The Code S01E01: "Numbers"

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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.
1:49 - 1:52

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.
3:38 - 3:42

The fourth-century Algerian cleric
St Augustine believed
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that seven was so special that it
represented the entire universe.
3:46 - 3:50

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.
5:50 - 5:55

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.
12:36 - 12:41

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.
12:51 - 12:55

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.
13:12 - 13:16

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
17:28 - 17:30

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.
17:35 - 17:38

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
17:53 - 17:57

harmonious combination of notes
that you can have.
17:57 - 18:03

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.
18:14 - 18:16

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.'
19:42 - 19:46

You can see just by looking at it
it's not going to sound nice.
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The wave looks a mess.
19:47 - 19:50

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.
19:56 - 20:01

It doesn't have any pitch. It sounds
harsh and I could make it louder
and that would make it harsher.
20:01 - 20:05

When the various frequencies aren't
simple multiples of one another,
20:05 - 20:08

there's no common pattern
for the ear to respond to,
20:08 - 20:12

and the more complex you make
the ratios, the more dissonant
and harsh the sound will get.
20:16 - 20:20

By monitoring her victims' reactions
to these appalling noises,
20:20 - 20:24

Professor Edworthy has found
they have a very different effect
20:24 - 20:25

on our minds than music.
20:25 - 20:27

ALARM BEEPS
20:27 - 20:30

HONKING
20:30 - 20:31

WHIRRING
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They're so unpleasant...
HAMMERING
20:34 - 20:37

..they shock our brains into action.
20:37 - 20:39

For example, a siren.
20:39 - 20:43

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.
20:50 - 20:54

Sometimes you find these sounds
in the animal world as well.
20:54 - 20:57

So this, for example, this is
a chimpanzee and an orang-utan.
20:57 - 21:00

INTERMITTENT SCREECHING
21:03 - 21:08

OK, these animals are obviously
quite bothered by something.
21:08 - 21:12

You don't need to know
what that sound means to know
that that animal's not happy
21:12 - 21:18

and also that the other animals in
that environment and us, for example,
should just get out of the way.
21:18 - 21:20

SHORT SCREECH
21:20 - 21:23

So it's interesting
that we really hear pattern,
21:23 - 21:28

and when it isn't there,
it creates an effect in all of us.
21:28 - 21:30

LOW-PITCHED SCREECH
21:37 - 21:41

Remarkably,
it's numerical patterns in the Code
21:41 - 21:45

that dictate the combinations
of sounds we hear as music...
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RUSTLING
21:47 - 21:51

..and those we hear simply as noise.
CHIRPING, SIREN
21:51 - 21:54

BELL TOLLS
21:54 - 21:59

And perhaps stranger still,
it's these same numbers
21:59 - 22:02

that are built into the walls
of this medieval cathedral.
22:08 - 22:13

Two notes
which are an octave apart are
going be in this one-to-two ratio.
22:20 - 22:24

The width of the nave here is twice
the distance between
22:24 - 22:30

each of the columns that run up
its length - a ratio of two to one.
22:30 - 22:35

The most harmonious
combination of notes from a pair.
22:35 - 22:39

The altar divides the nave
into a ratio of eight to five.
22:40 - 22:43

A minor sixth...
22:43 - 22:44

eight to five.
22:48 - 22:50

A perfect fifth...
22:50 - 22:52

three to two.
22:52 - 22:55

A perfect fourth is four to three.
22:55 - 22:58

Major third, five to four.
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And that's what music is all about.
23:04 - 23:09

St Augustine believed
these ratios were used by God
to construct the universe
23:09 - 23:13

and that that was why
they produced harmony in music.
23:18 - 23:22

By constructing their cathedral
using the same ratios,
23:22 - 23:26

the clergy at Chartres
hoped to echo God's creation.
23:26 - 23:30

This entire place
is a symphony set in stone.
23:33 - 23:38

Using the Code's numbers has created
a building of awe-inspiring beauty.
23:53 - 23:54

The only truth there is...
23:54 - 23:57

Seemingly significant numbers...
24:03 - 24:07

By searching
for divine meaning in numbers,
24:07 - 24:12

12th-century scholars had stumbled
across elements of the Code.
24:12 - 24:14

It's very difficult to see a pattern.
24:17 - 24:22

Mysterious numbers and patterns that
seem to be written into our biology.
24:23 - 24:26

Its only defence
is safety in numbers.
24:28 - 24:34

And as we've looked closer, we
haven't simply found more numbers -
24:34 - 24:42

we've begun to uncover their
strangest properties and started to
see deep connections between them.
24:46 - 24:50

Back in the distant past,
in Neolithic times,
24:50 - 24:55

around 4,000 years ago, an ancient
people brought these stones here
24:55 - 24:58

and arranged them like this.
24:58 - 25:02

This is Sunkenkirk stone circle in
Cumbria and it's one of around 1,000
25:02 - 25:07

such structures that our ancient
ancestors built across the UK.
25:14 - 25:17

Stretching back
into the mists of time,
25:17 - 25:21

the circle has been
steeped in mysticism.
25:25 - 25:28

But whether the people who built
this structure knew it or not,
25:28 - 25:32

there is deep significance
hidden inside this circle.
25:32 - 25:36

OK, so I need to start
by measuring the diameter
25:36 - 25:41

of my circle, so that's the
distance from one edge to the other.
25:44 - 25:46

I need to go roughly
through the centre.
25:49 - 25:51

So that's 27 and 90.
25:55 - 25:59

Right, so now I'm going
to measure the circumference
25:59 - 26:01

of the circle. So off we go.
26:01 - 26:03

So around the outside.
26:06 - 26:08

Oh, I've never got so much exercise
doing maths before!
26:11 - 26:13

And that's the circumference.
26:13 - 26:18

So I've got 91 metres
26:18 - 26:21

and 70 centimetres.
26:23 - 26:28

I'm going to do
a little calculation. I'm going
to divide the circumference
26:28 - 26:32

of the circle by the diameter.
26:32 - 26:36

So 917 divided by 279.
26:36 - 26:38

So that's roughly three...
26:38 - 26:42

Bit of, er, mental arithmetic, not
a mathematician's strongest point.
26:42 - 26:45

OK, two lots of 279,
26:45 - 26:47

so...
26:47 - 26:49

not far out
from what I was hoping for.
26:49 - 26:55

So when I do that,
I get roughly 3.2 as the answer.
27:00 - 27:03

My measurements
weren't very precise...
27:05 - 27:10

..but my answer is close
to a mysterious number
hidden within every circle.
27:15 - 27:20

So, for example,
let's take this circular plate here.
27:20 - 27:22

I'm going to measure its diameter.
27:22 - 27:25

26.4 centimetres.
Now its circumference.
27:27 - 27:29

That's a bit trickier.
27:29 - 27:32

82.9 centimetres.
27:32 - 27:36

Divide the circumference
by the diameter, I get 3.14.
27:36 - 27:39

Now let's take another circle.
Measure its diameter.
27:39 - 27:41

12.8 centimetres.
27:42 - 27:47

So the circumference
is 40.2 centimetres.
27:47 - 27:52

Divide the circumference
by the diameter and I get 3.14.
27:52 - 27:56

In fact, whatever circle I take,
divide the circumference
27:56 - 28:01

by the diameter and you're going
to get a number which starts 3.14.
28:01 - 28:04

This is a number we call pi.
28:09 - 28:14

No matter where the circles are,
no matter how big or small...
28:15 - 28:18

..they will always contain pi.
28:20 - 28:27

It's this universality of the
number pi which tells you you've
identified a piece of true Code.
28:27 - 28:29

In fact, if you get another number,
28:29 - 28:31

it means
that you haven't got a circle.
28:31 - 28:34

In some sense,
pi is the essence of circleness,
28:34 - 28:37

distilled into the language
of the Code.
28:38 - 28:43

And because circles and curves
crop up again and again in nature,
28:43 - 28:48

pi can be found all around us.
28:51 - 28:54

It's in the gentle curve
of a river...
28:56 - 28:58

..the sweep of a coast line...
29:00 - 29:04

..and the shifting patterns
of the desert sands.
29:07 - 29:13

Pi seems written into the structures
and processes of our planet.
29:19 - 29:22

But, strangely,
pi also appears in places
29:22 - 29:26

that seem to have nothing
to do with circles.
29:31 - 29:36

I started fishing Brighton in 1972.
29:36 - 29:39

I've been a fisherman 40 years,
catching Dover sole.
29:41 - 29:45

That's the main target species
for the English Channel.
29:47 - 29:49

How many fish
do you think you get a day?
29:49 - 29:51

300 some days, 150 other days,
29:51 - 29:53

so I'd say 200 would be average.
29:53 - 29:58

And you've got me some
Dover sole today so I can have a
weigh of what you've caught today.
29:58 - 30:00

Yeah, you can play with them! OK!
30:02 - 30:07

What's remarkable is that, with just
a small amount of information...
30:07 - 30:09

It's 180 grams.
30:10 - 30:12

..and by weighing a few fish...
30:12 - 30:13

That's a whopper.
30:13 - 30:15

..I can use the Code
30:15 - 30:17

to tell me things
about not just today's catch...
30:17 - 30:21

360 grams. 50 grams. 110 grams.
30:22 - 30:25

..but about all the Dover sole
Sam's ever fished...
30:25 - 30:28

Whoa, jeez, come back!
30:28 - 30:31

..I can even get an estimate
for the largest sole
30:31 - 30:33

that Sam is likely
to have caught during his career.
30:33 - 30:35

Right...
30:35 - 30:41

First , I need to work out what
the average weight of a fish is,
30:41 - 30:46

so 140 plus 190
30:46 - 30:48

plus 150...
30:48 - 30:53

So now I need to work out
the standard deviation,
so that's 140 minus square that...
30:53 - 30:56

Bear with me, all right?
Almost there.
30:56 - 31:01

So he said he fished for 40 years,
31:01 - 31:06

and eight weeks during the year,
six days out of the week
31:06 - 31:10

and 200 sole each day,
31:10 - 31:14

so that gives you
a total of 384,000 fish.
31:16 - 31:20

Using these numbers,
I can calculate that the largest one
31:20 - 31:23

out of those 384,000 fish
31:23 - 31:28

should be about 1.3 kilograms,
which is roughly three pounds.
31:30 - 31:34

So what's the largest Dover sole
that you've caught in your career?
31:34 - 31:37

We call them door mats,
the large ones,
31:37 - 31:40

and you maybe get
four or five a season.
31:40 - 31:45

The largest, I'd say, was three
to three and a half pounds.
31:45 - 31:50

An average Dover Sole
is that sort of size
31:50 - 31:51

and these...
31:51 - 31:55

Wow, that's huge! Yeah!
31:55 - 31:58

It's a whopper. It's always nice
to catch big stuff, you know.
31:58 - 32:01

Well, I think it is anyway.
HE CHUCKLES
32:05 - 32:09

Using the Code,
it's possible to estimate the size
32:09 - 32:12

of the biggest fish
Sam's ever caught,
32:12 - 32:16

despite not weighing a single fish
anywhere near that size.
32:21 - 32:28

Now, the reason this calculation is
possible is because the distribution
of the weights of fish,
32:28 - 32:33

in fact the distribution
of lots of things like the height
of people in the UK or IQ,
32:33 - 32:36

is given by this formula.
32:36 - 32:39

'This is the normal
distribution equation,
32:39 - 32:42

'one of the most important bits
of mathematics
32:42 - 32:46

'for understanding variation
in the natural world.'
32:46 - 32:51

The most remarkable thing about this
formula isn't so much what it does
32:51 - 32:54

as this term here, pi.
32:54 - 32:56

It seems totally bizarre
32:56 - 33:00

that a bit of the Code
that has something to do
with the geometry of a circle
33:00 - 33:02

can help you to calculate
the weight of fish.
33:02 - 33:07

Pi shouldn't have anything
to do with fish, yet there it is.
33:15 - 33:20

Just as the circle
appears everywhere in nature,
33:20 - 33:24

so pi crops up again and again
in the mathematical world.
33:26 - 33:32

It's an astonishing example of
the interconnectedness of the Code.
33:32 - 33:37

A glimpse into a world where numbers
don't just have strange connections,
33:37 - 33:41

they have deeply puzzling
properties of their own.
33:44 - 33:47

Pi is what's known
as an irrational number.
33:49 - 33:53

Written as a decimal,
it has an infinite number of digits
33:53 - 33:57

arranged in a sequence
that never repeats.
33:58 - 34:03

And it's thought that any number
you can possibly imagine
34:03 - 34:07

will appear in pi somewhere,
from my birthday
34:07 - 34:11

to the answer to life,
the universe and everything.
34:14 - 34:17

Because they go on for ever,
we can never know all the digits
34:17 - 34:19

that make up pi.
34:19 - 34:23

But, luckily,
we only need the first 39
34:23 - 34:28

to calculate the circumference
of a circle the size
of the entire observable universe,
34:28 - 34:31

accurate to the radius
of a single hydrogen atom.
34:38 - 34:43

But as strange as Pi is, it does
at least describe a physical object.
34:45 - 34:48

Some numbers don't make
any sense in real world,
34:48 - 34:51

despite the fact we use them
all the time.
34:51 - 34:54

Numbers, like negative numbers.
34:57 - 35:01

It's impossible to trade anything,
stocks, shares, currency,
35:01 - 35:04

even fish, without negative numbers.
35:04 - 35:06

Most of us are comfortable them.
35:06 - 35:09

Even though we may not like it,
we understand what it means
35:09 - 35:12

to have a negative bank balance.
35:12 - 35:14

But when you start
to think about it,
35:14 - 35:17

there's something deeply strange
about negative numbers,
35:17 - 35:21

cos they don't seem to correspond
to anything real at all.
35:24 - 35:29

The deeper we look into the Code,
the more bizarre it becomes.
35:34 - 35:40

It's easy to imagine one fish
or two fish, or no fish at all.
35:40 - 35:45

It's much harder to imagine
what minus-one fish looks like.
35:45 - 35:49

Negative numbers are so odd
that if I have minus-one fish
and you give me a fish,
35:49 - 35:53

then all you can be certain of
is that I've got no fish at all.
36:01 - 36:07

Numbers, can exist regardless
of whether they make any sense
in the physical world.
36:11 - 36:16

And if you think that's odd,
some numbers are so strange
36:16 - 36:19

they don't even seem
to make sense as numbers.
36:20 - 36:24

Now, this is one of the most
basic facts of mathematics.
36:24 - 36:29

A positive number multiplied
by another positive number
is a positive number.
36:29 - 36:35

So for example,
one times one is one.
36:35 - 36:38

A negative number multiplied
by another negative number
36:38 - 36:41

also gives a positive number.
36:41 - 36:47

So for example, minus-one
times minus-one is plus-one.
36:47 - 36:53

'It's not only a rule, it's a proven
truth of multiplication.
36:53 - 36:57

'Whenever the signs are the same,
the product is always positive.'
36:57 - 36:59

From this, it's obvious
36:59 - 37:02

if I take any number
and multiply it by itself,
37:02 - 37:04

then the answer
is going to be positive.
37:04 - 37:07

However, in the Code,
37:07 - 37:09

there's a special number
which breaks this rule.
37:09 - 37:13

When I multiply it by itself,
it gives the answer minus-one.
37:13 - 37:17

It's impossible to imagine what
this number could be,
37:17 - 37:21

because there simply is no number
37:21 - 37:25

that when multiplied by itself,
gives minus-one.
37:25 - 37:29

This isn't a number I can calculate.
I can't show you this number.
37:29 - 37:32

Nevertheless, we've given
this number a name.
37:32 - 37:35

It's called "i", and it's part
of a whole class of new numbers
37:35 - 37:37

called imaginary numbers.
37:38 - 37:43

Calculating with imaginary numbers
is the mathematical equivalent
37:43 - 37:45

of believing in fairies.
37:46 - 37:51

But even these strangest elements
of the Code turn out to have
37:51 - 37:53

some very practical applications.
37:58 - 38:02

The ground's close, will you call
me, please, 1-1-9 next...
38:04 - 38:09

Runway 25, clear to land. Surface
is 1-3-0, less than five minutes.
38:09 - 38:12

'Especially on a day like this.'
38:16 - 38:21

8-5 Foxtrot, thank you, vacate next
right and park yourself 1-3 short.
38:21 - 38:25

'8-5 Foxtrot, 8-2-0, both making
approach down direct and right, 2-5.'
38:25 - 38:28

So where's this one coming from?
38:28 - 38:32

That is from Barcelona.
It's an Easyjet flight, EZZ6402.
38:32 - 38:35

Don't know how many people are
on board, but it seats about 190.
38:35 - 38:38

And here he is.
He's getting pretty close now.
38:38 - 38:40

Just less than two miles
till he lands.
38:40 - 38:44

What information is the radar
giving you about the aeroplanes?
38:44 - 38:47

The first and most important thing
is the position of the aircraft.
38:47 - 38:51

The yellow slash there
is where the aircraft is.
38:51 - 38:55

You've got the blue trail,
the history of where
the aircraft's been.
38:55 - 38:59

From that you get two things -
you get its rough heading,
where he's going, and its speed.
38:59 - 39:02

The longer the trail,
the faster the aircraft's going.
39:08 - 39:11

Radar works by sending out
a pulse of radio waves
39:11 - 39:15

and analysing the small fraction
of the signal that's reflected back.
39:19 - 39:23

Complex computation is then needed
to distinguish moving objects,
39:23 - 39:27

like planes,
from the stationary background.
39:27 - 39:30

RADIO COMMUNICATION
39:30 - 39:36

At the heart of that analysis lies
"i", the number that cannot exist.
39:38 - 39:43

Imaginary numbers are useful
for working out the complex way
39:43 - 39:45

radio waves interact
with each other.
39:45 - 39:49

It seems to be the right language
to describe their behaviour.
39:49 - 39:52

Now, you could do these calculations
with ordinary numbers.
39:52 - 39:54

But they're so cumbersome,
39:54 - 39:57

by the time you've done
the calculation the plane's
moved to somewhere else.
39:57 - 40:02

Attitude 6,000
on a squawk of 7-7-1-5.
40:02 - 40:05

Using imaginary numbers
makes the calculation simpler
40:05 - 40:08

that you can track the planes
in real time.
40:08 - 40:13

In fact without them,
radar would be next to useless
for Air Traffic Control.
40:17 - 40:21

It's kind of amazing that this
abstract idea lands planes.
40:21 - 40:24

It's a bit surprising, you're talking
about imaginary numbers
40:24 - 40:26

and this isn't imaginary,
this is real. This is very real.
40:26 - 40:30

I'm surprised at the fact
that something so abstract
40:30 - 40:32

is being used
in such a concrete way.
40:47 - 40:50

As strange as it may seem,
the code provides us
40:50 - 40:54

with an astonishingly successful
description of our world.
41:00 - 41:04

Its most ethereal numbers
have starkly real applications.
41:04 - 41:10

Its patterns
can explain one of the most
profound processes in nature -
41:10 - 41:14

how living things grow.
41:17 - 41:20

This is a picture of something
I've been fascinated by
41:20 - 41:22

ever since I became a mathematician.
41:22 - 41:26

It's an X-ray of a marine animal
called a nautilus.
41:26 - 41:31

And this spiral here is one
of the iconic images of mathematics.
41:31 - 41:34

Now, while I've seen pictures
like this hundreds of times,
41:34 - 41:37

I've never actually seen
the animal for real.
41:41 - 41:45

'At Brooklyn College,
biologist Jennifer Basil keeps
five of these aquatic denizens,
41:45 - 41:49

'for her research
into the evolution of intelligence.'
41:51 - 41:56

We keep the animals
in these tall tanks because
they're naturally active at night
41:56 - 41:59

and they like darkness,
they live in deep water.
41:59 - 42:02

They also like to go up
and down in the water column,
42:02 - 42:04

that kind of makes them happy. OK!
42:04 - 42:07

We give them the five-star
treatment here. Right...
42:08 - 42:11

This is Number Five. Ah, wow. Yeah.
42:11 - 42:13

Gosh, big eyes.
42:13 - 42:17

They have huge eyes, great for seeing
in low light conditions. Right.
42:18 - 42:20

So, here's that beautiful shell.
Yeah.
42:20 - 42:23

And the striping pattern helps them
hide where they live.
42:40 - 42:45

I've never seen the animal before
inside the shell, what is it?
42:45 - 42:48

They're related to octopuses,
squids and cuttlefish.
42:48 - 42:50

It's a little bit like
an octopus with a shell
42:50 - 42:54

and what's amazing about them
is that their lineage
42:54 - 42:58

is hundreds of millions of years old
and they haven't changed very much
42:58 - 43:01

in all that time.
We call them a living fossil.
43:01 - 43:05

It's a great opportunity to look
at an ancient brain and behaviour
43:05 - 43:09

and they're a wonderful way to study
the evolution of intelligence.
43:09 - 43:11

So are these guys intelligent, then?
43:11 - 43:16

Some are smarter than others,
like that's Number Four,
43:16 - 43:18

he outperforms everybody
in all the memory tests.
43:18 - 43:22

He's quite active all the time,
he's quite engaging.
43:22 - 43:24

If you put your in the water
he comes up to you,
43:24 - 43:27

whereas Number Three,
who happens to be a teenager,
43:27 - 43:30

is I'd guess you'd say more shy
and you put him in a new place
43:30 - 43:34

and he sort of just attaches
to the wall and sits there.
43:34 - 43:37

I'm interested in the shell
as a mathematician,
43:37 - 43:40

but what does the nautilus
use the shell for?
43:40 - 43:42

I think the most obvious use
is protection.
43:44 - 43:46

They also use it for buoyancy.
43:46 - 43:48

They only live in the front chamber
43:48 - 43:50

and all the other chambers
are filled with gas
43:50 - 43:52

and with some fluid.
43:52 - 43:57

By regulating that, they can
gently and passively move up and down
43:57 - 43:59

in the water like a submarine.
43:59 - 44:01

The really cool thing they can do
44:01 - 44:04

is they can actually survive
on the oxygen in the chambers,
44:04 - 44:09

if there's a period where
the oxygen goes down in the oceans.
44:09 - 44:13

It's one of the reasons why
they've lived for millions of years.
44:13 - 44:16

It's a really great adaptation.
The shell is really amazing.
44:18 - 44:23

But perhaps even more remarkably,
the rules this ancient creature
44:23 - 44:24

uses to construct its home
44:24 - 44:28

are written in the language
of the Code.
44:28 - 44:31

HORNS BLARE
44:38 - 44:43

The nautilus shell is one
of the most beautiful and intricate
structures in nature.
44:43 - 44:46

Here you can see the chambers.
This is the one where it lives
44:46 - 44:48

and these are the ones
it uses for buoyancy.
44:48 - 44:52

Now, at first sight, this looks
like a really complex shape,
44:52 - 44:54

but if I measure the dimensions
of these chambers
44:54 - 44:57

a clear pattern begins to emerge.
45:11 - 45:15

Now there doesn't seem to be any
connection between these numbers,
45:15 - 45:18

but look what happens
when I take each number
45:18 - 45:21

and divide it
by the previous measurement.
45:21 - 45:26

If I take 3.32 and divide by 3.07,
45:26 - 45:28

I get 1.08.
45:28 - 45:32

Divide 3.59 by 3.32
45:32 - 45:35

and I get 1.08.
45:35 - 45:39

Take 3.88 and divide by 3.59
and I get, again, 1.08.
45:41 - 45:45

So every time I do this calculation,
I get the same number.
45:45 - 45:48

So although it's not clear
by looking at the shell,
45:48 - 45:53

this tells us that the nautilus
is growing at a constant rate.
45:53 - 45:56

Everytime the nautilus builds a new
room, the dimensions of that room
45:56 - 46:00

are 1.08 times the dimensions
of the previous one.
46:00 - 46:03

And it's just by following
this simple mathematical rule
46:03 - 46:07

that the nautilus builds
this elegant spiral.
46:10 - 46:13

And because many living things
grow in a similar way,
46:13 - 46:17

these spirals are everywhere.
46:19 - 46:24

The rules nature uses to create
its patterns are found in the Code.
46:51 - 46:56

Behind the world we inhabit,
there's a strange
and wonderful mathematical realm.
46:56 - 47:00

They're actually related
to octopus, squids and cuttlefish.
47:00 - 47:02

They're quite ticklish.
47:06 - 47:11

The numbers and connections
at its heart describe the processes
we see all around us.
47:11 - 47:13

Bear with me, all right?
47:17 - 47:22

But the Code doesn't just contain
the rules that govern our planet -
47:22 - 47:28

its numbers also describe the laws
that control the entire universe.
47:41 - 47:46

For centuries, we've gazed out
into the night's sky
47:46 - 47:50

and tried to make sense
of the patterns we see in the stars.
48:08 - 48:13

To take a closer look, I've come
to Switzerland's Sphinx Observatory,
48:13 - 48:19

perched precariously
on the Jungfrau mountain.
48:31 - 48:38

At nearly 3,600 metres, it's one
of the highest peaks in the Alps.
48:43 - 48:47

And after the sun
has sunk below the horizon...
48:49 - 48:52

..it's a great place
to gaze at the stars.
49:01 - 49:06

Well, it's a really clear night,
so you can see loads of stars.
49:06 - 49:09

There's Sirius over here,
the brightest star in the night sky
49:09 - 49:14

and right here a really recognisable
constellation, which is Orion.
49:14 - 49:16

Have people always picked out Orion
49:16 - 49:19

as a significant pattern
in the night sky?
49:19 - 49:22

It seems like different cultures
all picked out that group
49:22 - 49:24

as being a significant one.
49:24 - 49:26

They all have
different legends about it.
49:26 - 49:30

The Egyptians associated it
with Osiris, their god of death
and rebirth
49:30 - 49:33

Other cultures group them together.
49:33 - 49:35

A native American tribe
called the three stars of the belt,
49:35 - 49:38

the three footprints of the flee god.
49:38 - 49:43

One group of the Aborigines
in Australia called it the canoe.
49:48 - 49:52

Today, we don't need legends to
explain the patterns in the stars
49:52 - 49:57

because we know
their precise positions in space.
50:00 - 50:03

And we don't just know
where they are now,
50:03 - 50:07

we know where they were yesterday
and where they'll be
50:07 - 50:10

millions of years into the future.
50:11 - 50:15

So the Sun and all the stars in our
galaxy, including the stars in Orion,
50:15 - 50:19

are all moving in orbits
around the centre of the galaxy,
50:19 - 50:23

but like a swarm of bees,
although they're all moving
in roughly the same direction,
50:23 - 50:27

they all follow their own paths
and that means that
their positions will change,
50:27 - 50:30

as thousands of years tick by.
50:30 - 50:33

And now we're two-and-a-half
million years in the future
50:33 - 50:38

and the constellation of Orion
has completely gone.
50:39 - 50:44

In fact, thousands of years ago
our ancestors would have seen
different patterns in the sky
50:44 - 50:50

and our descendants,
millions of years in the future,
will also see different patterns.
50:58 - 51:03

The reason we can predict how the
stars will move into the far future
51:03 - 51:06

is because we've uncovered the rules
that govern their behaviour.
51:08 - 51:13

And we've found these rules
not in the heavens, but in numbers.
51:19 - 51:25

It's only through the Code
that we can understand
the laws that govern the universe.
51:49 - 51:53

Laws that describe everything
from the motion of the planets
51:53 - 51:55

to the flight of projectile.
51:57 - 52:00

When you watch the fireball
fly through the air
52:00 - 52:02

then it appears in the first
part of its flight,
52:02 - 52:04

when it's just left the trebuchet,
52:04 - 52:08

that it's accelerating upwards
and then it begins to slow down,
52:08 - 52:10

before it stops just above me
52:10 - 52:15

and then, finally, accelerates
back down towards the ground.
52:19 - 52:22

But if you analyse the flight
using numbers,
52:22 - 52:24

it reveals something
rather surprising.
52:26 - 52:31

When you plot a graph
of the projectile's vertical speed
52:31 - 52:33

against time...
52:34 - 52:37

..you then you get a graph
which looks like this.
52:41 - 52:44

To start with,
the projectile is moving upwards
52:44 - 52:48

so it's vertical speed is positive,
but decreasing.
52:49 - 52:53

As it reaches the top of its arc,
the vertical speed becomes negative
52:53 - 52:58

as the fireball turns round
and falls back to Earth.
53:02 - 53:06

Because the graph is going like
this, it means that the projectile,
53:06 - 53:10

from the moment it leaves the
trebuchet, is actually slowing down.
53:10 - 53:15

So at no point during the flight
is it ever accelerating upwards.
53:21 - 53:26

Throughout its flight, the fireball
is accelerating downwards
53:26 - 53:29

towards the Earth
at a constant rate.
53:31 - 53:34

Something you would never realise
simply by watching it
53:34 - 53:36

fly through the air.
53:39 - 53:41

And this is a profound truth
53:41 - 53:44

about one of the fundamental
forces of nature...
53:46 - 53:48

..gravity.
53:49 - 53:53

Drop, throw, fire or launch
anything you like -
53:53 - 53:56

a rock, a bullet,
a ball or even a pot plant
53:56 - 53:59

and it will accelerate towards
the ground at a constant rate
53:59 - 54:03

of 9.8 metres per second,
per second.
54:03 - 54:06

This is a fundamental law
of gravity on our planet.
54:06 - 54:11

But it's only revealed
by changing the flight path
of the object into numbers.
54:17 - 54:21

Appreciating this simple fact
about how gravity works on Earth
54:21 - 54:26

is the first step towards
understanding gravity everywhere.
54:40 - 54:45

It's the foundation stone
of Newton's Law
of Universal Gravitation.
54:46 - 54:51

A mathematical theory that can
describe the orbits of the planets,
54:51 - 54:56

predict the passage of the stars
into the distant future...
54:59 - 55:05

..and has even enabled human kind
to step foot on the Moon.
55:09 - 55:14

The laws that command the heavens
are written in the Code.
55:26 - 55:30

'We call them the door mats,
the large ones.
55:30 - 55:33

'Two-and-a-half million years
in the future...
55:33 - 55:35

'This isn't imaginery, this is real!
55:40 - 55:44

'You don't need to know
what that means to know
that animal's not happy.
55:44 - 55:46

'Whatever circle I take,
55:46 - 55:49

'you're going to get
a number which starts 3.14.'
55:53 - 55:58

It's an incredible thought
that the only way we can
really make sense of our world
55:58 - 56:01

is by using
the abstract world of numbers.
56:01 - 56:05

And yet those numbers have allowed
us to take our first tentative
steps off our planet.
56:05 - 56:10

They've also given us the technology
to transform our surroundings.
56:12 - 56:15

'A hidden Code
underpins the world around us.
56:18 - 56:22

'A Code that has the power
to unlock the rules that
cover the universe.'
56:26 - 56:30

This place was constructed
to satisfy a spiritual need.
56:30 - 56:34

But we couldn't have built it
without the power of the Code.
56:34 - 56:40

For me, it's an exquisite
example of the beauty
and potency of mathematics.
56:51 - 56:54

From the patterns and numbers
all around us,
56:54 - 56:57

we've deciphered a hidden code.
57:11 - 57:15

We've revealed a strange
and intriguing numerical world,
57:15 - 57:17

totally unlike our own.
57:19 - 57:25

Yet it's a Code that also describes
our world with astonishing accuracy.
57:31 - 57:34

And has given us
unprecedented power to describe...
57:38 - 57:39

..control...
57:42 - 57:44

..and predict our surroundings.
57:57 - 58:01

The fact that the Code
provides such a successful
description of nature
58:01 - 58:04

is for many one of the greatest
mysteries of science.
58:05 - 58:09

I think the only explanation
that makes sense for me
58:09 - 58:11

is that by discovering
these connections,
58:11 - 58:15

we have in fact uncovered
some deep truth about the world.
58:15 - 58:18

That perhaps, the Code
is THE truth of the universe
58:18 - 58:23

and it's numbers that dictate
the way the world must be.
58:30 - 58:31

Go to...
58:34 - 58:37

..to find clues to help you solve
the Code's treasure hunt.
58:37 - 58:41

Plus, get a free set of mathematical
puzzles and a treasure hunt clue
58:41 - 58:44

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Title:: The Code S01E01: "Numbers"
Description:: This video is part of the InternsUK Open Source Academy selection.
We select and share funny and instructive videos, to allow everyone to access useful information and stimulate an ongoing personal development.
This is for an educational purpose only.

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Video Language:: English
Duration:: 59:17

	Peter Rudenko edited English subtitles for The Code S01E01: "Numbers"
	Peter Rudenko added a translation

English subtitles

Revisions

Revision 1

Peter Rudenko

The Code S01E01: "Numbers"

Revisions

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