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