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Subtitles downloaded from www.OpenSubtitles.org

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BOY: 'One for sorrow

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'Two for mirth

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GIRL: 'Three for a wedding

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'And four for death

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BOY: 'Nine for hell.'

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GIRL: '666.'

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Hidden within this cathedral
are clues to a mystery,

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something that could help answer

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one of humanity's most
enduring questions...

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..why is the world the way it is?

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The 13th-century masons
who constructed this place

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had glimpsed a deep truth

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and they built a message
into its very walls

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in the precise proportions
of this magnificent cathedral.

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To the medieval clergy,

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these divine numbers
were created by God.

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But to me, they're evidence
of something else,

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a hidden code that underpins
the world around us,

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a code that has the power to unlock
the laws that govern the universe.

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As a mathematician,
I'm fascinated by the numbers

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and patterns we see all around us...

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..numbers and patterns
that connect everything

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from fish to circles

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and from our ancient past

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to the far future.

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INDISTINCT COMMENT

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Together they make up the Code...

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..an abstract world of numbers...

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..that has given us
the most detailed description
of our world we've ever had.

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For centuries, people have seen
significant numbers everywhere...

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..an obsession that's left
its mark in the stones
of this medieval cathedral.

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In the 12th century,
religious scholars here in Chartres

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became convinced these numbers
were intrinsically linked
to the divine...

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..an idea that dates back
to the dawn of Christianity.

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The fourth-century Algerian cleric
St Augustine believed

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that seven was so special that it
represented the entire universe.

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He described how seven
embraced all created things

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and ten was beyond even the universe

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because it was seven plus the three
aspects of the Holy Trinity -

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Father, Son and Holy Ghost.

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12 was also hugely important, not
simply because there are 12 tribes
of Israel or 12 disciples of Jesus,

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but because 12 is divisible by one,
two, three, four, six and 12 itself,

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more than any other number
around it.

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For St Augustine,
numbers had to come from God

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because they obey laws
that no man can change.

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Around 800 years after St Augustine,

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the 12th-century Chartres School
also recognised their significance.

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It's thought that, under
their influence, sacred numbers

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were built into the structure
of this majestic building.

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Numbers, they believed, held
the key to the mystery of creation.

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I've spent my entire working life
studying numbers,

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and for me they're more
than just abstract entities.

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They describe the world around us.

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Although I don't share their
religious beliefs, I can't help

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feeling something in common with
the people who built this place.

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I share their awe and wonder
at the beauty of numbers.

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For them, those numbers brought them
closer to God, but I think they're
important for another reason,

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because I believe they're the key
to making sense of our world.

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Numbers have given us
an unparalleled ability
to understand our universe.

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And in places, this code
literally emerges from the ground.

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Rural Alabama,

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spring 2011.

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Warm, lush and peaceful.

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But this year,
there's a plague coming.

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While some locals are moving out,

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Dr John Cooley has driven
thousands of miles to be here.

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He's on the trail of one
of the area's strangest residents.

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We have been driving around
looking for the emergences for
about three and a half weeks.

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I've driven 7,200 miles
since Good Friday trying to figure
out where these things are.

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What makes these insects
so remarkable is their
bizarre lifecycle.

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For 12 whole years, they live hidden
underground, in vast numbers.

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Then, in their 13th year...

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at precisely the same time...

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..they all burrow out
from the earth to breed.

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At the full part of the emergence,
there will be millions of insects
out per acre. They'll be everywhere.

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It really is insect mayhem.

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This is the periodical cicada.

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This one is a male...

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..and you know that
because on the abdomen,

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there's a pair
of organs called timbles,

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and they're sound-producing organs.

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It's a little membrane that's
vibrated, it makes a sound.

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Oh, yeah. I don't have to be
frightened of these, do I?

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No, no, they're absolutely harmless.
They make wonderful pets. Really?

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Mm-hm. They're quite ticklish.
It's a harmless insect.

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It doesn't bite, it doesn't sting,
nothing of that sort.

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Its only defence
is safety in numbers.

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By emerging in such vast numbers,
each individual cicada

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minimises its risk of being eaten.

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Because there are so many of them,

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their predators simply
can't eat them fast enough.

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Well, you can certainly hear
the cicadas.

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Yes, you can. There are probably
millions of them up there.

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Millions? Yeah, millions. What
you probably don't realise is you're
only hearing half the population.

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Only the males make
these loud sounds.

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There are just as many females
up there as well.

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And it's extraordinary to think
that if we came here next year,

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we wouldn't hear this sound at all?
You'll have to come back
in 13 years.

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So 2024 is when you'll hear the
forest singing like this again?

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That's right. That's amazing.

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Why have the cicadas evolved
with this 13-year lifecycle
as opposed to any other number?

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Well, you have to remember
that these cicadas require
large numbers to survive predators,

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and so we think that these
long lifecycles in some way help
them maintain large populations.

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John believes that,
by appearing every 13 years,

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the cicadas minimise their chances
of emerging at the same time

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as other cicadas
with different lifecycles...

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..because if they were
to interbreed, it could have
disastrous consequences.

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The offspring would have
unusual lifecycles.

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They're going to emerge a little
bit here, a little bit there, some
this year and some that year in small

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numbers, and that's key because
if they emerge in small numbers,
the predators eat them.

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The cicadas' survival
depends on avoiding other broods.

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Imagine you've got
a brood of cicadas
that appears every six years.

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Now, let's suppose
there's another brood

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which wants to try and avoid
the red cicadas.

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One way to do that would be
to appear less often in the
forest, and that actually works.

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So let's suppose
this brood appears every nine years.

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So if the green cicada appears
every nine years,

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then it only coincides
with the red cicada every 18 years.

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But, rather surprisingly, a smaller
number, seven, works even better.

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Coming out every seven years
instead of every nine

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means the cicadas appear together
much less often.

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Now they only
coincide every 42 years.

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That's just twice every century.

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And for the real cicadas,

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a 13-year lifecycle has exactly
the same effect as seven does here

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because they both belong
to a special series of numbers.

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Like 13, seven is a prime number.

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Unlike other numbers,
primes can only be divided
by themselves and one,

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and it's this property
that means that numbers
that are separated by primes

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are far less likely to coincide
with multiples of other numbers.

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Because 13 is a prime number,
a 13-year lifecycle

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makes the cicadas much less likely
to coincide with other groups.

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Up in Georgia, there is another
brood of periodical cicada

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and they, too,
have a prime number lifecycle.

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They come out every 17 years.

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Because 13 and 17
are both prime numbers,

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the two broods only emerge together
once every 221 years.

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Prime numbers are intimately
linked to the cicadas' survival

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and, intriguingly,

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they're one of the most
important elements of the Code,

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because the Code
is a mathematical world,

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built from numbers.

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Just as atoms
are the indivisible units
that make up every physical object,

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so prime numbers are the indivisible
building blocks of the Code.

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Prime numbers are indivisible,
which means they can't be made

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by multiplying
any other numbers together.

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But every non-prime number
can be created by multiplying
primes together.

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It's impossible to make
any numbers without them.

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And if any primes are missing,

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there will always be
some numbers you can't create.

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For me, the fact that the most
fundamental units of mathematics

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can be found woven
into the natural world

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is not only compelling evidence
that the Code exists,

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but also that numbers
underpin everything...

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..including our own biology.

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This is an innately human
characteristic.

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Music is one of the things which
defines who we are, and each culture
has its own particular style.

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These guys make it seem
so effortless, as if the notes

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are just thrown together,
but that's simply an illusion.

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MUSIC ENDS, APPLAUSE

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Because, just as numbers
govern the cicadas' lives,

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so they determine how WE hear sound.

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That's a C.

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And using this oscilloscope,
I can get a picture of that note.

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So I can actually
SEE the sound wave.

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Now, the height of the wave
corresponds to how loudly
I'm playing the note,

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so if I play the note
very quietly...

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play it very loudly...I suddenly
get a huge wave on the screen.

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The more important thing
is the distance between
the peaks of the wave,

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because that's determined by
the pitch or frequency of the note.

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'The higher the note...

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'the shorter the distance
between the peaks.'

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Now, look what happens
when I play a C...

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..and compare that with the same
note, a C, but an octave higher.

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Something rather surprising emerges,

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because now you can see
that the higher note has twice

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as many peaks as the lower note,

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which means the frequency of the
high C is twice that of the low C.

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And this happens whatever
two notes you choose.

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Provided they're an octave apart,
then their frequencies are going
to be in this one-to-two ratio.

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Two notes which are an octave
apart just sound nice together,
and they're actually the most

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harmonious combination of notes
that you can have.

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And that's because one to two
is the simplest possible frequency
relationship, and that's what

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music is all about, because it's
these simple whole-number ratios
that sound so good to the ear.

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A perfect fifth...

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is a frequency ratio
of three to two.

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A perfect fourth...

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is four to three.

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And a slightly more complex sound,
a minor sixth...

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..that's a frequency ratio
of five to eight.

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Every combination of notes used in
music is defined by simple ratios.

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Although we might not be aware of
it, these numerical rules underpin

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everything from the simplest song
to the most elaborate symphony.

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They're so deeply ingrained
that when they're broken,

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we intuitively know
something is wrong.

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Professor Judy Edworthy
understands this more than most.

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She spends her time subjecting
people to some of most unpleasant
noises imaginable.

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Hi, Judy.

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Ah, hello. Marcus.

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'Her research investigates
the psychological effects of sound.

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'And by using complex ratios
instead of simple ones, the noises
she creates are nothing like music.'

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You can see just by looking at it
it's not going to sound nice.

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The wave looks a mess.

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The wave is a mess.
It's very difficult to see a pattern.

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CONSTANT DRONE

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OK. It sounds really quite odd now.

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It doesn't have any pitch. It sounds
harsh and I could make it louder
and that would make it harsher.

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When the various frequencies aren't
simple multiples of one another,

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there's no common pattern
for the ear to respond to,

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and the more complex you make
the ratios, the more dissonant
and harsh the sound will get.

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By monitoring her victims' reactions
to these appalling noises,

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Professor Edworthy has found
they have a very different effect

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on our minds than music.

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ALARM BEEPS

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HONKING

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WHIRRING

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They're so unpleasant...
HAMMERING

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..they shock our brains into action.

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For example, a siren.

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HIGH-PITCHED SIREN BLARES

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That's quite a harsh sound,
but it's designed for a purpose -
to get you out of the way.

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Sometimes you find these sounds
in the animal world as well.

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So this, for example, this is
a chimpanzee and an orang-utan.

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INTERMITTENT SCREECHING

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OK, these animals are obviously
quite bothered by something.

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You don't need to know
what that sound means to know
that that animal's not happy

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and also that the other animals in
that environment and us, for example,
should just get out of the way.

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SHORT SCREECH

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So it's interesting
that we really hear pattern,

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and when it isn't there,
it creates an effect in all of us.

232
00:21:27,560 --> 00:21:30,480
LOW-PITCHED SCREECH

233
00:21:37,200 --> 00:21:41,280
Remarkably,
it's numerical patterns in the Code

234
00:21:41,280 --> 00:21:45,080
that dictate the combinations
of sounds we hear as music...

235
00:21:45,080 --> 00:21:47,360
RUSTLING

236
00:21:47,360 --> 00:21:51,000
..and those we hear simply as noise.
CHIRPING, SIREN

237
00:21:51,000 --> 00:21:54,120
BELL TOLLS

238
00:21:54,120 --> 00:21:58,840
And perhaps stranger still,
it's these same numbers

239
00:21:58,840 --> 00:22:02,160
that are built into the walls
of this medieval cathedral.

240
00:22:08,440 --> 00:22:12,600
Two notes
which are an octave apart are
going be in this one-to-two ratio.

241
00:22:20,240 --> 00:22:23,960
The width of the nave here is twice
the distance between

242
00:22:23,960 --> 00:22:30,360
each of the columns that run up
its length - a ratio of two to one.

243
00:22:30,360 --> 00:22:34,680
The most harmonious
combination of notes from a pair.

244
00:22:34,680 --> 00:22:38,520
The altar divides the nave
into a ratio of eight to five.

245
00:22:40,280 --> 00:22:42,560
A minor sixth...

246
00:22:42,560 --> 00:22:44,000
eight to five.

247
00:22:47,960 --> 00:22:49,680
A perfect fifth...

248
00:22:49,680 --> 00:22:51,920
three to two.

249
00:22:51,920 --> 00:22:55,440
A perfect fourth is four to three.

250
00:22:55,440 --> 00:22:57,600
Major third, five to four.

251
00:23:00,720 --> 00:23:04,360
And that's what music is all about.

252
00:23:04,360 --> 00:23:09,000
St Augustine believed
these ratios were used by God
to construct the universe

253
00:23:09,000 --> 00:23:13,040
and that that was why
they produced harmony in music.

254
00:23:18,480 --> 00:23:22,240
By constructing their cathedral
using the same ratios,

255
00:23:22,240 --> 00:23:26,280
the clergy at Chartres
hoped to echo God's creation.

256
00:23:26,280 --> 00:23:29,800
This entire place
is a symphony set in stone.

257
00:23:33,440 --> 00:23:38,440
Using the Code's numbers has created
a building of awe-inspiring beauty.

258
00:23:52,760 --> 00:23:54,480
The only truth there is...

259
00:23:54,480 --> 00:23:56,960
Seemingly significant numbers...

260
00:24:03,240 --> 00:24:06,680
By searching
for divine meaning in numbers,

261
00:24:06,680 --> 00:24:11,560
12th-century scholars had stumbled
across elements of the Code.

262
00:24:11,560 --> 00:24:14,280
It's very difficult to see a pattern.

263
00:24:16,960 --> 00:24:21,920
Mysterious numbers and patterns that
seem to be written into our biology.

264
00:24:22,960 --> 00:24:25,560
Its only defence
is safety in numbers.

265
00:24:27,880 --> 00:24:34,200
And as we've looked closer, we
haven't simply found more numbers -

266
00:24:34,200 --> 00:24:41,600
we've begun to uncover their
strangest properties and started to
see deep connections between them.

267
00:24:45,720 --> 00:24:49,760
Back in the distant past,
in Neolithic times,

268
00:24:49,760 --> 00:24:55,160
around 4,000 years ago, an ancient
people brought these stones here

269
00:24:55,160 --> 00:24:57,680
and arranged them like this.

270
00:24:57,680 --> 00:25:02,480
This is Sunkenkirk stone circle in
Cumbria and it's one of around 1,000

271
00:25:02,480 --> 00:25:07,360
such structures that our ancient
ancestors built across the UK.

272
00:25:13,840 --> 00:25:17,400
Stretching back
into the mists of time,

273
00:25:17,400 --> 00:25:21,000
the circle has been
steeped in mysticism.

274
00:25:24,720 --> 00:25:27,760
But whether the people who built
this structure knew it or not,

275
00:25:27,760 --> 00:25:31,800
there is deep significance
hidden inside this circle.

276
00:25:31,800 --> 00:25:36,080
OK, so I need to start
by measuring the diameter

277
00:25:36,080 --> 00:25:41,360
of my circle, so that's the
distance from one edge to the other.

278
00:25:43,600 --> 00:25:46,200
I need to go roughly
through the centre.

279
00:25:48,640 --> 00:25:51,480
So that's 27 and 90.

280
00:25:55,480 --> 00:25:58,680
Right, so now I'm going
to measure the circumference

281
00:25:58,680 --> 00:26:01,120
of the circle. So off we go.

282
00:26:01,120 --> 00:26:03,480
So around the outside.

283
00:26:05,520 --> 00:26:08,320
Oh, I've never got so much exercise
doing maths before!

284
00:26:10,680 --> 00:26:13,440
And that's the circumference.

285
00:26:13,440 --> 00:26:17,880
So I've got 91 metres

286
00:26:17,880 --> 00:26:20,760
and 70 centimetres.

287
00:26:23,000 --> 00:26:28,160
I'm going to do
a little calculation. I'm going
to divide the circumference

288
00:26:28,160 --> 00:26:32,120
of the circle by the diameter.

289
00:26:32,120 --> 00:26:36,160
So 917 divided by 279.

290
00:26:36,160 --> 00:26:38,440
So that's roughly three...

291
00:26:38,440 --> 00:26:42,320
Bit of, er, mental arithmetic, not
a mathematician's strongest point.

292
00:26:42,320 --> 00:26:45,040
OK, two lots of 279,

293
00:26:45,040 --> 00:26:46,600
so...

294
00:26:46,600 --> 00:26:49,400
not far out
from what I was hoping for.

295
00:26:49,400 --> 00:26:54,840
So when I do that,
I get roughly 3.2 as the answer.

296
00:27:00,000 --> 00:27:03,280
My measurements
weren't very precise...

297
00:27:04,920 --> 00:27:10,320
..but my answer is close
to a mysterious number
hidden within every circle.

298
00:27:15,000 --> 00:27:19,840
So, for example,
let's take this circular plate here.

299
00:27:19,840 --> 00:27:21,880
I'm going to measure its diameter.

300
00:27:21,880 --> 00:27:25,120
26.4 centimetres.
Now its circumference.

301
00:27:27,160 --> 00:27:29,080
That's a bit trickier.

302
00:27:29,080 --> 00:27:31,640
82.9 centimetres.

303
00:27:31,640 --> 00:27:35,640
Divide the circumference
by the diameter, I get 3.14.

304
00:27:35,640 --> 00:27:38,560
Now let's take another circle.
Measure its diameter.

305
00:27:38,560 --> 00:27:40,880
12.8 centimetres.

306
00:27:42,360 --> 00:27:47,200
So the circumference
is 40.2 centimetres.

307
00:27:47,200 --> 00:27:52,160
Divide the circumference
by the diameter and I get 3.14.

308
00:27:52,160 --> 00:27:56,240
In fact, whatever circle I take,
divide the circumference

309
00:27:56,240 --> 00:28:01,080
by the diameter and you're going
to get a number which starts 3.14.

310
00:28:01,080 --> 00:28:04,320
This is a number we call pi.

311
00:28:09,440 --> 00:28:13,920
No matter where the circles are,
no matter how big or small...

312
00:28:15,480 --> 00:28:17,920
..they will always contain pi.

313
00:28:20,200 --> 00:28:26,680
It's this universality of the
number pi which tells you you've
identified a piece of true Code.

314
00:28:26,680 --> 00:28:28,720
In fact, if you get another number,

315
00:28:28,720 --> 00:28:30,840
it means
that you haven't got a circle.

316
00:28:30,840 --> 00:28:34,000
In some sense,
pi is the essence of circleness,

317
00:28:34,000 --> 00:28:36,840
distilled into the language
of the Code.

318
00:28:37,880 --> 00:28:43,440
And because circles and curves
crop up again and again in nature,

319
00:28:43,440 --> 00:28:47,560
pi can be found all around us.

320
00:28:51,280 --> 00:28:54,480
It's in the gentle curve
of a river...

321
00:28:55,720 --> 00:28:58,360
..the sweep of a coast line...

322
00:29:00,440 --> 00:29:04,240
..and the shifting patterns
of the desert sands.

323
00:29:07,120 --> 00:29:12,960
Pi seems written into the structures
and processes of our planet.

324
00:29:18,800 --> 00:29:22,160
But, strangely,
pi also appears in places

325
00:29:22,160 --> 00:29:25,640
that seem to have nothing
to do with circles.

326
00:29:31,400 --> 00:29:35,560
I started fishing Brighton in 1972.

327
00:29:35,560 --> 00:29:39,200
I've been a fisherman 40 years,
catching Dover sole.

328
00:29:41,400 --> 00:29:45,480
That's the main target species
for the English Channel.

329
00:29:46,520 --> 00:29:48,520
How many fish
do you think you get a day?

330
00:29:48,520 --> 00:29:51,000
300 some days, 150 other days,

331
00:29:51,000 --> 00:29:53,040
so I'd say 200 would be average.

332
00:29:53,040 --> 00:29:58,080
And you've got me some
Dover sole today so I can have a
weigh of what you've caught today.

333
00:29:58,080 --> 00:29:59,920
Yeah, you can play with them! OK!

334
00:30:02,360 --> 00:30:06,600
What's remarkable is that, with just
a small amount of information...

335
00:30:06,600 --> 00:30:08,840
It's 180 grams.

336
00:30:09,840 --> 00:30:11,880
..and by weighing a few fish...

337
00:30:11,880 --> 00:30:13,120
That's a whopper.

338
00:30:13,120 --> 00:30:14,520
..I can use the Code

339
00:30:14,520 --> 00:30:17,360
to tell me things
about not just today's catch...

340
00:30:17,360 --> 00:30:21,320
360 grams. 50 grams. 110 grams.

341
00:30:22,000 --> 00:30:25,280
..but about all the Dover sole
Sam's ever fished...

342
00:30:25,280 --> 00:30:28,040
Whoa, jeez, come back!

343
00:30:28,040 --> 00:30:30,640
..I can even get an estimate
for the largest sole

344
00:30:30,640 --> 00:30:33,440
that Sam is likely
to have caught during his career.

345
00:30:33,440 --> 00:30:34,800
Right...

346
00:30:34,800 --> 00:30:41,320
First , I need to work out what
the average weight of a fish is,

347
00:30:41,320 --> 00:30:45,560
so 140 plus 190

348
00:30:45,560 --> 00:30:48,080
plus 150...

349
00:30:48,080 --> 00:30:53,040
So now I need to work out
the standard deviation,
so that's 140 minus square that...

350
00:30:53,040 --> 00:30:55,560
Bear with me, all right?
Almost there.

351
00:30:55,560 --> 00:31:00,800
So he said he fished for 40 years,

352
00:31:00,800 --> 00:31:06,000
and eight weeks during the year,
six days out of the week

353
00:31:06,000 --> 00:31:10,280
and 200 sole each day,

354
00:31:10,280 --> 00:31:14,160
so that gives you
a total of 384,000 fish.

355
00:31:15,880 --> 00:31:19,600
Using these numbers,
I can calculate that the largest one

356
00:31:19,600 --> 00:31:22,800
out of those 384,000 fish

357
00:31:22,800 --> 00:31:27,880
should be about 1.3 kilograms,
which is roughly three pounds.

358
00:31:30,000 --> 00:31:34,400
So what's the largest Dover sole
that you've caught in your career?

359
00:31:34,400 --> 00:31:37,160
We call them door mats,
the large ones,

360
00:31:37,160 --> 00:31:40,480
and you maybe get
four or five a season.

361
00:31:40,480 --> 00:31:45,240
The largest, I'd say, was three
to three and a half pounds.

362
00:31:45,240 --> 00:31:49,800
An average Dover Sole
is that sort of size

363
00:31:49,800 --> 00:31:51,240
and these...

364
00:31:51,240 --> 00:31:54,520
Wow, that's huge! Yeah!

365
00:31:54,520 --> 00:31:58,400
It's a whopper. It's always nice
to catch big stuff, you know.

366
00:31:58,400 --> 00:32:00,960
Well, I think it is anyway.
HE CHUCKLES

367
00:32:05,360 --> 00:32:08,520
Using the Code,
it's possible to estimate the size

368
00:32:08,520 --> 00:32:11,560
of the biggest fish
Sam's ever caught,

369
00:32:11,560 --> 00:32:16,280
despite not weighing a single fish
anywhere near that size.

370
00:32:21,120 --> 00:32:27,520
Now, the reason this calculation is
possible is because the distribution
of the weights of fish,

371
00:32:27,520 --> 00:32:32,840
in fact the distribution
of lots of things like the height
of people in the UK or IQ,

372
00:32:32,840 --> 00:32:35,720
is given by this formula.

373
00:32:35,720 --> 00:32:38,760
'This is the normal
distribution equation,

374
00:32:38,760 --> 00:32:42,160
'one of the most important bits
of mathematics

375
00:32:42,160 --> 00:32:46,480
'for understanding variation
in the natural world.'

376
00:32:46,480 --> 00:32:51,360
The most remarkable thing about this
formula isn't so much what it does

377
00:32:51,360 --> 00:32:53,680
as this term here, pi.

378
00:32:53,680 --> 00:32:55,840
It seems totally bizarre

379
00:32:55,840 --> 00:32:59,640
that a bit of the Code
that has something to do
with the geometry of a circle

380
00:32:59,640 --> 00:33:02,120
can help you to calculate
the weight of fish.

381
00:33:02,120 --> 00:33:07,080
Pi shouldn't have anything
to do with fish, yet there it is.

382
00:33:15,320 --> 00:33:19,800
Just as the circle
appears everywhere in nature,

383
00:33:19,800 --> 00:33:24,200
so pi crops up again and again
in the mathematical world.

384
00:33:25,840 --> 00:33:31,600
It's an astonishing example of
the interconnectedness of the Code.

385
00:33:31,600 --> 00:33:36,880
A glimpse into a world where numbers
don't just have strange connections,

386
00:33:36,880 --> 00:33:40,520
they have deeply puzzling
properties of their own.

387
00:33:43,960 --> 00:33:46,840
Pi is what's known
as an irrational number.

388
00:33:49,040 --> 00:33:53,120
Written as a decimal,
it has an infinite number of digits

389
00:33:53,120 --> 00:33:56,520
arranged in a sequence
that never repeats.

390
00:33:58,200 --> 00:34:02,720
And it's thought that any number
you can possibly imagine

391
00:34:02,720 --> 00:34:07,360
will appear in pi somewhere,
from my birthday

392
00:34:07,360 --> 00:34:11,080
to the answer to life,
the universe and everything.

393
00:34:14,120 --> 00:34:17,240
Because they go on for ever,
we can never know all the digits

394
00:34:17,240 --> 00:34:18,880
that make up pi.

395
00:34:18,880 --> 00:34:22,600
But, luckily,
we only need the first 39

396
00:34:22,600 --> 00:34:28,040
to calculate the circumference
of a circle the size
of the entire observable universe,

397
00:34:28,040 --> 00:34:31,480
accurate to the radius
of a single hydrogen atom.

398
00:34:38,440 --> 00:34:43,440
But as strange as Pi is, it does
at least describe a physical object.

399
00:34:44,680 --> 00:34:48,200
Some numbers don't make
any sense in real world,

400
00:34:48,200 --> 00:34:51,400
despite the fact we use them
all the time.

401
00:34:51,400 --> 00:34:54,240
Numbers, like negative numbers.

402
00:34:56,920 --> 00:35:01,320
It's impossible to trade anything,
stocks, shares, currency,

403
00:35:01,320 --> 00:35:04,200
even fish, without negative numbers.

404
00:35:04,200 --> 00:35:06,240
Most of us are comfortable them.

405
00:35:06,240 --> 00:35:09,240
Even though we may not like it,
we understand what it means

406
00:35:09,240 --> 00:35:11,520
to have a negative bank balance.

407
00:35:11,520 --> 00:35:13,760
But when you start
to think about it,

408
00:35:13,760 --> 00:35:17,400
there's something deeply strange
about negative numbers,

409
00:35:17,400 --> 00:35:21,240
cos they don't seem to correspond
to anything real at all.

410
00:35:23,760 --> 00:35:28,920
The deeper we look into the Code,
the more bizarre it becomes.

411
00:35:33,640 --> 00:35:40,160
It's easy to imagine one fish
or two fish, or no fish at all.

412
00:35:40,160 --> 00:35:44,520
It's much harder to imagine
what minus-one fish looks like.

413
00:35:44,520 --> 00:35:49,440
Negative numbers are so odd
that if I have minus-one fish
and you give me a fish,

414
00:35:49,440 --> 00:35:53,320
then all you can be certain of
is that I've got no fish at all.

415
00:36:00,880 --> 00:36:06,680
Numbers, can exist regardless
of whether they make any sense
in the physical world.

416
00:36:11,040 --> 00:36:15,680
And if you think that's odd,
some numbers are so strange

417
00:36:15,680 --> 00:36:18,720
they don't even seem
to make sense as numbers.

418
00:36:19,960 --> 00:36:24,080
Now, this is one of the most
basic facts of mathematics.

419
00:36:24,080 --> 00:36:28,520
A positive number multiplied
by another positive number
is a positive number.

420
00:36:28,520 --> 00:36:34,800
So for example,
one times one is one.

421
00:36:34,800 --> 00:36:38,200
A negative number multiplied
by another negative number

422
00:36:38,200 --> 00:36:41,200
also gives a positive number.

423
00:36:41,200 --> 00:36:47,400
So for example, minus-one
times minus-one is plus-one.

424
00:36:47,400 --> 00:36:53,080
'It's not only a rule, it's a proven
truth of multiplication.

425
00:36:53,080 --> 00:36:57,120
'Whenever the signs are the same,
the product is always positive.'

426
00:36:57,120 --> 00:36:59,160
From this, it's obvious

427
00:36:59,160 --> 00:37:01,840
if I take any number
and multiply it by itself,

428
00:37:01,840 --> 00:37:04,360
then the answer
is going to be positive.

429
00:37:04,360 --> 00:37:06,680
However, in the Code,

430
00:37:06,680 --> 00:37:09,480
there's a special number
which breaks this rule.

431
00:37:09,480 --> 00:37:13,400
When I multiply it by itself,
it gives the answer minus-one.

432
00:37:13,400 --> 00:37:17,160
It's impossible to imagine what
this number could be,

433
00:37:17,160 --> 00:37:21,120
because there simply is no number

434
00:37:21,120 --> 00:37:24,960
that when multiplied by itself,
gives minus-one.

435
00:37:24,960 --> 00:37:29,240
This isn't a number I can calculate.
I can't show you this number.

436
00:37:29,240 --> 00:37:31,720
Nevertheless, we've given
this number a name.

437
00:37:31,720 --> 00:37:35,040
It's called "i", and it's part
of a whole class of new numbers

438
00:37:35,040 --> 00:37:36,520
called imaginary numbers.

439
00:37:38,240 --> 00:37:42,800
Calculating with imaginary numbers
is the mathematical equivalent

440
00:37:42,800 --> 00:37:44,880
of believing in fairies.

441
00:37:46,080 --> 00:37:50,560
But even these strangest elements
of the Code turn out to have

442
00:37:50,560 --> 00:37:53,440
some very practical applications.

443
00:37:58,040 --> 00:38:01,720
The ground's close, will you call
me, please, 1-1-9 next...

444
00:38:04,360 --> 00:38:09,440
Runway 25, clear to land. Surface
is 1-3-0, less than five minutes.

445
00:38:09,440 --> 00:38:12,080
'Especially on a day like this.'

446
00:38:15,560 --> 00:38:21,040
8-5 Foxtrot, thank you, vacate next
right and park yourself 1-3 short.

447
00:38:21,040 --> 00:38:25,040
'8-5 Foxtrot, 8-2-0, both making
approach down direct and right, 2-5.'

448
00:38:25,040 --> 00:38:27,520
So where's this one coming from?

449
00:38:27,520 --> 00:38:31,680
That is from Barcelona.
It's an Easyjet flight, EZZ6402.

450
00:38:31,680 --> 00:38:35,440
Don't know how many people are
on board, but it seats about 190.

451
00:38:35,440 --> 00:38:37,880
And here he is.
He's getting pretty close now.

452
00:38:37,880 --> 00:38:40,120
Just less than two miles
till he lands.

453
00:38:40,120 --> 00:38:43,760
What information is the radar
giving you about the aeroplanes?

454
00:38:43,760 --> 00:38:47,240
The first and most important thing
is the position of the aircraft.

455
00:38:47,240 --> 00:38:50,520
The yellow slash there
is where the aircraft is.

456
00:38:50,520 --> 00:38:54,600
You've got the blue trail,
the history of where
the aircraft's been.

457
00:38:54,600 --> 00:38:59,240
From that you get two things -
you get its rough heading,
where he's going, and its speed.

458
00:38:59,240 --> 00:39:02,040
The longer the trail,
the faster the aircraft's going.

459
00:39:07,840 --> 00:39:11,040
Radar works by sending out
a pulse of radio waves

460
00:39:11,040 --> 00:39:14,840
and analysing the small fraction
of the signal that's reflected back.

461
00:39:19,040 --> 00:39:23,000
Complex computation is then needed
to distinguish moving objects,

462
00:39:23,000 --> 00:39:26,800
like planes,
from the stationary background.

463
00:39:26,800 --> 00:39:29,880
RADIO COMMUNICATION

464
00:39:29,880 --> 00:39:36,160
At the heart of that analysis lies
"i", the number that cannot exist.

465
00:39:37,800 --> 00:39:42,560
Imaginary numbers are useful
for working out the complex way

466
00:39:42,560 --> 00:39:44,920
radio waves interact
with each other.

467
00:39:44,920 --> 00:39:48,600
It seems to be the right language
to describe their behaviour.

468
00:39:48,600 --> 00:39:51,800
Now, you could do these calculations
with ordinary numbers.

469
00:39:51,800 --> 00:39:53,600
But they're so cumbersome,

470
00:39:53,600 --> 00:39:57,480
by the time you've done
the calculation the plane's
moved to somewhere else.

471
00:39:57,480 --> 00:40:02,000
Attitude 6,000
on a squawk of 7-7-1-5.

472
00:40:02,000 --> 00:40:05,040
Using imaginary numbers
makes the calculation simpler

473
00:40:05,040 --> 00:40:07,680
that you can track the planes
in real time.

474
00:40:07,680 --> 00:40:12,880
In fact without them,
radar would be next to useless
for Air Traffic Control.

475
00:40:16,640 --> 00:40:20,680
It's kind of amazing that this
abstract idea lands planes.

476
00:40:20,680 --> 00:40:23,520
It's a bit surprising, you're talking
about imaginary numbers

477
00:40:23,520 --> 00:40:26,120
and this isn't imaginary,
this is real. This is very real.

478
00:40:26,120 --> 00:40:30,000
I'm surprised at the fact
that something so abstract

479
00:40:30,000 --> 00:40:32,040
is being used
in such a concrete way.

480
00:40:46,560 --> 00:40:49,720
As strange as it may seem,
the code provides us

481
00:40:49,720 --> 00:40:53,760
with an astonishingly successful
description of our world.

482
00:40:59,680 --> 00:41:04,360
Its most ethereal numbers
have starkly real applications.

483
00:41:04,360 --> 00:41:10,400
Its patterns
can explain one of the most
profound processes in nature -

484
00:41:10,400 --> 00:41:13,880
how living things grow.

485
00:41:16,720 --> 00:41:19,840
This is a picture of something
I've been fascinated by

486
00:41:19,840 --> 00:41:22,000
ever since I became a mathematician.

487
00:41:22,000 --> 00:41:26,480
It's an X-ray of a marine animal
called a nautilus.

488
00:41:26,480 --> 00:41:31,160
And this spiral here is one
of the iconic images of mathematics.

489
00:41:31,160 --> 00:41:34,400
Now, while I've seen pictures
like this hundreds of times,

490
00:41:34,400 --> 00:41:37,080
I've never actually seen
the animal for real.

491
00:41:40,520 --> 00:41:45,240
'At Brooklyn College,
biologist Jennifer Basil keeps
five of these aquatic denizens,

492
00:41:45,240 --> 00:41:49,080
'for her research
into the evolution of intelligence.'

493
00:41:51,280 --> 00:41:56,120
We keep the animals
in these tall tanks because
they're naturally active at night

494
00:41:56,120 --> 00:41:59,360
and they like darkness,
they live in deep water.

495
00:41:59,360 --> 00:42:01,680
They also like to go up
and down in the water column,

496
00:42:01,680 --> 00:42:03,840
that kind of makes them happy. OK!

497
00:42:03,840 --> 00:42:06,720
We give them the five-star
treatment here. Right...

498
00:42:08,440 --> 00:42:11,400
This is Number Five. Ah, wow. Yeah.

499
00:42:11,400 --> 00:42:12,760
Gosh, big eyes.

500
00:42:12,760 --> 00:42:16,560
They have huge eyes, great for seeing
in low light conditions. Right.

501
00:42:17,680 --> 00:42:20,000
So, here's that beautiful shell.
Yeah.

502
00:42:20,000 --> 00:42:23,360
And the striping pattern helps them
hide where they live.

503
00:42:40,000 --> 00:42:44,680
I've never seen the animal before
inside the shell, what is it?

504
00:42:44,680 --> 00:42:47,520
They're related to octopuses,
squids and cuttlefish.

505
00:42:47,520 --> 00:42:50,480
It's a little bit like
an octopus with a shell

506
00:42:50,480 --> 00:42:54,240
and what's amazing about them
is that their lineage

507
00:42:54,240 --> 00:42:58,120
is hundreds of millions of years old
and they haven't changed very much

508
00:42:58,120 --> 00:43:00,520
in all that time.
We call them a living fossil.

509
00:43:00,520 --> 00:43:05,200
It's a great opportunity to look
at an ancient brain and behaviour

510
00:43:05,200 --> 00:43:08,800
and they're a wonderful way to study
the evolution of intelligence.

511
00:43:08,800 --> 00:43:11,320
So are these guys intelligent, then?

512
00:43:11,320 --> 00:43:15,760
Some are smarter than others,
like that's Number Four,

513
00:43:15,760 --> 00:43:18,400
he outperforms everybody
in all the memory tests.

514
00:43:18,400 --> 00:43:21,560
He's quite active all the time,
he's quite engaging.

515
00:43:21,560 --> 00:43:23,880
If you put your in the water
he comes up to you,

516
00:43:23,880 --> 00:43:27,160
whereas Number Three,
who happens to be a teenager,

517
00:43:27,160 --> 00:43:30,320
is I'd guess you'd say more shy
and you put him in a new place

518
00:43:30,320 --> 00:43:34,440
and he sort of just attaches
to the wall and sits there.

519
00:43:34,440 --> 00:43:37,480
I'm interested in the shell
as a mathematician,

520
00:43:37,480 --> 00:43:40,080
but what does the nautilus
use the shell for?

521
00:43:40,080 --> 00:43:42,440
I think the most obvious use
is protection.

522
00:43:43,600 --> 00:43:45,840
They also use it for buoyancy.

523
00:43:45,840 --> 00:43:47,880
They only live in the front chamber

524
00:43:47,880 --> 00:43:50,240
and all the other chambers
are filled with gas

525
00:43:50,240 --> 00:43:51,520
and with some fluid.

526
00:43:51,520 --> 00:43:56,560
By regulating that, they can
gently and passively move up and down

527
00:43:56,560 --> 00:43:58,600
in the water like a submarine.

528
00:43:58,600 --> 00:44:00,920
The really cool thing they can do

529
00:44:00,920 --> 00:44:04,320
is they can actually survive
on the oxygen in the chambers,

530
00:44:04,320 --> 00:44:08,600
if there's a period where
the oxygen goes down in the oceans.

531
00:44:08,600 --> 00:44:12,840
It's one of the reasons why
they've lived for millions of years.

532
00:44:12,840 --> 00:44:15,680
It's a really great adaptation.
The shell is really amazing.

533
00:44:18,120 --> 00:44:22,560
But perhaps even more remarkably,
the rules this ancient creature

534
00:44:22,560 --> 00:44:24,240
uses to construct its home

535
00:44:24,240 --> 00:44:28,280
are written in the language
of the Code.

536
00:44:28,280 --> 00:44:30,600
HORNS BLARE

537
00:44:38,120 --> 00:44:42,520
The nautilus shell is one
of the most beautiful and intricate
structures in nature.

538
00:44:42,520 --> 00:44:45,760
Here you can see the chambers.
This is the one where it lives

539
00:44:45,760 --> 00:44:48,200
and these are the ones
it uses for buoyancy.

540
00:44:48,200 --> 00:44:51,640
Now, at first sight, this looks
like a really complex shape,

541
00:44:51,640 --> 00:44:54,240
but if I measure the dimensions
of these chambers

542
00:44:54,240 --> 00:44:57,080
a clear pattern begins to emerge.

543
00:45:10,800 --> 00:45:15,000
Now there doesn't seem to be any
connection between these numbers,

544
00:45:15,000 --> 00:45:17,840
but look what happens
when I take each number

545
00:45:17,840 --> 00:45:20,680
and divide it
by the previous measurement.

546
00:45:20,680 --> 00:45:26,360
If I take 3.32 and divide by 3.07,

547
00:45:26,360 --> 00:45:28,400
I get 1.08.

548
00:45:28,400 --> 00:45:31,920
Divide 3.59 by 3.32

549
00:45:31,920 --> 00:45:35,120
and I get 1.08.

550
00:45:35,120 --> 00:45:38,760
Take 3.88 and divide by 3.59
and I get, again, 1.08.

551
00:45:40,960 --> 00:45:45,120
So every time I do this calculation,
I get the same number.

552
00:45:45,120 --> 00:45:47,920
So although it's not clear
by looking at the shell,

553
00:45:47,920 --> 00:45:52,560
this tells us that the nautilus
is growing at a constant rate.

554
00:45:52,560 --> 00:45:56,240
Everytime the nautilus builds a new
room, the dimensions of that room

555
00:45:56,240 --> 00:46:00,080
are 1.08 times the dimensions
of the previous one.

556
00:46:00,080 --> 00:46:03,160
And it's just by following
this simple mathematical rule

557
00:46:03,160 --> 00:46:06,800
that the nautilus builds
this elegant spiral.

558
00:46:09,640 --> 00:46:13,080
And because many living things
grow in a similar way,

559
00:46:13,080 --> 00:46:16,520
these spirals are everywhere.

560
00:46:18,600 --> 00:46:24,000
The rules nature uses to create
its patterns are found in the Code.

561
00:46:51,320 --> 00:46:56,360
Behind the world we inhabit,
there's a strange
and wonderful mathematical realm.

562
00:46:56,360 --> 00:47:00,200
They're actually related
to octopus, squids and cuttlefish.

563
00:47:00,200 --> 00:47:01,840
They're quite ticklish.

564
00:47:05,680 --> 00:47:11,360
The numbers and connections
at its heart describe the processes
we see all around us.

565
00:47:11,360 --> 00:47:12,760
Bear with me, all right?

566
00:47:17,480 --> 00:47:22,160
But the Code doesn't just contain
the rules that govern our planet -

567
00:47:22,160 --> 00:47:28,040
its numbers also describe the laws
that control the entire universe.

568
00:47:40,520 --> 00:47:45,800
For centuries, we've gazed out
into the night's sky

569
00:47:45,800 --> 00:47:50,160
and tried to make sense
of the patterns we see in the stars.

570
00:48:08,280 --> 00:48:13,320
To take a closer look, I've come
to Switzerland's Sphinx Observatory,

571
00:48:13,320 --> 00:48:18,600
perched precariously
on the Jungfrau mountain.

572
00:48:31,240 --> 00:48:38,280
At nearly 3,600 metres, it's one
of the highest peaks in the Alps.

573
00:48:43,200 --> 00:48:46,840
And after the sun
has sunk below the horizon...

574
00:48:49,080 --> 00:48:52,080
..it's a great place
to gaze at the stars.

575
00:49:00,680 --> 00:49:05,520
Well, it's a really clear night,
so you can see loads of stars.

576
00:49:05,520 --> 00:49:08,920
There's Sirius over here,
the brightest star in the night sky

577
00:49:08,920 --> 00:49:14,000
and right here a really recognisable
constellation, which is Orion.

578
00:49:14,000 --> 00:49:16,120
Have people always picked out Orion

579
00:49:16,120 --> 00:49:18,560
as a significant pattern
in the night sky?

580
00:49:18,560 --> 00:49:22,360
It seems like different cultures
all picked out that group

581
00:49:22,360 --> 00:49:23,880
as being a significant one.

582
00:49:23,880 --> 00:49:26,280
They all have
different legends about it.

583
00:49:26,280 --> 00:49:29,720
The Egyptians associated it
with Osiris, their god of death
and rebirth

584
00:49:29,720 --> 00:49:32,560
Other cultures group them together.

585
00:49:32,560 --> 00:49:35,360
A native American tribe
called the three stars of the belt,

586
00:49:35,360 --> 00:49:38,000
the three footprints of the flee god.

587
00:49:38,000 --> 00:49:42,560
One group of the Aborigines
in Australia called it the canoe.

588
00:49:47,600 --> 00:49:52,320
Today, we don't need legends to
explain the patterns in the stars

589
00:49:52,320 --> 00:49:56,880
because we know
their precise positions in space.

590
00:50:00,200 --> 00:50:03,440
And we don't just know
where they are now,

591
00:50:03,440 --> 00:50:06,680
we know where they were yesterday
and where they'll be

592
00:50:06,680 --> 00:50:09,600
millions of years into the future.

593
00:50:10,720 --> 00:50:15,440
So the Sun and all the stars in our
galaxy, including the stars in Orion,

594
00:50:15,440 --> 00:50:18,680
are all moving in orbits
around the centre of the galaxy,

595
00:50:18,680 --> 00:50:23,160
but like a swarm of bees,
although they're all moving
in roughly the same direction,

596
00:50:23,160 --> 00:50:27,360
they all follow their own paths
and that means that
their positions will change,

597
00:50:27,360 --> 00:50:29,640
as thousands of years tick by.

598
00:50:29,640 --> 00:50:33,200
And now we're two-and-a-half
million years in the future

599
00:50:33,200 --> 00:50:37,760
and the constellation of Orion
has completely gone.

600
00:50:38,880 --> 00:50:44,440
In fact, thousands of years ago
our ancestors would have seen
different patterns in the sky

601
00:50:44,440 --> 00:50:49,800
and our descendants,
millions of years in the future,
will also see different patterns.

602
00:50:58,200 --> 00:51:03,160
The reason we can predict how the
stars will move into the far future

603
00:51:03,160 --> 00:51:06,360
is because we've uncovered the rules
that govern their behaviour.

604
00:51:08,080 --> 00:51:12,880
And we've found these rules
not in the heavens, but in numbers.

605
00:51:19,440 --> 00:51:24,600
It's only through the Code
that we can understand
the laws that govern the universe.

606
00:51:49,160 --> 00:51:52,680
Laws that describe everything
from the motion of the planets

607
00:51:52,680 --> 00:51:55,400
to the flight of projectile.

608
00:51:56,560 --> 00:51:59,640
When you watch the fireball
fly through the air

609
00:51:59,640 --> 00:52:02,240
then it appears in the first
part of its flight,

610
00:52:02,240 --> 00:52:04,160
when it's just left the trebuchet,

611
00:52:04,160 --> 00:52:08,320
that it's accelerating upwards
and then it begins to slow down,

612
00:52:08,320 --> 00:52:10,440
before it stops just above me

613
00:52:10,440 --> 00:52:14,800
and then, finally, accelerates
back down towards the ground.

614
00:52:19,120 --> 00:52:22,000
But if you analyse the flight
using numbers,

615
00:52:22,000 --> 00:52:24,360
it reveals something
rather surprising.

616
00:52:26,440 --> 00:52:30,560
When you plot a graph
of the projectile's vertical speed

617
00:52:30,560 --> 00:52:32,680
against time...

618
00:52:33,760 --> 00:52:36,760
..you then you get a graph
which looks like this.

619
00:52:41,080 --> 00:52:44,160
To start with,
the projectile is moving upwards

620
00:52:44,160 --> 00:52:47,960
so it's vertical speed is positive,
but decreasing.

621
00:52:49,200 --> 00:52:53,040
As it reaches the top of its arc,
the vertical speed becomes negative

622
00:52:53,040 --> 00:52:58,360
as the fireball turns round
and falls back to Earth.

623
00:53:01,800 --> 00:53:05,920
Because the graph is going like
this, it means that the projectile,

624
00:53:05,920 --> 00:53:10,360
from the moment it leaves the
trebuchet, is actually slowing down.

625
00:53:10,360 --> 00:53:14,800
So at no point during the flight
is it ever accelerating upwards.

626
00:53:21,080 --> 00:53:26,160
Throughout its flight, the fireball
is accelerating downwards

627
00:53:26,160 --> 00:53:29,040
towards the Earth
at a constant rate.

628
00:53:30,840 --> 00:53:34,040
Something you would never realise
simply by watching it

629
00:53:34,040 --> 00:53:36,280
fly through the air.

630
00:53:39,120 --> 00:53:41,400
And this is a profound truth

631
00:53:41,400 --> 00:53:44,480
about one of the fundamental
forces of nature...

632
00:53:46,400 --> 00:53:48,160
..gravity.

633
00:53:49,320 --> 00:53:52,600
Drop, throw, fire or launch
anything you like -

634
00:53:52,600 --> 00:53:55,760
a rock, a bullet,
a ball or even a pot plant

635
00:53:55,760 --> 00:53:58,880
and it will accelerate towards
the ground at a constant rate

636
00:53:58,880 --> 00:54:02,600
of 9.8 metres per second,
per second.

637
00:54:02,600 --> 00:54:06,200
This is a fundamental law
of gravity on our planet.

638
00:54:06,200 --> 00:54:11,040
But it's only revealed
by changing the flight path
of the object into numbers.

639
00:54:16,760 --> 00:54:21,000
Appreciating this simple fact
about how gravity works on Earth

640
00:54:21,000 --> 00:54:26,160
is the first step towards
understanding gravity everywhere.

641
00:54:39,680 --> 00:54:45,160
It's the foundation stone
of Newton's Law
of Universal Gravitation.

642
00:54:46,400 --> 00:54:51,280
A mathematical theory that can
describe the orbits of the planets,

643
00:54:51,280 --> 00:54:56,160
predict the passage of the stars
into the distant future...

644
00:54:59,000 --> 00:55:04,640
..and has even enabled human kind
to step foot on the Moon.

645
00:55:08,920 --> 00:55:14,280
The laws that command the heavens
are written in the Code.

646
00:55:26,000 --> 00:55:29,840
'We call them the door mats,
the large ones.

647
00:55:29,840 --> 00:55:32,560
'Two-and-a-half million years
in the future...

648
00:55:32,560 --> 00:55:35,200
'This isn't imaginery, this is real!

649
00:55:39,520 --> 00:55:44,120
'You don't need to know
what that means to know
that animal's not happy.

650
00:55:44,120 --> 00:55:45,920
'Whatever circle I take,

651
00:55:45,920 --> 00:55:48,880
'you're going to get
a number which starts 3.14.'

652
00:55:53,040 --> 00:55:57,680
It's an incredible thought
that the only way we can
really make sense of our world

653
00:55:57,680 --> 00:56:00,960
is by using
the abstract world of numbers.

654
00:56:00,960 --> 00:56:05,400
And yet those numbers have allowed
us to take our first tentative
steps off our planet.

655
00:56:05,400 --> 00:56:10,240
They've also given us the technology
to transform our surroundings.

656
00:56:12,320 --> 00:56:15,120
'A hidden Code
underpins the world around us.

657
00:56:18,320 --> 00:56:21,840
'A Code that has the power
to unlock the rules that
cover the universe.'

658
00:56:25,520 --> 00:56:30,000
This place was constructed
to satisfy a spiritual need.

659
00:56:30,000 --> 00:56:34,240
But we couldn't have built it
without the power of the Code.

660
00:56:34,240 --> 00:56:39,920
For me, it's an exquisite
example of the beauty
and potency of mathematics.

661
00:56:51,120 --> 00:56:53,880
From the patterns and numbers
all around us,

662
00:56:53,880 --> 00:56:57,160
we've deciphered a hidden code.

663
00:57:11,000 --> 00:57:15,240
We've revealed a strange
and intriguing numerical world,

664
00:57:15,240 --> 00:57:16,960
totally unlike our own.

665
00:57:18,720 --> 00:57:24,840
Yet it's a Code that also describes
our world with astonishing accuracy.

666
00:57:30,800 --> 00:57:34,200
And has given us
unprecedented power to describe...

667
00:57:37,600 --> 00:57:39,200
..control...

668
00:57:41,640 --> 00:57:43,880
..and predict our surroundings.

669
00:57:56,920 --> 00:58:01,280
The fact that the Code
provides such a successful
description of nature

670
00:58:01,280 --> 00:58:04,160
is for many one of the greatest
mysteries of science.

671
00:58:05,240 --> 00:58:08,600
I think the only explanation
that makes sense for me

672
00:58:08,600 --> 00:58:11,360
is that by discovering
these connections,

673
00:58:11,360 --> 00:58:15,000
we have in fact uncovered
some deep truth about the world.

674
00:58:15,000 --> 00:58:18,240
That perhaps, the Code
is THE truth of the universe

675
00:58:18,240 --> 00:58:22,880
and it's numbers that dictate
the way the world must be.

676
00:58:29,520 --> 00:58:31,120
Go to...

677
00:58:34,280 --> 00:58:37,360
..to find clues to help you solve
the Code's treasure hunt.

678
00:58:37,360 --> 00:58:41,000
Plus, get a free set of mathematical
puzzles and a treasure hunt clue

679
00:58:41,000 --> 00:58:43,520
when you follow the links
to The Open University

680
00:58:43,520 --> 00:58:46,160
or call 0845 366 8026.

681
00:59:00,880 --> 00:59:03,920
Subtitles by Red Bee Media Ltd

682
00:59:03,920 --> 00:59:06,960
E-mail subtitling@bbc.co.uk

683
00:59:07,000 --> 00:59:10,117
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