
0:20:12 > 0:20:17So what this tells me is the force the apple feels is its mass
0:20:17 > 0:20:20times this ten and this is...
0:20:20 > 0:20:24- Mass times ten. - Ten is... This is the sort of,
0:20:24 > 0:20:27how fast gravity is going to cause the apple to start to fall.
0:20:27 > 0:20:31So the force on the apple here is simply two.
0:20:31 > 0:20:35And that unit is called the Newton.
0:20:35 > 0:20:37Ah! N for Newton.
0:20:37 > 0:20:39- N for Newton.- Fantastic.
0:20:40 > 0:20:45The number of Newtons measures the force of gravity acting on the apple.
0:20:45 > 0:20:47It's a complicated equation,
0:20:47 > 0:20:49but I'm beginning to understand the key parts.
0:20:49 > 0:20:53The force depends on the mass of the two objects
0:20:53 > 0:20:56and the distance between them.
0:20:57 > 0:21:00The bigger the objects, the bigger the force.
0:21:00 > 0:21:03And the further apart they are, the weaker the force.
0:21:03 > 0:21:07The two masses, M1 and M2, could be anything.
0:21:07 > 0:21:11The earth and the apple. Or the earth and the moon.
0:21:11 > 0:21:13Or the earth and the sun.
0:21:16 > 0:21:21Ruth told me Newton's equation allowed us to understand why
0:21:21 > 0:21:25the moons and planets move around the solar system.
0:21:25 > 0:21:29His equation seemed to make sense of, well, the universe.
0:21:34 > 0:21:39So the equation itself, F = G x M1 x M2/R squared,
0:21:39 > 0:21:44that's Newton's equation of gravity, but how we use it,
0:21:44 > 0:21:47this is a sort of process, you know doing science,
0:21:47 > 0:21:50of calculating things, of making predictions.
0:21:50 > 0:21:53You've now showed me how we use that equation.
0:21:53 > 0:21:55How we would use it, yes.
0:21:55 > 0:21:57This is our paint, how we paint the world.
0:21:57 > 0:22:00We paint it in equations.
0:22:00 > 0:22:02In fact we use that a lot, we say, "I'm painting,"
0:22:02 > 0:22:05you know, we tend to use this word, "painting".
0:22:05 > 0:22:09If you, if you can use that metaphor of paint and colours etcetera
0:22:09 > 0:22:14is there a place also for beauty in this world of calculating things?
0:22:14 > 0:22:18I don't expect everyone to find this beautiful,
0:22:18 > 0:22:20but it certainly is for us and for me.
0:22:20 > 0:22:22Great!
0:22:37 > 0:22:40'A few decades after Newton came up with his law, it was used
0:22:40 > 0:22:45'to successfully predict the return of a comet, Halley's comet.
0:22:45 > 0:22:48'His law of gravity had been confirmed.'
0:22:52 > 0:22:55'With his equation, Newton had transformed
0:22:55 > 0:22:58'the way mathematics modelled the world,
0:22:58 > 0:23:02'and his work went unchallenged for over 200 years.'
0:23:15 > 0:23:18'Everything changed at the beginning of the 20th century
0:23:18 > 0:23:22'with the arrival of Einstein and his Theory of Relativity.
0:23:22 > 0:23:27'In that same decade, something else entered, and that was modern art.
0:23:27 > 0:23:30'In the world of art many believe that Picasso was involved
0:23:30 > 0:23:33'in the same revolution as Einstein.'
0:23:35 > 0:23:38Weirdly, the one place in which I had heard about relativity
0:23:38 > 0:23:43before embarking on this programme was art school when I was young.
0:23:43 > 0:23:48As art students we all had to absorb the idea that
0:23:48 > 0:23:53relativity had something to do with cubist paintings.
0:24:00 > 0:24:07I'm about to look at a cubist painting by Picasso from about 1909-1910.
0:24:07 > 0:24:09It's of a woman in an armchair.
0:24:09 > 0:24:17I think cubism was really seen as something quite terrifying and shocking when it first came out.
0:24:22 > 0:24:24It's not like a Renaissance painting
0:24:24 > 0:24:29where you feel you're looking through a kind of window onto the world.
0:24:29 > 0:24:33With cubism the artist is deliberately confusing you
0:24:33 > 0:24:37as to where thing are, and indeed what things are.
0:24:37 > 0:24:41So that the space in the room
0:24:41 > 0:24:44seems to be eating into the side of the woman.
0:24:44 > 0:24:48And the textures of the room seem to be no different from the textures
0:24:48 > 0:24:55of the woman. So there's all this moving around of objects and space
0:24:55 > 0:24:59in a way that is deliberately confusing if you were thinking,
0:24:59 > 0:25:02"Well, where is the thing that looks like ordinary reality?"
0:25:08 > 0:25:11'I think it's right to say that cubism was a new kind of beauty
0:25:11 > 0:25:14'that looked a bit like science.
0:25:14 > 0:25:17'But I'm not convinced that cubism is science.
0:25:17 > 0:25:21'I've arranged to meet historian of science, Arthur Miller,
0:25:21 > 0:25:25'who's going to attempt to change my mind.'
0:25:25 > 0:25:29I've got to tell you, Arthur, that at art school, and subsequently,
0:25:29 > 0:25:35I felt oppressed by the idea that I had to think of a connection between
0:25:35 > 0:25:39Einstein and relativity and cubism.
0:25:39 > 0:25:41Einstein and relativity and Picasso.
0:25:41 > 0:25:44But there is one in a sense that I'll say they both worked on
0:25:44 > 0:25:47the same problem, the nature of space and time.
0:25:47 > 0:25:51OK. The connection is that time and space are important to them both.
0:25:51 > 0:25:52That's right.
0:25:52 > 0:25:59Where I find the proposal difficult is that, just because
0:25:59 > 0:26:03he's doing something with time and space that he's therefore
0:26:03 > 0:26:09something like Einstein, or that cubism is something like science.
0:26:09 > 0:26:12Cubism was very much of a scientific research programme, as I've said.
0:26:12 > 0:26:16It had, you know, an explicit intent to reduce forms
0:26:16 > 0:26:20- to geometry.- Why is that?- Picasso...
0:26:20 > 0:26:22Why is that scientific and not artistic?
0:26:22 > 0:26:25I mean, medieval artists reduced forms to geometry,
0:26:25 > 0:26:29and African artists reduce it to geometry, archaic art reduces it to geometry.
0:26:29 > 0:26:35Well, that's because Picasso had in mind scientific texts as a way to do it.
0:26:35 > 0:26:40For example, we know that he looked at a text written by a mathematician
0:26:40 > 0:26:44and the text discussed how you represent in four dimensions
0:26:44 > 0:26:47complex polyhedra and Picasso took a look at these.
0:26:47 > 0:26:49Of course, he didn't know what the equations meant,
0:26:49 > 0:26:53but when the author of the books specialised the equations
0:26:53 > 0:26:57of the two dimensions and then could generate illustrations,
0:26:57 > 0:27:00Picasso was interested in the illustrations.
0:27:00 > 0:27:04It's correct to call Picasso a revolutionary artist,
0:27:04 > 0:27:07it's not hyperbole, but for me, I don't know enough about Einstein
0:27:07 > 0:27:11to see the way in which Einstein is a revolutionary too, or how
0:27:11 > 0:27:16Einstein's ideas and Picasso's are the same level of revolution
0:27:16 > 0:27:18and also going in the same direction.
0:27:18 > 0:27:21Well, Einstein was a revolutionary scientist because what he did
0:27:21 > 0:27:26was to go take the next step beyond Newton.
0:27:26 > 0:27:31Newtonian science is based on our sense perceptions that all time,
0:27:31 > 0:27:33your time is the same as my time.
0:27:33 > 0:27:36What Einstein was able to do was to raise himself to
0:27:36 > 0:27:40heights of abstraction so he could glimpse a world beyond appearances.
0:27:40 > 0:27:45The real objective world out there where there is scientific truth.
0:27:47 > 0:27:51I still think the connections between Einstein and Picasso are
0:27:51 > 0:27:53more superficial than substantial,
0:27:53 > 0:27:57but I am very interested to hear more about Einstein.
0:27:57 > 0:27:59Arthur will attempt to explain to me
0:27:59 > 0:28:02one of the key equations of the Special Theory of Relativity.
0:28:05 > 0:28:07When Einstein came up with this equation,
0:28:07 > 0:28:11he wasn't even officially a scientist.
0:28:11 > 0:28:14The days when he wrote the relativity theory, he worked as a patent clerk
0:28:14 > 0:28:17in the Swiss federal patent office in Bern.
0:28:17 > 0:28:20In fact he worked there from 1902 to 1909.
0:28:20 > 0:28:22He was also a conscientious daydreamer.
0:28:22 > 0:28:25And in his dreams and visions he soared over the landscape
0:28:25 > 0:28:30of physics and realised what the fundamental problem was.
0:28:30 > 0:28:32The nature of space and time.
0:28:32 > 0:28:36People were beginning to think that maybe there was something wrong with
0:28:36 > 0:28:39classical, intuitive notions of space and time,
0:28:39 > 0:28:41but they couldn't put their finger on it.
0:28:41 > 0:28:45What they especially wanted to do was to leave alone the notion of time.
0:28:45 > 0:28:48Why was time sacrosanct, because it was obvious what it was,
0:28:48 > 0:28:52it didn't need any more inquiry, or they were afraid that they couldn't find out anything more?
0:28:52 > 0:28:54It seemed that your time is the same as my time.
0:28:54 > 0:28:57No matter how fast we're moving with respect to one another.
0:28:57 > 0:28:59There's no mystery there. We know what time is.
0:28:59 > 0:29:03That's right. It's like Superman said, "Leave time alone."
0:29:03 > 0:29:06- Don't mess with time. - Don't mess with time, yeah.
0:29:06 > 0:29:09OK I've got a book, if you've got a pen?
0:29:09 > 0:29:14Absolutely, let me show you one of the spectacular results
0:29:14 > 0:29:15of relativity theory.
0:29:15 > 0:29:17Let's do a little thought experiment.
0:29:17 > 0:29:24Suppose here is Matt one standing on a train platform
0:29:24 > 0:29:29and here is Matt two, just call him Matt, standing on a train
0:29:29 > 0:29:33and he's moving along with some velocity, call it V,
0:29:33 > 0:29:35relative to the Matt standing on the platform.
0:29:35 > 0:29:39The Matt on the moving train is wearing a wristwatch
0:29:39 > 0:29:42and his time, call it t prime,
0:29:42 > 0:29:45and call the times of all the clocks on the platform t.
0:29:45 > 0:29:48And what we want to do is to compare the time
0:29:48 > 0:29:55on Matt's wristwatch with clocks that remain at rest on the platform.
0:29:55 > 0:29:57They all read the same time.
0:29:57 > 0:30:00I'm going to assume that, even though the clocks are at rest
0:30:00 > 0:30:03and my clock is moving that they're all the same,
0:30:03 > 0:30:06because clocks always tell the same time, assuming they're all synchronised.
0:30:06 > 0:30:09One would think so, yeah. Now let's call the Matt on the train...
0:30:09 > 0:30:11But you're going to show me that they don't.
0:30:11 > 0:30:15I'm going show you that they don't, convince you that they don't.
0:30:15 > 0:30:16t prime and t.
0:30:16 > 0:30:18Now it turns out Matt on the train's time t prime is
0:30:18 > 0:30:24equal to t times the square root of 1 - V squared over C squared.
0:30:24 > 0:30:26So the time here is equal to something complicated.
0:30:26 > 0:30:28It's not just the same as that time.
0:30:28 > 0:30:31No, it's not the same as that time. Your time is not the same as my time.
0:30:31 > 0:30:33These two times are different...
0:30:33 > 0:30:38'If I understand the equation correctly, it says something unbelievable -
0:30:38 > 0:30:43'that time runs at different rates depending on how fast you're moving.
0:30:43 > 0:30:46'Take a train zooming through a station.
0:30:46 > 0:30:50'This equation predicts that a clock on the train, reading time t-,
0:30:50 > 0:30:54'would run slower than clocks reading time t
0:30:54 > 0:30:57'on the station platform.
0:30:57 > 0:31:00'I've never noticed it and here's why.
0:31:00 > 0:31:04'This bit of the equation is what makes the two clock times different,
0:31:04 > 0:31:07'but it only has a significant effect if the velocity, V,
0:31:07 > 0:31:12'of the train is very fast, close to the speed of light.
0:31:12 > 0:31:16'If the train could reach the speed of light, you get 1 - 1,
0:31:16 > 0:31:18'which equals zero.
0:31:18 > 0:31:21'And then t- equals zero.
0:31:21 > 0:31:26'Relative to the platform, time on the train completely stops.
0:31:28 > 0:31:31'This stretching of time seems impossible
0:31:31 > 0:31:35'but according to Arthur it's been proven by practical experiment.'
0:31:40 > 0:31:42Now that's really something. That's wild.
0:31:42 > 0:31:46And he realised that's because time is a relative quantity.
0:31:46 > 0:31:50Just as I discussed with you.
0:31:50 > 0:31:53Your time is only the same as my time if we're standing still
0:31:53 > 0:31:57next to each other, but if you go away and come back, your clock,
0:31:57 > 0:31:59although it'd be very difficult to perceive it,
0:31:59 > 0:32:01will read a slower time than mine.
0:32:01 > 0:32:04Well, I'm taking in a lot of what you're saying so that
0:32:04 > 0:32:07- I'm far more informed than I was before you spoke.- Good.
0:32:07 > 0:32:10But the thing that's really big for me is this idea
0:32:10 > 0:32:14of the physical nature of time and that seems a marvellous idea.
0:32:14 > 0:32:19Oh, it turns out that there's not space and time. There's space-time.
0:32:19 > 0:32:23Right, they are a single entity. Is entity the right word?
0:32:23 > 0:32:26Time and space are connected by the velocity of light.
0:32:29 > 0:32:32'That was definitely the hardest equation so far,
0:32:32 > 0:32:37'not just the maths but because of the ideas it contained.
0:32:37 > 0:32:40'You might be worrying about time on a tube train,
0:32:40 > 0:32:44'but you wouldn't think time was actually changing shape.'
0:32:45 > 0:32:50'Einstein worked out that time and space are inextricably linked
0:32:50 > 0:32:52'through the speed of light.'
0:32:55 > 0:33:00'It was a thought that it was simply impossible to have before,
0:33:00 > 0:33:01'reality had changed,
0:33:01 > 0:33:04'and Einstein did it with equations.'
0:33:08 > 0:33:11'I'm beginning to get a crush on science.'
0:33:11 > 0:33:15'Before, I literally didn't know what an equation was.
0:33:15 > 0:33:21'Now, in some ways I know the basics of what an equation is,
0:33:21 > 0:33:25'but I also know the implications of what an equation is,
0:33:25 > 0:33:26'so there's a sort of excitement
0:33:26 > 0:33:29'about the philosophy of an equation,'
0:33:29 > 0:33:32or the use of an equation in some kind of profound way
0:33:32 > 0:33:36as opposed to something like a railway timetable that tells you very detailed information.
0:33:36 > 0:33:42You know the process of learning is a mixture of pain and pleasure.
0:33:42 > 0:33:45It's quite hard to dislodge the pattern of the world that
0:33:45 > 0:33:49you've already got in place, and bring in a whole load of new stuff.
0:33:49 > 0:33:52You can appreciate it on mythological levels.
0:33:52 > 0:33:56Someone's telling you the myth of equations, or the myth of science,
0:33:56 > 0:33:59or the myth of Newton, or the myth of Einstein,
0:33:59 > 0:34:01but they all do sound like myths to me.
0:34:01 > 0:34:06But as the days go by they acquire more and more reality as each
0:34:06 > 0:34:11scientist adds to the stories that the other scientists have told me.
0:34:20 > 0:34:25There's one scientist who stands out in the story of equations,
0:34:25 > 0:34:30because he took the idea of beauty in science further than anyone else.
0:34:30 > 0:34:33His name is Paul Dirac.
0:34:34 > 0:34:38He too revolutionised our view of the universe,
0:34:38 > 0:34:43yet virtually no-one outside scientific circles has heard of Dirac.
0:34:43 > 0:34:49So, I've arranged to meet the biographer of this mysterious genius.
0:34:51 > 0:34:56This is a particularly favourite part of Cambridge for Paul Dirac.
0:34:56 > 0:34:59Dirac was the greatest English theoretician since
0:34:59 > 0:35:03Isaac Newton and that's how... That's his reputation in 1927,
0:35:03 > 0:35:07when he was looking for what became his greatest achievement -
0:35:07 > 0:35:08his equation.
0:35:08 > 0:35:10Why is he... Being so great,
0:35:10 > 0:35:16why is he totally unknown to the general public?
0:35:16 > 0:35:20He actually wanted anonymity, he really had no interest at all in celebrity.
0:35:20 > 0:35:24He simply wanted to get on with his work and be unknown
0:35:24 > 0:35:27to the outside world.
0:35:27 > 0:35:32I love the idea that for Dirac, beauty is important.
0:35:32 > 0:35:37Is there a sense in which it is more important for him
0:35:37 > 0:35:39than I've been hearing so far about other scientists?
0:35:39 > 0:35:45Oh, yeah, Dirac was the first scientist actually to elevate this idea of beauty to a principle.
0:35:45 > 0:35:47He called it the principle of mathematical beauty.
0:35:47 > 0:35:52And what he meant by that was that as we advance in fundamental,
0:35:52 > 0:35:56theoretical physics, the theories as they get closer and closer to nature,
0:35:56 > 0:35:58become more and more beautiful.
0:35:58 > 0:36:03So, for him, it was a method of sifting out theories,
0:36:03 > 0:36:07right from wrong because if it wasn't beautiful, if it was ugly
0:36:07 > 0:36:11in his opinion, it just wouldn't cut pass muster with nature.
0:36:11 > 0:36:17So for him, a theory had to be beautiful for it to stand a chance of describing nature.
0:36:17 > 0:36:19Incredible.
0:36:19 > 0:36:23Here's a scientist who insisted science went through a "filter"
0:36:23 > 0:36:27of beauty. And by pursuing beauty, you end up with truth.
0:36:27 > 0:36:33It's an idea that's often used metaphorically, but Dirac meant it literally.
0:36:33 > 0:36:36This is the Bridge of Sighs, which he walked across as a Fellow.
0:36:36 > 0:36:43He walked back to his rooms here and this is where he did his great work on the Dirac Equation.
0:36:43 > 0:36:47In fact, he was staying in a room just here.
0:36:47 > 0:36:52That's where he was working in the late months of 1927
0:36:52 > 0:36:57on what came to be known as the Dirac Equation, one of the greatest achievements in modern science.
0:37:09 > 0:37:14Here we are, Room A4. Newcourt. Where Dirac discovered his great equation.
0:37:14 > 0:37:19Completely free of distraction. The only noise you get is a bit of noise from the punters outside.
0:37:19 > 0:37:22Apart from that, no radio, just nothing.
0:37:22 > 0:37:29Dirac was not given to luxury. In late 1927, all he did, apparently, was to work on that equation.
0:37:29 > 0:37:34Tell me about that equation, what was he trying to accomplish with it?
0:37:34 > 0:37:38Well, what he was trying to do was come up with an equation for the electron,
0:37:38 > 0:37:44the first material fundamental particle to have been discovered.
0:37:44 > 0:37:49- What does that mean, "the first fundamental material particle"?- OK.
0:37:49 > 0:37:52A fundamental particle has no constituents.
0:37:52 > 0:37:56It's a completely basic particle, you can't subdivide it.
0:37:56 > 0:37:59The point of the tiny, tiny thing, this electron,
0:37:59 > 0:38:03- is that nothing else is more basic than it.- That's right.
0:38:03 > 0:38:08So you had a chance of giving a fundamental description in nature.
0:38:08 > 0:38:12I've got a notebook in my bag.
0:38:12 > 0:38:15- If I give that to you and you find a blank page...- Yep.
0:38:15 > 0:38:19And I then give you my pen, could you write out for me
0:38:19 > 0:38:21- the equation...- I will.
0:38:21 > 0:38:23- ..that Dirac came up with.- I will.
0:38:23 > 0:38:25It's called the Dirac Equation?
0:38:25 > 0:38:28That's right. This is the Dirac Equation.
0:38:28 > 0:38:35And this equation applies to every electron that's ever existed, or ever will exist,
0:38:35 > 0:38:40in the entire universe, so this is the ultimate compact equation that
0:38:40 > 0:38:43has this universal significance.
0:38:43 > 0:38:46This is a miracle, one of the miracles of 20th century science.
0:38:46 > 0:38:50You've shown me the miracle, now tell me what it is.
0:38:50 > 0:38:55I see something like "I followed by squiggle, followed by P followed by
0:38:55 > 0:38:57"a squiggle, followed by equals, followed by m,
0:38:57 > 0:38:58"followed by squiggle."
0:38:58 > 0:39:04OK, you say, "I, gamma, P, psi = M psi".
0:39:04 > 0:39:09OK, so it's like E = M C squared, only you say these new things that
0:39:09 > 0:39:12he thought up himself, a bit like the Lord of the Rings language.
0:39:12 > 0:39:15- That's right.- And what is the most important symbol there?
0:39:15 > 0:39:16Right, OK.
0:39:16 > 0:39:19This is called a spinner, all right?
0:39:19 > 0:39:24This is a thing that encodes the information about the behaviour of the electron.
0:39:24 > 0:39:30So, you tell the equation what situation the electron is in and out
0:39:30 > 0:39:35of the equation comes the prediction for how the electron will behave.
0:39:35 > 0:39:40What's the thing in the ordinary world that is the closest that
0:39:40 > 0:39:44- I could visualise, to tell me what a spinner really means?- There is none.
0:39:44 > 0:39:46- OK, so I've got to accept that. - Exactly.- Fine.
0:39:46 > 0:39:49This was a complete Dirac concoction, right?
0:39:49 > 0:39:51So spinners didn't exist before him?
0:39:51 > 0:39:55- No, they didn't.- Do you have to learn his new language before you can say that equation?- Yeah.
0:39:55 > 0:39:59Seriously, people for six months a year were struggling. Brilliant,
0:39:59 > 0:40:03world-leading physicists had no clue about what this equation meant.
0:40:03 > 0:40:07This is why he was so far ahead of his time, they were having to say,
0:40:07 > 0:40:08"What the hell do these symbols mean?"
0:40:08 > 0:40:11It was on extremely good ground and moreover...
0:40:11 > 0:40:17'If it stumps the world's top scientists then I think it's OK for it to be beyond me.
0:40:17 > 0:40:19'This really is a foreign language.
0:40:19 > 0:40:25'But I was getting a broader sense of how equations have advanced knowledge.'
0:40:27 > 0:40:32I do feel from your talk that I'm starting to get a picture filled in
0:40:32 > 0:40:34for me of science, the big points.
0:40:34 > 0:40:37Newton, Einstein and now Dirac.
0:40:37 > 0:40:44- That's right.- And a sort of journey that the spheres, the planets,
0:40:44 > 0:40:48the stars, this earth, everything on it, all the objects
0:40:48 > 0:40:53can be somehow described and understood in mechanical terms.
0:40:53 > 0:40:57That's right. Einstein said that the most incomprehensible thing
0:40:57 > 0:41:00about the universe is that it is comprehensible.
0:41:00 > 0:41:06And Dirac, Newton, Einstein, they all had faith that they could,
0:41:06 > 0:41:09if they thought hard enough, they could come up with these laws that
0:41:09 > 0:41:11describe nature at a fundamental level.
0:41:11 > 0:41:14But faith doesn't produce more faith, it actually produces equations.
0:41:14 > 0:41:16Oh, absolutely.
0:41:16 > 0:41:20- It's not like a faith that you can't verify.- Faith oils the works.- Yeah.
0:41:20 > 0:41:27Dirac actually said that the principle of mathematical beauty was a kind of religion to him.
0:41:27 > 0:41:30He actually used those words because he really did believe
0:41:30 > 0:41:36with all his heart and soul that a mathematically beautiful theory
0:41:36 > 0:41:38was going to be the kind of theory that nature backed
0:41:38 > 0:41:43and that that was the direction in which you should travel, so he really did believe that.
0:41:43 > 0:41:45It was an article of faith.
0:41:45 > 0:41:48Why is the spinner beautiful?
0:41:48 > 0:41:52This is beautiful because Dirac used this equation
0:41:52 > 0:41:56to predict the first example of anti-matter.
0:41:56 > 0:42:00This was perhaps the greatest triumph of 20th century physics.
0:42:00 > 0:42:04Now just to give you a sense of how monumental that is,
0:42:04 > 0:42:08now cosmologists believe that the very beginning of the universe,
0:42:08 > 0:42:11half the universe was anti-matter.
0:42:11 > 0:42:15So by that token, Dirac conceived, using this equation,
0:42:15 > 0:42:17half the universe in his head.
0:42:32 > 0:42:37'Scientists now stand in awe of Dirac's Equation.
0:42:37 > 0:42:39'But at the time, things were very different.
0:42:39 > 0:42:44'In the late 1920's, anti-matter was totally unknown.
0:42:44 > 0:42:48'The idea that every electron, proton, and neutron
0:42:48 > 0:42:51'had an opposite partner was preposterous.
0:42:51 > 0:42:56'If his equation predicted this make-believe stuff
0:42:56 > 0:42:58'then it must be wrong.'
0:43:00 > 0:43:04OK, so what we can do now is go into the teaching lab.
0:43:04 > 0:43:07What we have is an experiment set up where we can
0:43:07 > 0:43:11actually see tracks of particles that have been produced by anti-matter.
0:43:11 > 0:43:14So you'll be showing me some anti-matter in action.
0:43:14 > 0:43:17'Five years after Dirac came up with his prediction,
0:43:17 > 0:43:19'anti-matter was discovered.'
0:43:21 > 0:43:24'The equation had turned out to be true.
0:43:24 > 0:43:26'Now, I too want to see the proof.'
0:43:26 > 0:43:30This is the first practical place I've been to.
0:43:30 > 0:43:33I'm surprised at how quaint everything looks.
0:43:33 > 0:43:36This is a very simple experiment. This is very low tech.
0:43:36 > 0:43:38You could do this in your kitchen.
0:43:38 > 0:43:41- Really?- OK, so, this is a magnet.
0:43:41 > 0:43:47It's a fairly powerful magnet and we're going to put dry ice on here, so that will be very cold.
0:43:47 > 0:43:50- A sort of cookery element at the moment.- It is yeah.
0:43:50 > 0:43:52Cooking fish in salt.
0:43:57 > 0:44:00Now the Perspex box is going to go on top.
0:44:00 > 0:44:03And there's alcohol that we put in the upper layer.
0:44:03 > 0:44:07In order to see the tracks, they're actually quite faint,
0:44:07 > 0:44:10- we have to illuminate it with a very bright lamp.- OK.
0:44:10 > 0:44:13And then, one of the other ingredients that we should
0:44:13 > 0:44:16explain here is the radioactive sources that we're going to use.
0:44:16 > 0:44:18So we have two radioactive sources.
0:44:18 > 0:44:22One emits electrons and the other emits positrons.
0:44:22 > 0:44:26And so what we have here is the isotope of strontium called strontium 90.
0:44:26 > 0:44:32'Glen told me these radioactive materials would let us see the tracks of electrons.
0:44:32 > 0:44:36'And more importantly, the anti-matter partner to the electron.
0:44:36 > 0:44:41'Known as the positron, this is the particle predicted by Dirac's Equation.'
0:44:41 > 0:44:44It emits positrons and we'll see tracks that are very similar.
0:44:44 > 0:44:49Maybe slightly lower energy actually and they will be bending to the left.
0:44:49 > 0:44:55So that really is the demonstration, that we have two types of particles that really look very similar
0:44:55 > 0:44:56in terms of the tracks that they make,
0:44:56 > 0:45:01except that one is positively charged and the other is negatively charged.
0:45:02 > 0:45:04Yeah, yeah, I saw one going that way.
0:45:04 > 0:45:08Furthermore, they should be bending to the right and they are.
0:45:08 > 0:45:12Yeah, they're thin and irregular. It's like a string of beads almost.
0:45:12 > 0:45:15OK, so all I've really convinced you that you can see so far are
0:45:15 > 0:45:17bog standard electrons.
0:45:17 > 0:45:20Even at the bog standard level, it's pretty impressive.
0:45:20 > 0:45:22We're all made of plenty of those.
0:45:22 > 0:45:26And so, maybe what we can try now, is to put in the positron source.
0:45:26 > 0:45:30What we should see, is that they will bend in the opposite direction.
0:45:30 > 0:45:33- The other one slotted in scientifically.- That's right.
0:45:33 > 0:45:37We're just going to hold it on to the entrance way.
0:45:37 > 0:45:40Now I should expect to see things going to the left.
0:45:43 > 0:45:49I'm seeing activity but not necessarily lines going to the left.
0:45:50 > 0:45:53'We'd seen the electrons bend to the right.
0:45:53 > 0:45:58'Now Glen hoped that we might spot the rarer anti-matter tracks
0:45:58 > 0:46:01'as they curve towards the other side.'
0:46:05 > 0:46:08One there! Very, very clear.
0:46:08 > 0:46:10- There you go.- Fantastic!
0:46:10 > 0:46:13So that's the first time in this experiment that I've seen the anti-matter.
0:46:13 > 0:46:16That was definitely coming from the source.
0:46:18 > 0:46:21The amazing thing is to have something from...
0:46:21 > 0:46:26a sort of comic world of science fiction, anti-matter,
0:46:26 > 0:46:33- to have it presented to us in reality.- There we go.
0:46:33 > 0:46:35Except I wasn't looking at that one.
0:46:35 > 0:46:39Every 30, 40 seconds a little blip occurs
0:46:39 > 0:46:44within a sort of 10p size radius of the source.
0:46:47 > 0:46:51It shoots out, curls around, doesn't go very far.
0:46:51 > 0:46:56- One there, very curly one, shot right round!- Very good.
0:46:56 > 0:47:01- Yeah, yeah.- So, we're really seeing a physical thing,
0:47:01 > 0:47:06which connects to the very complicated mind-world of Paul Dirac.
0:47:06 > 0:47:09That's right. Somehow the existence of anti-matter
0:47:09 > 0:47:13emerges as a necessary consequence of the theory that he wrote down
0:47:13 > 0:47:16and that's pretty difficult to see. To just look at his equation and say
0:47:16 > 0:47:20that should give us anti-matter, but really if you analyse it carefully
0:47:20 > 0:47:24it's clear that that is one of its necessary predictions and that's what you're seeing.
0:47:24 > 0:47:27So, those curves and blips in that sort of molten sea,
0:47:27 > 0:47:31is the Dirac Equation being shown to us in physical form.
0:47:43 > 0:47:47'These elusive symbols point to a beautiful idea.
0:47:47 > 0:47:50'There is something magical about them.
0:47:50 > 0:47:55'The existence of anti-matter proved his theory true.
0:47:55 > 0:48:00'Keats' romantic poem goes "Beauty is truth, truth is beauty,"
0:48:00 > 0:48:02'as if one leads to the other.
0:48:02 > 0:48:06'And that's exactly what Dirac, the scientist, believed.
0:48:06 > 0:48:11'That the search for beauty powers the advance of science.'
0:48:20 > 0:48:26I'm reading a paper by Dirac, which he delivered in February 1939.
0:48:26 > 0:48:29He says, "What makes the theory of relativity so acceptable to
0:48:29 > 0:48:34"physicists in spite of its going against the principle of simplicity,
0:48:34 > 0:48:37"is its great mathematical beauty.
0:48:37 > 0:48:41"This is a quality which cannot be defined any more than beauty in art
0:48:41 > 0:48:44"can be defined, but which people who study mathematics usually
0:48:44 > 0:48:47"have no difficulty in appreciating."
0:48:47 > 0:48:51So, he's saying that beauty in art can't be ultimately defined
0:48:51 > 0:48:54any more than beauty in anything can be ultimately defined.
0:48:54 > 0:48:59But what he is saying is that people in the world of very, very high
0:48:59 > 0:49:05and complex mathematics agree that beauty is something that
0:49:05 > 0:49:08they all appreciate and follow.
0:49:08 > 0:49:11And it may be that what Dirac is saying is that
0:49:11 > 0:49:14there's a sort of high or true or pure beauty that
0:49:14 > 0:49:17mathematicians are interested in,
0:49:17 > 0:49:22which sounds to me a bit like the inner, true, deep beauty of art.
0:49:22 > 0:49:25But you have to go on a bit of a journey to find,
0:49:25 > 0:49:28you can't expect it to come leaping out and waving at you
0:49:28 > 0:49:33straightaway when you haven't really bothered to get involved with art
0:49:33 > 0:49:35and try and find out what it is.
0:49:57 > 0:50:00I like these buildings very much.
0:50:00 > 0:50:03But I think they have a sort of comic element.
0:50:03 > 0:50:09They seem like a Hollywood mock up of some kind of scientific base
0:50:09 > 0:50:15where something sinister is being worked out behind the scenes.
0:50:15 > 0:50:17You wouldn't even really think you were in England.
0:50:17 > 0:50:19You could be anywhere in the world.
0:50:22 > 0:50:29I'm ending my foray into science with an equation about black holes.
0:50:29 > 0:50:32I'd always thought they were the stuff of science fiction,
0:50:32 > 0:50:35but the inner workings of black holes are explained
0:50:35 > 0:50:39by the fifth of my great equations.
0:50:40 > 0:50:47All the previous equations have come from historical figures - Newton, Einstein and Dirac.
0:50:47 > 0:50:54This will be my chance to hear about the entropy equation direct from its creator, Stephen Hawking.
0:50:54 > 0:50:59And find out if he agrees with Paul Dirac about beauty and the truth of science.
0:51:09 > 0:51:13Thanks very much for allowing me into your department, Stephen.
0:51:13 > 0:51:15Can I ask you straight away,
0:51:15 > 0:51:18is beauty important for you in your scientific work?
0:51:18 > 0:51:20I don't know about beauty,
0:51:20 > 0:51:25but the fundamental laws of the universe should be elegant.
0:51:25 > 0:51:28What do you mean by elegant?
0:51:28 > 0:51:34An equation is elegant if it is short, simple and explains
0:51:34 > 0:51:39properties of the universe that were previously not accounted for.
0:51:39 > 0:51:43My most elegant equation is very simple.
0:51:43 > 0:51:47It is S = a quarter A.
0:51:47 > 0:51:51Here, A is the area of the boundary of a black hole.
0:51:51 > 0:51:55And S is its entropy, a measure of how much heat it contains.
0:51:57 > 0:51:58What does that mean?
0:52:00 > 0:52:06This equation shows that black holes aren't completely black.
0:52:06 > 0:52:11They glow like hot bodies and lose energy and mass.
0:52:11 > 0:52:17Eventually they will disappear in a tremendous explosion.
0:52:17 > 0:52:21Why is that an elegant equation?
0:52:22 > 0:52:27The equation came from a rather messy calculation.
0:52:27 > 0:52:32It seemed a miracle that such a concise equation should result.
0:52:34 > 0:52:38This equation unravels the physics of black holes,
0:52:38 > 0:52:41one of the most mysterious objects in the universe.
0:52:41 > 0:52:44As I understand it, the equation says that as stuff
0:52:44 > 0:52:48falls into the black hole, the surface area of the black hole
0:52:48 > 0:52:50gets bigger, and the entropy does too.
0:52:52 > 0:52:56In 1975, when Stephen Hawking came up with his equation,
0:52:56 > 0:52:59there was still some doubt as to whether black holes existed.
0:52:59 > 0:53:0335 years on, all scientists agree they do.
0:53:03 > 0:53:07Black holes have entered the realm of science fact.
0:53:09 > 0:53:12While making this film, I found out that Paul Dirac
0:53:12 > 0:53:16believed that it was more important to have beauty in one's equation
0:53:16 > 0:53:21than to have the equation backed up by actual experiment.
0:53:21 > 0:53:25Is this too extreme a view for you?
0:53:25 > 0:53:30I think what Dirac meant was that although a beautiful equation
0:53:30 > 0:53:33might not agree with experiment at a particular time,
0:53:33 > 0:53:38it will eventually turn out to be true in the long run.
0:53:38 > 0:53:44I think elegance is a good guide for equations but not an infallible one.
0:53:44 > 0:53:47In art, an artist like Picasso say,
0:53:47 > 0:53:50will just be working from hour to hour,
0:53:50 > 0:53:54from work to work, pushing his ideas along with his work.
0:53:54 > 0:53:58He doesn't necessarily think, "Now, I've discovered cubism."
0:53:58 > 0:54:03That accolade will be bestowed upon his work
0:54:03 > 0:54:04a bit later by other people.
0:54:04 > 0:54:07But he probably will, at some point, think,
0:54:07 > 0:54:11"I have made some kind of breakthrough here."
0:54:11 > 0:54:14And I wonder if that breakthrough feeling,
0:54:14 > 0:54:18if there's an equivalent for you in your type of enquiry.
0:54:20 > 0:54:24There's nothing like the Eureka moment of discovering
0:54:24 > 0:54:27something that no-one knew before.
0:54:27 > 0:54:33I won't compare it to sex, but it lasts longer.
0:54:33 > 0:54:35Thank you very much, Stephen.
0:54:35 > 0:54:37Thank you.
0:54:41 > 0:54:45The very fact that Stephen agreed to be interviewed by me,
0:54:45 > 0:54:49when it's not an easy task for him,
0:54:49 > 0:54:54it's not something that he does a lot,
0:54:54 > 0:54:58proves to me that he believes in the thesis that beauty
0:54:58 > 0:55:02is a significant element in the work of a theoretical scientist.
0:55:02 > 0:55:08That making an equation calls for some kind of,
0:55:08 > 0:55:12not just a sense of beauty, but almost a pursuit of it.
0:55:12 > 0:55:17The pursuit of beauty really is a sort of driving force
0:55:17 > 0:55:20in evolving an equation.
0:55:20 > 0:55:25I've got to let all that sink in now.
0:56:02 > 0:56:06I've been very happy to have my head crammed full of unfamiliar ideas,
0:56:06 > 0:56:10but now there's one more thing I need to do.
0:56:10 > 0:56:13Hello, Cary, how nice to see you!
0:56:13 > 0:56:19I'm at the opening of my own exhibition, the work I do with my partner, Emma.
0:56:19 > 0:56:23I've invited the scientists and most of them have turned up.
0:56:24 > 0:56:28Throughout this film, the word "beauty" has often cropped up.
0:56:28 > 0:56:30But it's hard to define and I can't help but feel that
0:56:30 > 0:56:33while there are similarities, there are differences too
0:56:33 > 0:56:36in what artists and scientists mean by beauty.
0:56:36 > 0:56:40- Sorry, which are your paintings? - All these paintings.
0:56:40 > 0:56:42We do all these.
0:56:42 > 0:56:46I'm trying to imagine what Paul Dirac would make of this painting.
0:56:46 > 0:56:50My guess is he would ask you what you are representing here,
0:56:50 > 0:56:52because he had a very literal mind.
0:56:52 > 0:56:54I know what you're saying.
0:56:54 > 0:56:56Are you conscious of representing anything?
0:56:56 > 0:56:59There's no representation in the room at all,
0:56:59 > 0:57:03but I think there is the idea of a model of the visual world.
0:57:05 > 0:57:07There's a lot going on. There's a lot of them.
0:57:07 > 0:57:12You come back in a couple of minutes from looking at something else. You can't find that order again.
0:57:12 > 0:57:13Right.
0:57:13 > 0:57:15That's really the point of them.
0:57:15 > 0:57:19They should have a restlessly changing sense of order.
0:57:19 > 0:57:24It's like looking at a fire where the fire always looks the same, but it's never exactly the same.
0:57:24 > 0:57:27Exactly. Anything in nature that is permanent and changeable.
0:57:28 > 0:57:31Are all the panels the same, or are they different?
0:57:31 > 0:57:32I think they're all pretty different.
0:57:32 > 0:57:35It's interesting because you'd look at it and think there's an algorithm
0:57:35 > 0:57:39that tells you how you would paint that in terms of the things around.
0:57:39 > 0:57:43But he says no, there's also a global point of view.
0:57:45 > 0:57:48- A non-repeating pattern of some sort. - Exactly.
0:57:48 > 0:57:50Ultimately, it is highly mathematical,
0:57:50 > 0:57:54but actually there is no... We didn't sit down and work it out.
0:57:54 > 0:57:57Well, randomness is also mathematical.
0:57:59 > 0:58:05It's interesting to see mathematical symmetries come out of aesthetic pursuits.
0:58:05 > 0:58:06Well, that's arrived at...
0:58:06 > 0:58:10'All my life, science has been totally out of my orbit.
0:58:10 > 0:58:13'What was so illuminating for me in this programme was to
0:58:13 > 0:58:18'find out that equations are the most important tool in science,
0:58:18 > 0:58:21'forever pushing the boundaries of knowledge.
0:58:21 > 0:58:24'And that the greatest and most beautiful equations
0:58:24 > 0:58:26'have a life of their own.
0:58:26 > 0:58:32'They've given us ideas beyond the human imagination.'
0:58:48 > 0:58:50Subtitles by Red Bee Media Ltd
0:58:50 > 0:58:52E-mail subtitling@bbc.co.uk