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Royal Society.
Royal Society. OK. Thank you.

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Anything in particular you're doing
there tonight, or is it just...?

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I've got to attend some presentation
of, you know the scientist,
Stephen Hawking?

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Oh, yeah. Yeah, I know who he is.

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Well, I'm doing this programme
about equations

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and he deals with the enormity of
the universe... OK. ..and his tool

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for scientific research is the
equation, the mathematical equation.

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Oh, OK.

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My name's Matthew Collings.

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I'm an artist and art critic.

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That's what I know and understand,

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but I'm about to enter
an alien world.

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To me, equations have always been
incomprehensible hieroglyphs.

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What do they describe?

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Are they just a mathematical game?

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In this film, I'll learn about
some of the most important
equations in science.

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They're actually masterpieces that
explain the universe we live in.

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APPLAUSE

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I would like to thank
Dame Stephanie Shirley

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for commissioning
this magnificent portrait.

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It will be an honour
to have my picture

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join the Royal Society's collection
of the greats of British science.

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I only wish I could remain
looking as good as this picture!

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LAUGHTER

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With art,
I think beauty is very important

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and I'm always trying to define it,
and work out what it is.

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Now I want to apply that knowledge
to mathematics and maybe
understand why scientists talk

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of "beautiful" equations.

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Hello, Stephen.
I'm Matthew Collings.

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I'm doing this BBC programme
about equations and beauty.

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Hello.
That sounds an interesting idea.

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Thank you.
I look forward to speaking...

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I'm glad the most respected
living scientist thinks
I'm on to something.

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It's a busy night for Stephen,
so I've arranged to meet him
again in a week's time.

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Now, you yourself
must work with equations?

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I do, I do, I'm...

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I mean, technically
I'm an astrophysicist.

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I'm really what we call a theorist.
What I like to do is noodle around

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with equations and work things out
and make predictions.

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Equations is what I do every day. I
mean, my colleagues who do astronomy

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like to show pretty pictures and
beautiful pictures of the cosmos.

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I like to show equations.
Very much so.

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Come and visit me in Oxford
and I will tell you all about this.
We can't do this here,

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but in Oxford
we've got blackboards and I can
explain the beauty of equations.

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Fantastic,
thank you very much, Pedro.

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I've come
to the University of Oxford
to take up Pedro's invitation.

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And he's going to tell me about
the most famous equation of all,

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the one that everyone's heard of,

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E = mc2.

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This equation conjures up
a whole load of thoughts in my mind,

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but the main ones are that it's got
something to do with the atomic bomb

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and of course, it's by Einstein.

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But there's cultural knowledge
and then there's maths.

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I don't know anything at all
about how E = mc2 works.

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When Einstein first published
the equation in 1905,

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it started a scientific revolution.

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Hey! Hello. Hello, Pedro.

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How are you?
Very nice to see you again.

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Thanks for coming.
Well, it's a pleasure.

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Thank you very much for having me.
Now you've got this tall order

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to explain to me so that
I can totally understand it.

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We'll give it a go, we'll give it
a go. Let me just clear this up.

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'Uh-oh, what am I doing?

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'Pedro lives and breathes
abstract numbers.

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'I'm an art guy
who left school when I was 13.'

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So what maths do you know?
Well, I must confess that I don't
know any maths, any geometry,

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or any algebra or anything
in that realm of experience.

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I'm completely ignorant
about all that. OK.

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I know about art
and that's about it.

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Ok, that's a good starting point.
Let me get a pen.

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It seems a very bad
starting point to me, but...!

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So, you know nothing
about what an equation is?

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Only, uh, I think it's a sort of...

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code or some kind of metaphor
for the natural world.

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It's the natural world
reduced to a formula.

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That's pretty good.
Let's start with a really famous one.

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Have you ever seen this equation?

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Well, I've certainly heard of it.
I know it's E = mc2. Very good.

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E...

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E stands for energy.
Do you know what energy is?

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It's a difficult question, so...

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You're having energy
as you talk to me. Yes.

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A certain amount of energy
is keeping me alive
so I don't die and decay.

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Very good, very good.

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That's the limit.
That's what I think energy is.

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Energy, I mean, energy is kind
of a funny thing to try to define.

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The best way I can think of it is,
it's the capacity to do things.

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It's the capacity to lift something
up, to heat something up. All right.

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Then you've got this thing here.
Do you know what the m stands for?

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I think it stands for mass.

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Exactly. Mass, and mass is basically
the amount of stuff in a thing.

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So when you pick up a book, it's the
amount of stuff that that book is
made of. Mass is kind of interesting.

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For example, suppose you've got
a nail and you weigh it, all right?

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And then you leave it out in the air
and you weigh it three weeks later,
it will have rusted and so...

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Its mass has changed. More particle
things. It's gone up, exactly.

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Stuff has stuck onto it, there have
been chemical reactions so the mass
of it really does have to do

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with what it's made of
and how it changes. And then we've
got this thing over here, the c.

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Do you know what the c is? No.
There's no reason for you to know,
it's the speed of light. OK?

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C is incredibly important because c
is the speed at which light rays
propagate through empty space.

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I know what squared is, that means a
thing multiplied by itself. Exactly.

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So this is a kind of
fascinating statement.

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This is saying suppose
you have some mass, right,

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it's possible to convert that mass
into a certain amount of energy.

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I can see that E = mc2,
like all equations,

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is about balancing two sides.

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That's what
the equals sign is all about.

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So this equation allows us
to calculate how much energy

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is contained in any given mass.

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It's a surprise to me
that it applies to everything.

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Toothpaste, a book, a nail,
or uranium for that matter.

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This equation is universal.
And since "c2" is such a big number

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a tiny lump of matter contains
an enormous amount of energy.

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What this equation doesn't tell you
is how to unlock that energy.

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The most dramatic proof
that the equation was true

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came 40 years after Einstein
first worked it out,

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when the atomic bomb
was dropped on Hiroshima.

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Pedro walked me through
the chilling sums.

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You have a mass which
is something like half a gramme,

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I write it as a kilogramme.

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You need the speed of light and
the speed of light looks like this -

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it's about 300 million metres
per second. OK.

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OK. And we can work out
how much energy there is, OK?

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All we've got to do we say that
energy is going to be that mass

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times the speed of light,
squared, and what you get is this.

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Joules. This is the unit of energy.

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So you get
a phenomenal amount of energy.

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Now, if I told you this was something
like 15 kilotons of TNT from,

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something the size of a pill,

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giving enough energy... Producing
an explosion of 15 kilotons...

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Which is equivalent tons of TNT.

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I want to throw you, I don't know
if this is a stupid question and you
might have nothing to say about it,

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but supposing the sign
for squared was changed to a three.

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Would that just be nonsense, or...?
It would be nonsense,

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and the reason it would be nonsense
is because we've tested it.

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We've gone into a lab and tested
this relationship. We've weighed
something, done something to it,

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weighed it again,
worked out the amount of energy
that came out and it was on balance

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so the left side
was balanced with the right side.

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I'm impressed that E = mc2
was created before it was shown
to be true.

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The equation was a prophecy.

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The five symbols explain the link
between energy and all matter
across the cosmos.

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This universality
is part of its power.

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Einstein once claimed "the only
physical theories that we're willing
to accept are the beautiful ones".

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00:10:06,360 --> 00:10:08,920
But what do scientists mean
by "beautiful"?

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They talk about equations
being testable, being universal.

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Is that what they think beauty is?

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I'm going to take you
to the Rhodes building...

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..because Einstein actually
came here in, I think 1933,

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to give the Herbert Spencer lecture.
And it's an interesting lecture
because it's a lecture

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where he basically
discusses his philosophy.

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Right. Why he does science the way
he does, and his craft, what he does
as a theoretical physicist.

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And he basically said two things.

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The first is that the endgame
of what he does is experience.

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It's experiment.
It's the natural world.

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It's not theory for theory's sake.
It's always relating to reality.

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Exactly.

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But the bulk of what he says
is that what guides him

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is mathematical beauty,
or mathematical simplicity.

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That's what guides his research.
He says, "It is essential from
our point of view that we can arrive

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"at these constructions
and the laws relating them,
one with another, by adhering

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"to the principle of searching
for the mathematically simplest
concepts and their connections".

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So go for simplicity,
go for the simplest relationships
which are mathematically true,

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and that underpins the way
that he thought about what he did.

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So he was telling people this in
a lecture that was really about the
philosophy of what he did. Exactly.

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What his ultimate aims were,
and what the use of what
he did was to the world.

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It's a practical philosophy,
it's what he actually did on an
everyday basis. That's how he worked.

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So it gives us an insight into...

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what science at that level is about.

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00:11:51,080 --> 00:11:52,800
Exactly. Yeah.

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00:12:04,560 --> 00:12:09,680
Einstein believed that the laws
which govern the universe
would have an elegant simplicity

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and this would be shared
by their equations.

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I paint abstracts in collaboration
with my partner, Emma.

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It occurs to me that when we
intuitively put shapes and colours
together in a visual order,

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we too, like people
who come up with equations,

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00:12:25,720 --> 00:12:29,400
try to arrive
at a convincing metaphor for nature.

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For us, art tells you something
important about the world.

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This is a coloured engraving
of Isaac Newton by William Blake.

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It shows Newton studying
a tiny corner of the world

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00:13:01,720 --> 00:13:03,280
with a pair of dividers.

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00:13:04,320 --> 00:13:06,960
Blake despised Newton,
who he felt reduced

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00:13:06,960 --> 00:13:11,680
the magnificence of existence
to cold and mechanistic equations.

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00:13:17,280 --> 00:13:20,560
So today I'm coming to a place...

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00:13:21,720 --> 00:13:26,560
..where I'm actually
going to find out a bit more
about what Newton actually did.

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00:13:30,800 --> 00:13:35,320
This is Newton's house, where
he developed his ideas on gravity.

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00:13:35,320 --> 00:13:38,920
I'm going back to the 17th century
because it's when scientists

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00:13:38,920 --> 00:13:42,440
first used equations
to try to explain the natural order.

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00:13:47,960 --> 00:13:50,680
Hello.
Hello, welcome to Woolsthorpe.

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00:13:50,680 --> 00:13:54,640
I'm Margaret Winn, the house steward.
Pleased to meet you.

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00:13:54,640 --> 00:13:56,480
Likewise. Hi, I'm Ruth.

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00:13:56,480 --> 00:13:59,240
I'm professor
of theoretical physics from Durham.

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00:13:59,240 --> 00:14:02,080
Thank you both very much
for seeing me.

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00:14:02,080 --> 00:14:04,760
It's nice to meet you.
Have you been here before?

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00:14:04,760 --> 00:14:06,680
No, never. This is my first time.

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00:14:06,680 --> 00:14:12,240
Right, well, this is the house Newton
was born in, Christmas Day, 1642.

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00:14:12,240 --> 00:14:17,440
Yes. Ruth, the only thing I know
about Newton is an image of him
observing apples falling off a tree.

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00:14:17,440 --> 00:14:21,880
Falling from a tree! And he suddenly
works out that that means gravity.

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00:14:21,880 --> 00:14:26,040
Well, we call him
the father of modern science,
and that is not an understatement.

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00:14:26,040 --> 00:14:28,520
We can date our modern way

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00:14:28,520 --> 00:14:34,080
of doing physics or science as
trying to write down equations

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00:14:34,080 --> 00:14:35,680
as coming from Newton.

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00:14:35,680 --> 00:14:39,680
That's very clear, that equations
come from beginning of equations.

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00:14:39,680 --> 00:14:43,920
Yes, I think equations as a method,
as a means of encapsulating,

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00:14:43,920 --> 00:14:48,800
of modelling, of saying what physics
is and what the world around us is.

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00:15:05,880 --> 00:15:09,080
Why do you think the image
of the apples falling

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00:15:09,080 --> 00:15:11,760
is needed
in the mythology of Newton?

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00:15:11,760 --> 00:15:16,320
I think it's the link more than
anything else. If we take an apple

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00:15:16,320 --> 00:15:19,120
and just look at what happens

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00:15:19,120 --> 00:15:22,800
as it goes up and down
under gravity...

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00:15:24,640 --> 00:15:28,280
Gravity is something that I think
we often take for granted.

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00:15:28,280 --> 00:15:35,200
And the apple falling, he realised
that the same thing that made that
apple fall down to the ground was

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00:15:35,200 --> 00:15:41,840
the same thing that kept the Moon
going round the Earth, or indeed
the Earth going round the Sun.

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00:15:41,840 --> 00:15:47,680
Begs a lot of questions. How does he
go from that to realising something
about that? A lot of hard work!

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00:15:47,680 --> 00:15:51,160
Is it assuming that perhaps
there's some kind of force

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00:15:51,160 --> 00:15:54,640
connected to the moon that's similar
to the thing that makes...?

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00:15:54,640 --> 00:16:00,840
That's right, so as soon as you
start thinking about planetary
bodies or things moving round,

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00:16:00,840 --> 00:16:07,760
round other objects... I think
people at the time, they would have
felt, "ell that's a mystery of God,

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00:16:07,760 --> 00:16:13,240
"and we're not supposed
to understand that,"
but by using this apple

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00:16:13,240 --> 00:16:16,680
as this sort of metaphor
for the moon or the sun,

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00:16:16,680 --> 00:16:22,680
Newton managed to say,
"No, actually man can start
plumbing those mysteries."

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00:16:22,680 --> 00:16:28,240
I'm absorbing everything you've told
and as I'm starting to freeze a bit,
maybe we could go in the house!

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00:16:28,240 --> 00:16:31,640
Shall we go up to the house?
You talked about he didn't want

221
00:16:31,640 --> 00:16:34,680
his theories to be thought of
as the final word...

222
00:16:40,080 --> 00:16:46,840
Newton realised that mathematics
could provide a precise and
universal language to describe

223
00:16:46,840 --> 00:16:51,160
things as diverse as the fall of
an apple and the orbit of the moon.

224
00:16:56,440 --> 00:17:00,640
He put his ideas in a revolutionary
book, Principia Mathematica.

225
00:17:06,000 --> 00:17:08,400
I can barely tear my eyes away
from this!

226
00:17:08,400 --> 00:17:10,080
THEY ALL LAUGH

227
00:17:10,080 --> 00:17:12,840
That is our very prized possession,

228
00:17:12,840 --> 00:17:16,400
a third edition copy
of the Principia Mathematica.

229
00:17:16,400 --> 00:17:22,000
If we turn to the relevant page,
I'm going to leave you to our book.
Thank you very much. Wonderful.

230
00:17:22,000 --> 00:17:25,440
The first things that we notice here
is not a single equation,

231
00:17:25,440 --> 00:17:28,920
having talked about Newton as being
the father of modern science.

232
00:17:28,920 --> 00:17:33,680
The other thing is of course it's
in Latin, which the language of...

233
00:17:33,680 --> 00:17:35,120
It's hard enough...!

234
00:17:35,120 --> 00:17:39,240
The universal language at the time.
Propositio eight, theorema eight.

235
00:17:39,240 --> 00:17:44,240
Essentially, he is giving us
his equation for gravity in words.

236
00:17:44,240 --> 00:17:50,560
So he starts off, "Si globorum
duroum in se mutuo gravitantium
materia undique in regionibus..."

237
00:17:53,920 --> 00:17:59,680
Newton's written version
eventually formed the basis
for the equation for gravity.

238
00:17:59,680 --> 00:18:03,400
So I want Ruth to unpick
the different elements,

239
00:18:03,400 --> 00:18:05,640
a mathematical version of the words.

240
00:18:05,640 --> 00:18:08,880
I've noticed you've got a book,
so we could try and translate

241
00:18:08,880 --> 00:18:13,160
what he said into
one of these beautiful equations.

242
00:18:13,160 --> 00:18:15,200
Absolutely, find a blank page.

243
00:18:15,200 --> 00:18:17,640
Anywhere will do. Right.

244
00:18:17,640 --> 00:18:21,480
So we write both
of these objects as M1 and M2.

245
00:18:21,480 --> 00:18:25,200
So these are just the masses.
But then Newton talked about

246
00:18:25,200 --> 00:18:28,560
the force between the two spheres,

247
00:18:28,560 --> 00:18:32,640
these two bodies,
is inversely proportional,

248
00:18:32,640 --> 00:18:36,640
which means we divide,
to the distance squared.

249
00:18:36,640 --> 00:18:39,080
The two bodies or spheres
could be any size -

250
00:18:39,080 --> 00:18:42,920
the Earth, the Moon,
or even an apple.

251
00:18:42,920 --> 00:18:46,360
And this is G, for gravity.

252
00:18:46,360 --> 00:18:48,680
It's actually called
Newton's constant.

253
00:18:48,680 --> 00:18:52,160
You've written out
an equation for me there. Yes.

254
00:18:52,160 --> 00:18:56,240
And earlier you threw an apple in
the air and it fell to the ground.

255
00:18:56,240 --> 00:18:58,160
Can you give me some numbers...

256
00:18:58,160 --> 00:19:01,840
Certainly. ..that will show me
what the apple is doing?

257
00:19:01,840 --> 00:19:03,880
Let's talk about the apple.

258
00:19:04,960 --> 00:19:08,800
OK, so one of the Ms is an apple?
An apple. What does an apple weigh?

259
00:19:08,800 --> 00:19:15,000
Half... ? You get a pound of apples
so I guess that's about four apples,
so that's a quarter of a pound.

260
00:19:15,000 --> 00:19:17,280
We work in kilograms!
SHE LAUGHS

261
00:19:19,680 --> 00:19:22,000
Let's just say it's 200 grams.

262
00:19:22,000 --> 00:19:27,560
But is the other M the Earth?
You don't need explaining, do you?
You know this already. I'm guessing!

263
00:19:27,560 --> 00:19:31,880
But I don't know how much
the Earth weighs, I very rarely
buy one from the grocer!

264
00:19:31,880 --> 00:19:34,800
Well, I can give you a rough idea.

265
00:19:34,800 --> 00:19:38,600
Five times ten
to the 24 kilograms. Got it.

266
00:19:38,600 --> 00:19:41,560
So it's ten to the power of 24.

267
00:19:41,560 --> 00:19:43,840
Which is a trillion trillion.

268
00:19:43,840 --> 00:19:45,560
OK, good.

269
00:19:45,560 --> 00:19:51,360
Now the radius of the Earth
is 6,000 kilometres.

270
00:19:51,360 --> 00:19:54,320
We've got a 200 gram apple,

271
00:19:54,320 --> 00:19:58,200
several trillion kilograms Earth

272
00:19:58,200 --> 00:20:00,400
and radius of Earth 6,000.

273
00:20:00,400 --> 00:20:05,280
Now, what I'm going to do is cancel
all those off to make it easy.

274
00:20:05,280 --> 00:20:08,520
Then what I end up with is
a simple ten on the top

275
00:20:08,520 --> 00:20:12,600
times the 0.2 of the apple.

276
00:20:12,600 --> 00:20:17,080
So what this tells me is the
force the apple feels is its mass

277
00:20:17,080 --> 00:20:20,640
times this ten and this is...

278
00:20:20,640 --> 00:20:24,040
Mass times ten.
Ten is... This is the sort of,

279
00:20:24,040 --> 00:20:27,240
how fast gravity is going to
cause the apple to start to fall.

280
00:20:27,240 --> 00:20:31,240
So the force on the apple here
is simply two.

281
00:20:31,240 --> 00:20:35,040
And that unit is called the Newton.

282
00:20:35,040 --> 00:20:37,280
Ah! N for Newton.

283
00:20:37,280 --> 00:20:38,840
N for Newton. Fantastic.

284
00:20:40,720 --> 00:20:45,800
The number of Newtons
measures the force of gravity
acting on the apple.

285
00:20:45,800 --> 00:20:47,400
It's a complicated equation,

286
00:20:47,400 --> 00:20:49,840
but I'm beginning to understand
the key parts.

287
00:20:49,840 --> 00:20:53,440
The force depends on the
mass of the two objects

288
00:20:53,440 --> 00:20:55,840
and the distance between them.

289
00:20:57,400 --> 00:21:00,080
The bigger the objects,
the bigger the force.

290
00:21:00,080 --> 00:21:03,760
And the further apart they are,
the weaker the force.

291
00:21:03,760 --> 00:21:07,160
The two masses,
M1 and M2, could be anything.

292
00:21:07,160 --> 00:21:11,080
The earth and the apple.
Or the earth and the moon.

293
00:21:11,080 --> 00:21:13,320
Or the earth and the sun.

294
00:21:16,640 --> 00:21:21,200
Ruth told me Newton's equation
allowed us to understand why

295
00:21:21,200 --> 00:21:25,000
the moons and planets move
around the solar system.

296
00:21:25,000 --> 00:21:28,960
His equation seemed to make
sense of, well, the universe.

297
00:21:34,520 --> 00:21:38,920
So the equation itself,
F = G x M1 x M2/R squared,

298
00:21:38,920 --> 00:21:43,960
that's Newton's equation of gravity,
but how we use it,

299
00:21:43,960 --> 00:21:47,400
this is a sort of process,
you know doing science,

300
00:21:47,400 --> 00:21:50,720
of calculating things,
of making predictions.

301
00:21:50,720 --> 00:21:53,160
You've now showed me
how we use that equation.

302
00:21:53,160 --> 00:21:55,200
How we would use it, yes.

303
00:21:55,200 --> 00:21:57,520
This is our paint,
how we paint the world.

304
00:21:57,520 --> 00:22:00,240
We paint it in equations.

305
00:22:00,240 --> 00:22:02,840
In fact we use that a lot,
we say, "I'm painting,"

306
00:22:02,840 --> 00:22:05,320
you know, we tend to use this word,
"painting".

307
00:22:05,320 --> 00:22:09,400
If you, if you can use that metaphor
of paint and colours etcetera

308
00:22:09,400 --> 00:22:14,240
is there a place also for beauty
in this world of calculating things?

309
00:22:14,240 --> 00:22:17,960
I don't expect everyone to find
this beautiful,

310
00:22:17,960 --> 00:22:20,720
but it certainly is
for us and for me.

311
00:22:20,720 --> 00:22:22,200
Great!

312
00:22:37,240 --> 00:22:40,640
'A few decades after Newton came up
with his law, it was used

313
00:22:40,640 --> 00:22:45,200
'to successfully predict the return
of a comet, Halley's comet.

314
00:22:45,200 --> 00:22:48,360
'His law of gravity
had been confirmed.'

315
00:22:52,560 --> 00:22:55,640
'With his equation,
Newton had transformed

316
00:22:55,640 --> 00:22:58,800
'the way mathematics
modelled the world,

317
00:22:58,800 --> 00:23:02,040
'and his work went unchallenged
for over 200 years.'

318
00:23:15,600 --> 00:23:18,360
'Everything changed at the beginning
of the 20th century

319
00:23:18,360 --> 00:23:22,120
'with the arrival of Einstein
and his Theory of Relativity.

320
00:23:22,120 --> 00:23:27,120
'In that same decade, something else
entered, and that was modern art.

321
00:23:27,120 --> 00:23:30,800
'In the world of art many believe
that Picasso was involved

322
00:23:30,800 --> 00:23:33,640
'in the same revolution
as Einstein.'

323
00:23:35,520 --> 00:23:38,680
Weirdly, the one place in which
I had heard about relativity

324
00:23:38,680 --> 00:23:43,680
before embarking on this programme
was art school when I was young.

325
00:23:43,680 --> 00:23:48,320
As art students we all had to
absorb the idea that

326
00:23:48,320 --> 00:23:53,400
relativity had something to do with
cubist paintings.

327
00:24:00,600 --> 00:24:07,360
I'm about to look at a
cubist painting by Picasso
from about 1909-1910.

328
00:24:07,360 --> 00:24:09,240
It's of a woman in an armchair.

329
00:24:09,240 --> 00:24:17,120
I think cubism was really seen as
something quite terrifying and
shocking when it first came out.

330
00:24:22,120 --> 00:24:24,320
It's not like a Renaissance painting

331
00:24:24,320 --> 00:24:29,320
where you feel you're looking
through a kind of window onto
the world.

332
00:24:29,320 --> 00:24:33,120
With cubism the artist is
deliberately confusing you

333
00:24:33,120 --> 00:24:37,120
as to where thing are,
and indeed what things are.

334
00:24:37,120 --> 00:24:41,080
So that the space in the room

335
00:24:41,080 --> 00:24:44,120
seems to be eating into
the side of the woman.

336
00:24:44,120 --> 00:24:48,880
And the textures of the room seem
to be no different from the textures

337
00:24:48,880 --> 00:24:54,960
of the woman. So there's all this
moving around of objects and space

338
00:24:54,960 --> 00:24:59,280
in a way that is deliberately
confusing if you were thinking,

339
00:24:59,280 --> 00:25:02,560
"Well, where is the thing that looks
like ordinary reality?"

340
00:25:08,400 --> 00:25:11,560
'I think it's right to say that
cubism was a new kind of beauty

341
00:25:11,560 --> 00:25:14,120
'that looked a bit like science.

342
00:25:14,120 --> 00:25:17,480
'But I'm not convinced that
cubism is science.

343
00:25:17,480 --> 00:25:21,480
'I've arranged to meet historian
of science, Arthur Miller,

344
00:25:21,480 --> 00:25:25,000
'who's going to attempt
to change my mind.'

345
00:25:25,000 --> 00:25:28,920
I've got to tell you, Arthur, that
at art school, and subsequently,

346
00:25:28,920 --> 00:25:35,440
I felt oppressed by the idea that I
had to think of a connection between

347
00:25:35,440 --> 00:25:38,920
Einstein and relativity and cubism.

348
00:25:38,920 --> 00:25:41,320
Einstein and relativity and Picasso.

349
00:25:41,320 --> 00:25:44,280
But there is one in a sense that
I'll say they both worked on

350
00:25:44,280 --> 00:25:46,920
the same problem,
the nature of space and time.

351
00:25:46,920 --> 00:25:51,360
OK. The connection is that time and
space are important to them both.

352
00:25:51,360 --> 00:25:52,680
That's right.

353
00:25:52,680 --> 00:25:59,680
Where I find the proposal difficult
is that, just because

354
00:25:59,680 --> 00:26:03,040
he's doing something with time
and space that he's therefore

355
00:26:03,040 --> 00:26:09,000
something like Einstein, or that
cubism is something like science.

356
00:26:09,000 --> 00:26:12,760
Cubism was very much of a scientific
research programme, as I've said.

357
00:26:12,760 --> 00:26:16,080
It had, you know, an explicit
intent to reduce forms

358
00:26:16,080 --> 00:26:20,160
to geometry. Why is that? Picasso...

359
00:26:20,160 --> 00:26:22,640
Why is that scientific and
not artistic?

360
00:26:22,640 --> 00:26:25,080
I mean, medieval artists
reduced forms to geometry,

361
00:26:25,080 --> 00:26:29,440
and African artists reduce it
to geometry, archaic art
reduces it to geometry.

362
00:26:29,440 --> 00:26:35,680
Well, that's because Picasso had
in mind scientific texts
as a way to do it.

363
00:26:35,680 --> 00:26:40,560
For example, we know that he looked
at a text written by a mathematician

364
00:26:40,560 --> 00:26:44,480
and the text discussed how you
represent in four dimensions

365
00:26:44,480 --> 00:26:47,160
complex polyhedra and Picasso took
a look at these.

366
00:26:47,160 --> 00:26:49,760
Of course, he didn't know what
the equations meant,

367
00:26:49,760 --> 00:26:53,040
but when the author of the books
specialised the equations

368
00:26:53,040 --> 00:26:57,120
of the two dimensions and then could
generate illustrations,

369
00:26:57,120 --> 00:27:00,120
Picasso was interested
in the illustrations.

370
00:27:00,120 --> 00:27:04,280
It's correct to call Picasso
a revolutionary artist,

371
00:27:04,280 --> 00:27:07,640
it's not hyperbole, but for me, I
don't know enough about Einstein

372
00:27:07,640 --> 00:27:11,480
to see the way in which Einstein
is a revolutionary too, or how

373
00:27:11,480 --> 00:27:16,280
Einstein's ideas and Picasso's are
the same level of revolution

374
00:27:16,280 --> 00:27:18,080
and also going in
the same direction.

375
00:27:18,080 --> 00:27:21,560
Well, Einstein was a revolutionary
scientist because what he did

376
00:27:21,560 --> 00:27:26,480
was to go take the next step
beyond Newton.

377
00:27:26,480 --> 00:27:30,920
Newtonian science is based on our
sense perceptions that all time,

378
00:27:30,920 --> 00:27:33,080
your time is the same as my time.

379
00:27:33,080 --> 00:27:36,720
What Einstein was able to
do was to raise himself to

380
00:27:36,720 --> 00:27:40,440
heights of abstraction so he could
glimpse a world beyond appearances.

381
00:27:40,440 --> 00:27:45,040
The real objective world out there
where there is scientific truth.

382
00:27:47,640 --> 00:27:51,560
I still think the connections
between Einstein and Picasso are

383
00:27:51,560 --> 00:27:53,520
more superficial than substantial,

384
00:27:53,520 --> 00:27:57,120
but I am very interested to hear
more about Einstein.

385
00:27:57,120 --> 00:27:59,000
Arthur will attempt to explain to me

386
00:27:59,000 --> 00:28:02,760
one of the key equations of the
Special Theory of Relativity.

387
00:28:05,080 --> 00:28:07,320
When Einstein came up
with this equation,

388
00:28:07,320 --> 00:28:11,080
he wasn't even officially
a scientist.

389
00:28:11,080 --> 00:28:14,360
The days when he wrote the relativity
theory, he worked as a patent clerk

390
00:28:14,360 --> 00:28:17,040
in the Swiss federal
patent office in Bern.

391
00:28:17,040 --> 00:28:20,120
In fact he worked
there from 1902 to 1909.

392
00:28:20,120 --> 00:28:22,160
He was also a conscientious
daydreamer.

393
00:28:22,160 --> 00:28:25,880
And in his dreams and visions
he soared over the landscape

394
00:28:25,880 --> 00:28:29,960
of physics and realised what
the fundamental problem was.

395
00:28:29,960 --> 00:28:32,080
The nature of space and time.

396
00:28:32,080 --> 00:28:36,240
People were beginning to think that
maybe there was something wrong with

397
00:28:36,240 --> 00:28:39,120
classical, intuitive notions
of space and time,

398
00:28:39,120 --> 00:28:41,600
but they couldn't put
their finger on it.

399
00:28:41,600 --> 00:28:45,240
What they especially wanted to do was
to leave alone the notion of time.

400
00:28:45,240 --> 00:28:47,920
Why was time sacrosanct, because it
was obvious what it was,

401
00:28:47,920 --> 00:28:52,040
it didn't need any more inquiry,
or they were afraid that they
couldn't find out anything more?

402
00:28:52,040 --> 00:28:54,320
It seemed that your time
is the same as my time.

403
00:28:54,320 --> 00:28:57,680
No matter how fast we're moving
with respect to one another.

404
00:28:57,680 --> 00:28:59,440
There's no mystery there.
We know what time is.

405
00:28:59,440 --> 00:29:03,120
That's right. It's like Superman
said, "Leave time alone."

406
00:29:03,120 --> 00:29:06,480
Don't mess with time.
Don't mess with time, yeah.

407
00:29:06,480 --> 00:29:09,520
OK I've got a book,
if you've got a pen?

408
00:29:09,520 --> 00:29:13,920
Absolutely, let me show you
one of the spectacular results

409
00:29:13,920 --> 00:29:15,600
of relativity theory.

410
00:29:15,600 --> 00:29:17,800
Let's do a little thought experiment.

411
00:29:17,800 --> 00:29:24,640
Suppose here is Matt one
standing on a train platform

412
00:29:24,640 --> 00:29:29,320
and here is Matt two, just call him
Matt, standing on a train

413
00:29:29,320 --> 00:29:33,240
and he's moving along with some
velocity, call it V,

414
00:29:33,240 --> 00:29:35,720
relative to the Matt standing
on the platform.

415
00:29:35,720 --> 00:29:38,960
The Matt on the moving train
is wearing a wristwatch

416
00:29:38,960 --> 00:29:42,240
and his time, call it t prime,

417
00:29:42,240 --> 00:29:45,680
and call the times of all the clocks
on the platform t.

418
00:29:45,680 --> 00:29:48,280
And what we want to do
is to compare the time

419
00:29:48,280 --> 00:29:55,520
on Matt's wristwatch with clocks
that remain at rest on the platform.

420
00:29:55,520 --> 00:29:57,280
They all read the same time.

421
00:29:57,280 --> 00:30:00,360
I'm going to assume that,
even though the clocks are at rest

422
00:30:00,360 --> 00:30:03,040
and my clock is moving
that they're all the same,

423
00:30:03,040 --> 00:30:06,440
because clocks always tell
the same time, assuming
they're all synchronised.

424
00:30:06,440 --> 00:30:09,640
One would think so, yeah. Now let's
call the Matt on the train...

425
00:30:09,640 --> 00:30:11,480
But you're going to show me
that they don't.

426
00:30:11,480 --> 00:30:15,000
I'm going show you that they don't,
convince you that they don't.

427
00:30:15,000 --> 00:30:16,040
t prime and t.

428
00:30:16,040 --> 00:30:18,840
Now it turns out Matt on
the train's time t prime is

429
00:30:18,840 --> 00:30:23,920
equal to t times the square root
of 1 - V squared over C squared.

430
00:30:23,920 --> 00:30:26,680
So the time here is equal to
something complicated.

431
00:30:26,680 --> 00:30:28,640
It's not just the same as that time.

432
00:30:28,640 --> 00:30:31,760
No, it's not the same as that time.
Your time is not the same as my time.

433
00:30:31,760 --> 00:30:33,640
These two times are different...

434
00:30:33,640 --> 00:30:38,680
'If I understand the equation
correctly, it says something
unbelievable -

435
00:30:38,680 --> 00:30:43,520
'that time runs at different rates
depending on how fast you're moving.

436
00:30:43,520 --> 00:30:46,040
'Take a train zooming
through a station.

437
00:30:46,040 --> 00:30:50,840
'This equation predicts that a clock
on the train, reading time t-,

438
00:30:50,840 --> 00:30:54,400
'would run slower than clocks
reading time t

439
00:30:54,400 --> 00:30:57,000
'on the station platform.

440
00:30:57,000 --> 00:31:00,160
'I've never noticed it
and here's why.

441
00:31:00,160 --> 00:31:04,080
'This bit of the equation is what
makes the two clock times different,

442
00:31:04,080 --> 00:31:07,800
'but it only has a significant
effect if the velocity, V,

443
00:31:07,800 --> 00:31:12,840
'of the train is very fast,
close to the speed of light.

444
00:31:12,840 --> 00:31:16,840
'If the train could reach the speed
of light, you get 1 - 1,

445
00:31:16,840 --> 00:31:18,840
'which equals zero.

446
00:31:18,840 --> 00:31:21,600
'And then t- equals zero.

447
00:31:21,600 --> 00:31:26,320
'Relative to the platform,
time on the train completely stops.

448
00:31:27,880 --> 00:31:31,600
'This stretching of time
seems impossible

449
00:31:31,600 --> 00:31:35,360
'but according to Arthur it's been
proven by practical experiment.'

450
00:31:40,360 --> 00:31:42,800
Now that's really something.
That's wild.

451
00:31:42,800 --> 00:31:46,720
And he realised that's because
time is a relative quantity.

452
00:31:46,720 --> 00:31:49,880
Just as I discussed with you.

453
00:31:49,880 --> 00:31:53,600
Your time is only the same as my time
if we're standing still

454
00:31:53,600 --> 00:31:57,000
next to each other, but if you go
away and come back, your clock,

455
00:31:57,000 --> 00:31:59,240
although it'd be very difficult
to perceive it,

456
00:31:59,240 --> 00:32:01,080
will read a slower time than mine.

457
00:32:01,080 --> 00:32:04,640
Well, I'm taking in a lot of what
you're saying so that

458
00:32:04,640 --> 00:32:07,560
I'm far more informed than
I was before you spoke. Good.

459
00:32:07,560 --> 00:32:10,240
But the thing that's really big
for me is this idea

460
00:32:10,240 --> 00:32:14,680
of the physical nature of time
and that seems a marvellous idea.

461
00:32:14,680 --> 00:32:18,960
Oh, it turns out that there's not
space and time. There's space-time.

462
00:32:18,960 --> 00:32:23,200
Right, they are a single entity.
Is entity the right word?

463
00:32:23,200 --> 00:32:26,480
Time and space are connected by
the velocity of light.

464
00:32:29,640 --> 00:32:32,760
'That was definitely the
hardest equation so far,

465
00:32:32,760 --> 00:32:36,960
'not just the maths but because
of the ideas it contained.

466
00:32:36,960 --> 00:32:40,600
'You might be worrying about time
on a tube train,

467
00:32:40,600 --> 00:32:44,080
'but you wouldn't think time was
actually changing shape.'

468
00:32:45,640 --> 00:32:50,200
'Einstein worked out that time and
space are inextricably linked

469
00:32:50,200 --> 00:32:52,080
'through the speed of light.'

470
00:32:55,840 --> 00:33:00,120
'It was a thought that it was simply
impossible to have before,

471
00:33:00,120 --> 00:33:01,640
'reality had changed,

472
00:33:01,640 --> 00:33:04,320
'and Einstein did it
with equations.'

473
00:33:07,880 --> 00:33:11,480
'I'm beginning to get
a crush on science.'

474
00:33:11,480 --> 00:33:15,160
'Before, I literally didn't
know what an equation was.

475
00:33:15,160 --> 00:33:21,040
'Now, in some ways I know the
basics of what an equation is,

476
00:33:21,040 --> 00:33:25,080
'but I also know the implications
of what an equation is,

477
00:33:25,080 --> 00:33:26,840
'so there's a sort of excitement

478
00:33:26,840 --> 00:33:29,000
'about the philosophy
of an equation,'

479
00:33:29,000 --> 00:33:31,960
or the use of an equation
in some kind of profound way

480
00:33:31,960 --> 00:33:36,640
as opposed to something like
a railway timetable that tells
you very detailed information.

481
00:33:36,640 --> 00:33:41,960
You know the process of learning
is a mixture of pain and pleasure.

482
00:33:41,960 --> 00:33:45,520
It's quite hard to dislodge
the pattern of the world that

483
00:33:45,520 --> 00:33:49,200
you've already got in place, and
bring in a whole load of new stuff.

484
00:33:49,200 --> 00:33:52,520
You can appreciate it
on mythological levels.

485
00:33:52,520 --> 00:33:56,000
Someone's telling you the myth of
equations, or the myth of science,

486
00:33:56,000 --> 00:33:59,400
or the myth of Newton,
or the myth of Einstein,

487
00:33:59,400 --> 00:34:01,720
but they all do sound like
myths to me.

488
00:34:01,720 --> 00:34:06,560
But as the days go by they acquire
more and more reality as each

489
00:34:06,560 --> 00:34:11,560
scientist adds to the stories that
the other scientists have told me.

490
00:34:20,240 --> 00:34:25,360
There's one scientist who stands
out in the story of equations,

491
00:34:25,360 --> 00:34:30,160
because he took the idea of beauty
in science further than anyone else.

492
00:34:30,160 --> 00:34:32,920
His name is Paul Dirac.

493
00:34:34,600 --> 00:34:38,280
He too revolutionised our view
of the universe,

494
00:34:38,280 --> 00:34:43,280
yet virtually no-one outside
scientific circles has heard
of Dirac.

495
00:34:43,280 --> 00:34:49,120
So, I've arranged to meet
the biographer of this
mysterious genius.

496
00:34:51,360 --> 00:34:56,360
This is a particularly favourite
part of Cambridge for Paul Dirac.

497
00:34:56,360 --> 00:34:59,240
Dirac was the greatest
English theoretician since

498
00:34:59,240 --> 00:35:03,000
Isaac Newton and that's how...
That's his reputation in 1927,

499
00:35:03,000 --> 00:35:07,200
when he was looking for what became
his greatest achievement -

500
00:35:07,200 --> 00:35:08,240
his equation.

501
00:35:08,240 --> 00:35:10,760
Why is he... Being so great,

502
00:35:10,760 --> 00:35:16,320
why is he totally unknown
to the general public?

503
00:35:16,320 --> 00:35:20,160
He actually wanted anonymity,
he really had no interest
at all in celebrity.

504
00:35:20,160 --> 00:35:24,400
He simply wanted to get on
with his work and be unknown

505
00:35:24,400 --> 00:35:27,160
to the outside world.

506
00:35:27,160 --> 00:35:32,640
I love the idea that
for Dirac, beauty is important.

507
00:35:32,640 --> 00:35:37,200
Is there a sense in which
it is more important for him

508
00:35:37,200 --> 00:35:39,600
than I've been hearing so far
about other scientists?

509
00:35:39,600 --> 00:35:44,960
Oh, yeah, Dirac was the first
scientist actually to elevate this
idea of beauty to a principle.

510
00:35:44,960 --> 00:35:47,600
He called it the principle
of mathematical beauty.

511
00:35:47,600 --> 00:35:52,360
And what he meant by that was
that as we advance in fundamental,

512
00:35:52,360 --> 00:35:56,680
theoretical physics, the theories as
they get closer and closer to nature,

513
00:35:56,680 --> 00:35:58,520
become more and more beautiful.

514
00:35:58,520 --> 00:36:03,720
So, for him, it was a
method of sifting out theories,

515
00:36:03,720 --> 00:36:06,960
right from wrong because if it wasn't
beautiful, if it was ugly

516
00:36:06,960 --> 00:36:11,000
in his opinion, it just wouldn't cut
pass muster with nature.

517
00:36:11,000 --> 00:36:16,880
So for him, a theory had
to be beautiful for it to stand
a chance of describing nature.

518
00:36:16,880 --> 00:36:18,920
Incredible.

519
00:36:18,920 --> 00:36:23,080
Here's a scientist who insisted
science went through a "filter"

520
00:36:23,080 --> 00:36:27,920
of beauty. And by pursuing beauty,
you end up with truth.

521
00:36:27,920 --> 00:36:33,240
It's an idea that's often
used metaphorically,
but Dirac meant it literally.

522
00:36:33,240 --> 00:36:36,720
This is the Bridge of Sighs,
which he walked across as a Fellow.

523
00:36:36,720 --> 00:36:43,480
He walked back to his rooms here
and this is where he did his
great work on the Dirac Equation.

524
00:36:43,480 --> 00:36:47,880
In fact, he was staying in a room
just here.

525
00:36:47,880 --> 00:36:52,800
That's where he was working
in the late months of 1927

526
00:36:52,800 --> 00:36:57,480
on what came to be known as the
Dirac Equation, one of the greatest
achievements in modern science.

527
00:37:09,200 --> 00:37:14,680
Here we are, Room A4. Newcourt. Where
Dirac discovered his great equation.

528
00:37:14,680 --> 00:37:19,200
Completely free of distraction.
The only noise you get is a bit of
noise from the punters outside.

529
00:37:19,200 --> 00:37:22,080
Apart from that, no radio,
just nothing.

530
00:37:22,080 --> 00:37:29,000
Dirac was not given to luxury.
In late 1927, all he did, apparently,
was to work on that equation.

531
00:37:29,000 --> 00:37:34,280
Tell me about that equation, what
was he trying to accomplish with it?

532
00:37:34,280 --> 00:37:38,640
Well, what he was trying to do
was come up with an equation
for the electron,

533
00:37:38,640 --> 00:37:44,160
the first material fundamental
particle to have been discovered.

534
00:37:44,160 --> 00:37:49,880
What does that mean, "the first
fundamental material particle"? OK.

535
00:37:49,880 --> 00:37:52,720
A fundamental particle
has no constituents.

536
00:37:52,720 --> 00:37:56,320
It's a completely basic particle,
you can't subdivide it.

537
00:37:56,320 --> 00:37:59,680
The point of the tiny, tiny thing,
this electron,

538
00:37:59,680 --> 00:38:03,440
is that nothing else is more basic
than it. That's right.

539
00:38:03,440 --> 00:38:08,600
So you had a chance of giving
a fundamental description in nature.

540
00:38:08,600 --> 00:38:12,120
I've got a notebook in my bag.

541
00:38:12,120 --> 00:38:15,040
If I give that to you and
you find a blank page... Yep.

542
00:38:15,040 --> 00:38:19,680
And I then give you my pen,
could you write out for me

543
00:38:19,680 --> 00:38:21,680
the equation... I will.

544
00:38:21,680 --> 00:38:23,560
..that Dirac came up with. I will.

545
00:38:23,560 --> 00:38:25,640
It's called the Dirac Equation?

546
00:38:25,640 --> 00:38:28,440
That's right.
This is the Dirac Equation.

547
00:38:28,440 --> 00:38:35,080
And this equation applies
to every electron that's ever
existed, or ever will exist,

548
00:38:35,080 --> 00:38:40,560
in the entire universe, so this is
the ultimate compact equation that

549
00:38:40,560 --> 00:38:43,400
has this universal significance.

550
00:38:43,400 --> 00:38:46,640
This is a miracle, one of the
miracles of 20th century science.

551
00:38:46,640 --> 00:38:50,640
You've shown me the miracle,
now tell me what it is.

552
00:38:50,640 --> 00:38:55,360
I see something like "I followed by
squiggle, followed by P followed by

553
00:38:55,360 --> 00:38:57,320
"a squiggle, followed by equals,
followed by m,

554
00:38:57,320 --> 00:38:58,440
"followed by squiggle."

555
00:38:58,440 --> 00:39:04,280
OK, you say, "I, gamma, P, psi
= M psi".

556
00:39:04,280 --> 00:39:09,080
OK, so it's like E = M C squared,
only you say these new things that

557
00:39:09,080 --> 00:39:12,240
he thought up himself, a bit like
the Lord of the Rings language.

558
00:39:12,240 --> 00:39:14,920
That's right. And what is the
most important symbol there?

559
00:39:14,920 --> 00:39:16,160
Right, OK.

560
00:39:16,160 --> 00:39:19,440
This is called a spinner, all right?

561
00:39:19,440 --> 00:39:24,280
This is a thing that encodes
the information about the
behaviour of the electron.

562
00:39:24,280 --> 00:39:30,640
So, you tell the equation what
situation the electron is in and out

563
00:39:30,640 --> 00:39:35,480
of the equation comes the prediction
for how the electron will behave.

564
00:39:35,480 --> 00:39:39,880
What's the thing in the ordinary
world that is the closest that

565
00:39:39,880 --> 00:39:44,120
I could visualise, to tell me what a
spinner really means? There is none.

566
00:39:44,120 --> 00:39:46,840
OK, so I've got to accept that.
Exactly. Fine.

567
00:39:46,840 --> 00:39:49,320
This was a complete Dirac
concoction, right?

568
00:39:49,320 --> 00:39:51,280
So spinners didn't exist before him?

569
00:39:51,280 --> 00:39:55,680
No, they didn't. Do you have
to learn his new language before you
can say that equation? Yeah.

570
00:39:55,680 --> 00:39:59,360
Seriously, people for six months a
year were struggling. Brilliant,

571
00:39:59,360 --> 00:40:03,720
world-leading physicists had no
clue about what this equation meant.

572
00:40:03,720 --> 00:40:06,920
This is why he was so far ahead
of his time, they were having to say,

573
00:40:06,920 --> 00:40:08,680
"What the hell do
these symbols mean?"

574
00:40:08,680 --> 00:40:11,800
It was on extremely good ground
and moreover...

575
00:40:11,800 --> 00:40:17,160
'If it stumps the world's top
scientists then I think it's OK
for it to be beyond me.

576
00:40:17,160 --> 00:40:19,800
'This really is a foreign language.

577
00:40:19,800 --> 00:40:25,320
'But I was getting a broader sense
of how equations have
advanced knowledge.'

578
00:40:27,240 --> 00:40:32,160
I do feel from your talk that I'm
starting to get a picture filled in

579
00:40:32,160 --> 00:40:34,640
for me of science, the big points.

580
00:40:34,640 --> 00:40:37,680
Newton, Einstein and now Dirac.

581
00:40:37,680 --> 00:40:44,680
That's right. And a sort of journey
that the spheres, the planets,

582
00:40:44,680 --> 00:40:48,520
the stars, this earth, everything
on it, all the objects

583
00:40:48,520 --> 00:40:53,520
can be somehow described
and understood in mechanical terms.

584
00:40:53,520 --> 00:40:57,440
That's right. Einstein said that
the most incomprehensible thing

585
00:40:57,440 --> 00:41:00,280
about the universe
is that it is comprehensible.

586
00:41:00,280 --> 00:41:06,120
And Dirac, Newton, Einstein, they all
had faith that they could,

587
00:41:06,120 --> 00:41:09,520
if they thought hard enough, they
could come up with these laws that

588
00:41:09,520 --> 00:41:11,760
describe nature
at a fundamental level.

589
00:41:11,760 --> 00:41:14,840
But faith doesn't produce
more faith, it actually
produces equations.

590
00:41:14,840 --> 00:41:16,080
Oh, absolutely.

591
00:41:16,080 --> 00:41:20,240
It's not like a faith that you can't
verify. Faith oils the works. Yeah.

592
00:41:20,240 --> 00:41:27,120
Dirac actually said that the
principle of mathematical beauty
was a kind of religion to him.

593
00:41:27,120 --> 00:41:30,840
He actually used those words
because he really did believe

594
00:41:30,840 --> 00:41:36,200
with all his heart and soul that a
mathematically beautiful theory

595
00:41:36,200 --> 00:41:38,840
was going to be the kind of theory
that nature backed

596
00:41:38,840 --> 00:41:43,840
and that that was the direction
in which you should travel,
so he really did believe that.

597
00:41:43,840 --> 00:41:45,520
It was an article of faith.

598
00:41:45,520 --> 00:41:48,400
Why is the spinner beautiful?

599
00:41:48,400 --> 00:41:52,440
This is beautiful because
Dirac used this equation

600
00:41:52,440 --> 00:41:56,080
to predict the first example
of anti-matter.

601
00:41:56,080 --> 00:42:00,480
This was perhaps the greatest
triumph of 20th century physics.

602
00:42:00,480 --> 00:42:04,200
Now just to give you a sense
of how monumental that is,

603
00:42:04,200 --> 00:42:08,720
now cosmologists believe that the
very beginning of the universe,

604
00:42:08,720 --> 00:42:11,240
half the universe was anti-matter.

605
00:42:11,240 --> 00:42:15,400
So by that token,
Dirac conceived, using this equation,

606
00:42:15,400 --> 00:42:17,560
half the universe in his head.

607
00:42:32,400 --> 00:42:37,000
'Scientists now stand in awe
of Dirac's Equation.

608
00:42:37,000 --> 00:42:39,720
'But at the time,
things were very different.

609
00:42:39,720 --> 00:42:44,120
'In the late 1920's,
anti-matter was totally unknown.

610
00:42:44,120 --> 00:42:47,880
'The idea that every electron,
proton, and neutron

611
00:42:47,880 --> 00:42:51,040
'had an opposite partner
was preposterous.

612
00:42:51,040 --> 00:42:56,120
'If his equation predicted this
make-believe stuff

613
00:42:56,120 --> 00:42:58,240
'then it must be wrong.'

614
00:43:00,040 --> 00:43:04,840
OK, so what we can do now
is go into the teaching lab.

615
00:43:04,840 --> 00:43:07,480
What we have is an
experiment set up where we can

616
00:43:07,480 --> 00:43:11,600
actually see tracks of particles that
have been produced by anti-matter.

617
00:43:11,600 --> 00:43:14,400
So you'll be showing me some
anti-matter in action.

618
00:43:14,400 --> 00:43:17,160
'Five years after Dirac came up with
his prediction,

619
00:43:17,160 --> 00:43:19,000
'anti-matter was discovered.'

620
00:43:21,160 --> 00:43:24,040
'The equation had
turned out to be true.

621
00:43:24,040 --> 00:43:26,800
'Now, I too want to see the proof.'

622
00:43:26,800 --> 00:43:30,000
This is the first practical place
I've been to.

623
00:43:30,000 --> 00:43:33,640
I'm surprised at how
quaint everything looks.

624
00:43:33,640 --> 00:43:36,120
This is a very simple experiment.
This is very low tech.

625
00:43:36,120 --> 00:43:38,200
You could do this in your kitchen.

626
00:43:38,200 --> 00:43:41,600
Really? OK, so, this is a magnet.

627
00:43:41,600 --> 00:43:47,160
It's a fairly powerful magnet
and we're going to put dry ice on
here, so that will be very cold.

628
00:43:47,160 --> 00:43:50,280
A sort of cookery element
at the moment. It is yeah.

629
00:43:50,280 --> 00:43:52,040
Cooking fish in salt.

630
00:43:57,000 --> 00:44:00,560
Now the Perspex box
is going to go on top.

631
00:44:00,560 --> 00:44:03,680
And there's alcohol that
we put in the upper layer.

632
00:44:03,680 --> 00:44:07,560
In order to see the tracks,
they're actually quite faint,

633
00:44:07,560 --> 00:44:10,480
we have to illuminate it
with a very bright lamp. OK.

634
00:44:10,480 --> 00:44:13,280
And then, one of the other
ingredients that we should

635
00:44:13,280 --> 00:44:16,240
explain here is the radioactive
sources that we're going to use.

636
00:44:16,240 --> 00:44:18,200
So we have two radioactive sources.

637
00:44:18,200 --> 00:44:22,440
One emits electrons
and the other emits positrons.

638
00:44:22,440 --> 00:44:26,360
And so what we have here
is the isotope of strontium
called strontium 90.

639
00:44:26,360 --> 00:44:32,080
'Glen told me these
radioactive materials would let us
see the tracks of electrons.

640
00:44:32,080 --> 00:44:36,000
'And more importantly, the
anti-matter partner to the electron.

641
00:44:36,000 --> 00:44:41,560
'Known as the positron,
this is the particle
predicted by Dirac's Equation.'

642
00:44:41,560 --> 00:44:44,640
It emits positrons and we'll
see tracks that are very similar.

643
00:44:44,640 --> 00:44:49,680
Maybe slightly lower energy actually
and they will be bending to the left.

644
00:44:49,680 --> 00:44:55,120
So that really is the demonstration,
that we have two types of particles
that really look very similar

645
00:44:55,120 --> 00:44:56,840
in terms of the tracks
that they make,

646
00:44:56,840 --> 00:45:01,240
except that one is positively charged
and the other is negatively charged.

647
00:45:02,840 --> 00:45:04,880
Yeah, yeah, I saw one going
that way.

648
00:45:04,880 --> 00:45:08,440
Furthermore, they should be bending
to the right and they are.

649
00:45:08,440 --> 00:45:12,120
Yeah, they're thin and irregular.
It's like a string of beads almost.

650
00:45:12,120 --> 00:45:15,560
OK, so all I've really convinced
you that you can see so far are

651
00:45:15,560 --> 00:45:17,480
bog standard electrons.

652
00:45:17,480 --> 00:45:20,560
Even at the bog standard level,
it's pretty impressive.

653
00:45:20,560 --> 00:45:22,600
We're all made of plenty of those.

654
00:45:22,600 --> 00:45:26,520
And so, maybe what we can try now,
is to put in the positron source.

655
00:45:26,520 --> 00:45:30,320
What we should see, is that they will
bend in the opposite direction.

656
00:45:30,320 --> 00:45:33,640
The other one slotted in
scientifically. That's right.

657
00:45:33,640 --> 00:45:37,760
We're just going to hold it on to
the entrance way.

658
00:45:37,760 --> 00:45:40,360
Now I should expect to see
things going to the left.

659
00:45:43,560 --> 00:45:49,120
I'm seeing activity but not
necessarily lines going to the left.

660
00:45:50,720 --> 00:45:53,480
'We'd seen the electrons
bend to the right.

661
00:45:53,480 --> 00:45:58,440
'Now Glen hoped that we might spot
the rarer anti-matter tracks

662
00:45:58,440 --> 00:46:01,320
'as they curve towards
the other side.'

663
00:46:05,840 --> 00:46:08,160
One there! Very, very clear.

664
00:46:08,160 --> 00:46:10,200
There you go. Fantastic!

665
00:46:10,200 --> 00:46:13,760
So that's the first time
in this experiment that
I've seen the anti-matter.

666
00:46:13,760 --> 00:46:16,640
That was definitely
coming from the source.

667
00:46:18,240 --> 00:46:21,120
The amazing thing is
to have something from...

668
00:46:21,120 --> 00:46:26,320
a sort of comic world of
science fiction, anti-matter,

669
00:46:26,320 --> 00:46:32,960
to have it presented to us
in reality. There we go.

670
00:46:32,960 --> 00:46:35,280
Except I wasn't looking at that one.

671
00:46:35,280 --> 00:46:39,600
Every 30, 40 seconds
a little blip occurs

672
00:46:39,600 --> 00:46:44,360
within a sort of 10p size radius
of the source.

673
00:46:47,400 --> 00:46:51,560
It shoots out, curls
around, doesn't go very far.

674
00:46:51,560 --> 00:46:56,560
One there, very curly one,
shot right round! Very good.

675
00:46:56,560 --> 00:47:01,040
Yeah, yeah. So, we're really
seeing a physical thing,

676
00:47:01,040 --> 00:47:05,960
which connects to the very
complicated mind-world
of Paul Dirac.

677
00:47:05,960 --> 00:47:09,000
That's right.
Somehow the existence of anti-matter

678
00:47:09,000 --> 00:47:13,000
emerges as a necessary consequence
of the theory that he wrote down

679
00:47:13,000 --> 00:47:16,680
and that's pretty difficult to see.
To just look at his equation and say

680
00:47:16,680 --> 00:47:19,960
that should give us anti-matter, but
really if you analyse it carefully

681
00:47:19,960 --> 00:47:24,080
it's clear that that is one
of its necessary predictions
and that's what you're seeing.

682
00:47:24,080 --> 00:47:27,280
So, those curves and blips
in that sort of molten sea,

683
00:47:27,280 --> 00:47:30,920
is the Dirac Equation being
shown to us in physical form.

684
00:47:43,440 --> 00:47:47,800
'These elusive symbols
point to a beautiful idea.

685
00:47:47,800 --> 00:47:50,040
'There is something
magical about them.

686
00:47:50,040 --> 00:47:55,320
'The existence of anti-matter proved
his theory true.

687
00:47:55,320 --> 00:48:00,560
'Keats' romantic poem goes
"Beauty is truth, truth is beauty,"

688
00:48:00,560 --> 00:48:02,680
'as if one leads to the other.

689
00:48:02,680 --> 00:48:06,760
'And that's exactly what Dirac,
the scientist, believed.

690
00:48:06,760 --> 00:48:11,760
'That the search for beauty
powers the advance of science.'

691
00:48:20,160 --> 00:48:26,120
I'm reading a paper by Dirac,
which he delivered in February 1939.

692
00:48:26,120 --> 00:48:29,880
He says, "What makes the theory
of relativity so acceptable to

693
00:48:29,880 --> 00:48:34,880
"physicists in spite of its going
against the principle of simplicity,

694
00:48:34,880 --> 00:48:37,280
"is its great mathematical beauty.

695
00:48:37,280 --> 00:48:41,120
"This is a quality which cannot be
defined any more than beauty in art

696
00:48:41,120 --> 00:48:44,760
"can be defined, but which people
who study mathematics usually

697
00:48:44,760 --> 00:48:47,000
"have no difficulty in
appreciating."

698
00:48:47,000 --> 00:48:50,960
So, he's saying that beauty in
art can't be ultimately defined

699
00:48:50,960 --> 00:48:54,000
any more than beauty in
anything can be ultimately defined.

700
00:48:54,000 --> 00:48:58,920
But what he is saying is that people
in the world of very, very high

701
00:48:58,920 --> 00:49:05,360
and complex mathematics agree that
beauty is something that

702
00:49:05,360 --> 00:49:08,760
they all appreciate and follow.

703
00:49:08,760 --> 00:49:11,720
And it may be that what Dirac
is saying is that

704
00:49:11,720 --> 00:49:14,880
there's a sort of high or true
or pure beauty that

705
00:49:14,880 --> 00:49:17,200
mathematicians are interested in,

706
00:49:17,200 --> 00:49:22,720
which sounds to me a bit like
the inner, true, deep beauty of art.

707
00:49:22,720 --> 00:49:25,480
But you have to go on a bit of
a journey to find,

708
00:49:25,480 --> 00:49:28,480
you can't expect it to come
leaping out and waving at you

709
00:49:28,800 --> 00:49:33,080
straightaway when you haven't really
bothered to get involved with art

710
00:49:33,080 --> 00:49:34,880
and try and find out what it is.

711
00:49:57,560 --> 00:49:59,920
I like these buildings very much.

712
00:49:59,920 --> 00:50:03,120
But I think they have a sort of
comic element.

713
00:50:03,120 --> 00:50:09,680
They seem like a Hollywood mock up
of some kind of scientific base

714
00:50:09,680 --> 00:50:14,920
where something sinister is
being worked out behind the scenes.

715
00:50:14,920 --> 00:50:17,760
You wouldn't even really think
you were in England.

716
00:50:17,760 --> 00:50:19,560
You could be anywhere in the world.

717
00:50:22,760 --> 00:50:29,040
I'm ending my foray into science
with an equation about black holes.

718
00:50:29,040 --> 00:50:32,840
I'd always thought they were
the stuff of science fiction,

719
00:50:32,840 --> 00:50:35,720
but the inner workings of black
holes are explained

720
00:50:35,720 --> 00:50:39,160
by the fifth of my great equations.

721
00:50:40,760 --> 00:50:47,040
All the previous equations have come
from historical figures -
Newton, Einstein and Dirac.

722
00:50:47,040 --> 00:50:54,160
This will be my chance to hear
about the entropy equation direct
from its creator, Stephen Hawking.

723
00:50:54,160 --> 00:50:59,560
And find out if he agrees with
Paul Dirac about beauty
and the truth of science.

724
00:51:09,680 --> 00:51:13,200
Thanks very much for allowing me
into your department, Stephen.

725
00:51:13,200 --> 00:51:15,480
Can I ask you straight away,

726
00:51:15,480 --> 00:51:18,240
is beauty important for you
in your scientific work?

727
00:51:18,240 --> 00:51:20,440
I don't know about beauty,

728
00:51:20,440 --> 00:51:25,400
but the fundamental laws of
the universe should be elegant.

729
00:51:25,400 --> 00:51:28,480
What do you mean by elegant?

730
00:51:28,480 --> 00:51:33,880
An equation is elegant if it is
short, simple and explains

731
00:51:33,880 --> 00:51:38,920
properties of the universe that
were previously not accounted for.

732
00:51:38,920 --> 00:51:43,000
My most elegant
equation is very simple.

733
00:51:43,000 --> 00:51:47,040
It is S = a quarter A.

734
00:51:47,040 --> 00:51:51,040
Here, A is the area of the
boundary of a black hole.

735
00:51:51,040 --> 00:51:55,720
And S is its entropy, a measure
of how much heat it contains.

736
00:51:57,280 --> 00:51:58,760
What does that mean?

737
00:52:00,680 --> 00:52:06,280
This equation shows that black holes
aren't completely black.

738
00:52:06,280 --> 00:52:11,720
They glow like hot bodies
and lose energy and mass.

739
00:52:11,720 --> 00:52:17,080
Eventually they will disappear
in a tremendous explosion.

740
00:52:17,080 --> 00:52:21,160
Why is that an elegant equation?

741
00:52:22,720 --> 00:52:27,440
The equation came
from a rather messy calculation.

742
00:52:27,440 --> 00:52:32,320
It seemed a miracle that such a
concise equation should result.

743
00:52:34,480 --> 00:52:38,080
This equation unravels the physics
of black holes,

744
00:52:38,080 --> 00:52:41,120
one of the most mysterious objects
in the universe.

745
00:52:41,120 --> 00:52:44,280
As I understand it,
the equation says that as stuff

746
00:52:44,280 --> 00:52:48,240
falls into the black hole, the
surface area of the black hole

747
00:52:48,240 --> 00:52:50,720
gets bigger, and
the entropy does too.

748
00:52:52,320 --> 00:52:56,640
In 1975, when Stephen Hawking
came up with his equation,

749
00:52:56,640 --> 00:52:59,880
there was still some doubt as
to whether black holes existed.

750
00:52:59,880 --> 00:53:02,960
35 years on, all scientists
agree they do.

751
00:53:02,960 --> 00:53:06,920
Black holes have entered the realm
of science fact.

752
00:53:09,080 --> 00:53:12,320
While making this film,
I found out that Paul Dirac

753
00:53:12,320 --> 00:53:16,680
believed that it was more important
to have beauty in one's equation

754
00:53:16,680 --> 00:53:20,920
than to have the equation
backed up by actual experiment.

755
00:53:20,920 --> 00:53:25,600
Is this too extreme a view for you?

756
00:53:25,600 --> 00:53:29,960
I think what Dirac meant was that
although a beautiful equation

757
00:53:29,960 --> 00:53:33,640
might not agree with experiment at a
particular time,

758
00:53:33,640 --> 00:53:38,240
it will eventually turn out to be
true in the long run.

759
00:53:38,240 --> 00:53:44,600
I think elegance is a good guide for
equations but not an infallible one.

760
00:53:44,600 --> 00:53:45,800
In art, an artist like Picasso say,

761
00:53:45,880 --> 00:53:47,720
In art, an artist like Picasso say,

762
00:53:47,720 --> 00:53:50,160
will just be working from
hour to hour,

763
00:53:50,160 --> 00:53:54,000
from work to work, pushing
his ideas along with his work.

764
00:53:54,000 --> 00:53:57,960
He doesn't necessarily think,
"Now, I've discovered cubism."

765
00:53:57,960 --> 00:54:03,000
That accolade will be
bestowed upon his work

766
00:54:03,000 --> 00:54:04,760
a bit later by other people.

767
00:54:04,760 --> 00:54:07,880
But he probably will,
at some point, think,

768
00:54:07,880 --> 00:54:11,160
"I have made some kind of
breakthrough here."

769
00:54:11,160 --> 00:54:14,360
And I wonder if that
breakthrough feeling,

770
00:54:14,360 --> 00:54:18,400
if there's an equivalent
for you in your type of enquiry.

771
00:54:20,440 --> 00:54:24,480
There's nothing like the
Eureka moment of discovering

772
00:54:24,480 --> 00:54:27,160
something that no-one knew before.

773
00:54:27,160 --> 00:54:33,080
I won't compare it to sex,
but it lasts longer.

774
00:54:33,080 --> 00:54:35,400
Thank you very much, Stephen.

775
00:54:35,400 --> 00:54:36,880
Thank you.

776
00:54:41,440 --> 00:54:45,480
The very fact that Stephen agreed to
be interviewed by me,

777
00:54:45,480 --> 00:54:49,720
when it's not an easy task for him,

778
00:54:49,720 --> 00:54:53,960
it's not something
that he does a lot,

779
00:54:53,960 --> 00:54:58,320
proves to me that he believes
in the thesis that beauty

780
00:54:58,320 --> 00:55:02,840
is a significant element in the work
of a theoretical scientist.

781
00:55:02,840 --> 00:55:08,760
That making an equation calls
for some kind of,

782
00:55:08,760 --> 00:55:12,720
not just a sense of beauty,
but almost a pursuit of it.

783
00:55:12,720 --> 00:55:17,600
The pursuit of beauty really is
a sort of driving force

784
00:55:17,600 --> 00:55:20,200
in evolving an equation.

785
00:55:20,200 --> 00:55:25,000
I've got to
let all that sink in now.

786
00:56:02,360 --> 00:56:06,840
I've been very happy to have my head
crammed full of unfamiliar ideas,

787
00:56:06,840 --> 00:56:10,160
but now there's one more thing
I need to do.

788
00:56:10,160 --> 00:56:13,760
Hello, Cary, how nice to see you!

789
00:56:13,760 --> 00:56:19,240
I'm at the opening of
my own exhibition,
the work I do with my partner, Emma.

790
00:56:19,240 --> 00:56:23,080
I've invited the scientists and
most of them have turned up.

791
00:56:24,680 --> 00:56:28,080
Throughout this film, the word
"beauty" has often cropped up.

792
00:56:28,080 --> 00:56:30,880
But it's hard to define
and I can't help but feel that

793
00:56:30,880 --> 00:56:33,880
while there are similarities,
there are differences too

794
00:56:33,880 --> 00:56:36,680
in what artists and scientists
mean by beauty.

795
00:56:36,680 --> 00:56:40,160
Sorry, which are your paintings?
All these paintings.

796
00:56:40,160 --> 00:56:42,400
We do all these.

797
00:56:42,400 --> 00:56:46,160
I'm trying to imagine what Paul Dirac
would make of this painting.

798
00:56:46,160 --> 00:56:50,040
My guess is he would ask you what you
are representing here,

799
00:56:50,040 --> 00:56:52,400
because he had a very literal mind.

800
00:56:52,400 --> 00:56:54,200
I know what you're saying.

801
00:56:54,200 --> 00:56:56,240
Are you conscious
of representing anything?

802
00:56:56,240 --> 00:56:59,080
There's no representation
in the room at all,

803
00:56:59,080 --> 00:57:03,240
but I think there is the idea
of a model of the visual world.

804
00:57:05,240 --> 00:57:07,240
There's a lot going on.
There's a lot of them.

805
00:57:07,240 --> 00:57:12,000
You come back in a couple of minutes
from looking at something else.
You can't find that order again.

806
00:57:12,000 --> 00:57:13,600
Right.

807
00:57:13,600 --> 00:57:15,880
That's really the point of them.

808
00:57:15,880 --> 00:57:18,960
They should have a restlessly
changing sense of order.

809
00:57:18,960 --> 00:57:23,960
It's like looking at a fire where
the fire always looks the same,
but it's never exactly the same.

810
00:57:23,960 --> 00:57:27,280
Exactly. Anything in nature that is
permanent and changeable.

811
00:57:28,640 --> 00:57:31,280
Are all the panels the same,
or are they different?

812
00:57:31,280 --> 00:57:32,640
I think they're all
pretty different.

813
00:57:32,640 --> 00:57:35,840
It's interesting because you'd look
at it and think there's an algorithm

814
00:57:35,840 --> 00:57:39,720
that tells you how you would paint
that in terms of the things around.

815
00:57:39,720 --> 00:57:43,040
But he says no, there's also
a global point of view.

816
00:57:45,120 --> 00:57:48,160
A non-repeating pattern of some sort.
Exactly.

817
00:57:48,160 --> 00:57:50,760
Ultimately,
it is highly mathematical,

818
00:57:50,760 --> 00:57:54,800
but actually there is no...
We didn't sit down and work it out.

819
00:57:54,800 --> 00:57:57,440
Well, randomness
is also mathematical.

820
00:57:59,400 --> 00:58:04,960
It's interesting to
see mathematical symmetries come
out of aesthetic pursuits.

821
00:58:04,960 --> 00:58:06,640
Well, that's arrived at...

822
00:58:06,640 --> 00:58:10,320
'All my life, science has been
totally out of my orbit.

823
00:58:10,320 --> 00:58:13,560
'What was so illuminating
for me in this programme was to

824
00:58:13,560 --> 00:58:18,120
'find out that equations are the
most important tool in science,

825
00:58:18,120 --> 00:58:21,360
'forever pushing the boundaries
of knowledge.

826
00:58:21,360 --> 00:58:24,720
'And that the greatest and most
beautiful equations

827
00:58:24,720 --> 00:58:26,760
'have a life of their own.

828
00:58:26,760 --> 00:58:31,840
'They've given us ideas
beyond the human imagination.'

829
00:58:48,520 --> 00:58:50,600
Subtitles by Red Bee Media Ltd

830
00:58:50,600 --> 00:58:52,720
E-mail subtitling@bbc.co.uk