Original subtitles

BRIAN COX: The natural world is beautiful

but complex.

The skies dance with color.

CHILDREN: Yay! Yeah!

COX: Shapes form

and disappear.

(CROWDS CHEERING)

But this seemingly infinite complexity

is just a shadow of something deeper,

the underlying laws of nature.

The world is beautiful to look at

but it's even more beautiful to understand.

Come on.

COX: A regular day in the snow.

CHILD: Bingo! Bingo!

COX: But if you look carefully,

there's something deeper.

CHILD: This is fun.

Everyone is perfect, pretty much. (CHUCKLING)

Looks like they've been cut out of thin paper.

I got one.

Snowflakes are complex intricate things. They're all different,

but there's something similar about them.

They are beautiful.

But there is also, I think, a deeper beauty,

and that beauty is in an idea.

The idea is that all the similarities and difference,

the structure of snowflakes, can be explained

using a few simple laws of nature.

And that idea goes to the very heart of science,

because those laws themselves are beautiful and they're universal.

They can explain so many things from snowflakes to stars.

How do snowflakes form?

Why are they all different and yet tantalizingly similar?

These are questions that can be asked about any

naturally occurring structure.

Why are beehives regular hexagons?

Why do icebergs float?

Why are planets spherical?

And what's this got to do with free-diving grannies?

The answers allow us to glimpse

the underlying laws of nature that shaped them.

This is why when you look at a snowflake,

you're peering beyond the everyday world.

At the deep structure of nature itself.

The universe in a snowflake.

GIRL: Wow, it's like a little star.

It really looks like snow crystals stuck in a bubble.

GIRL: (GASPS) Aww...

(IN DISTINCT TALKING)

Wow!

COX: There '5 a shape that appears at all scales in the universe.

Seen from space,

the Earth is a near-perfect sphere,

sculpted by one of the fundamental forces of nature.

(SPEAKING OWN LANGUAGE)

Ah!

Carla and her friends are about to pit themselves

against the force that shaped our planet.

(SPEAKING OWN LANGUAGE)

(CROWDS CHEERING)

(CROWDS CHEERING)

(CROWDS CHANTING)

(SPEAKING OWN LANGUAGE)

(SPEAKING OWN LANGUAGE)

COX: These children are going into battle

with gravity.

(CROWDS CHEERING)

(CROWDS CHANTING)

COX: Towns from across Catalonia

have gathered to enter into a fierce competition.

To build a human tower

as high as possible.

(SPEAKING OWN LANGUAGE)

COX: Mum and dad are here with their daughters

Mariana and Carla

to represent the town of Vilafranca.

People of all ages take part,

but it's the lightest members of the team,

children as young as five,

who ascend daringly to the summit.

(SPEAKING OWN LANGUAGE)

COX: The family put their trust in the most experienced

members of the team,

like David Miret.

(DAVID SPEAKING OWN LANGUAGE)

COX: David feels the weight of everyone above him

as gravity pulls them down to the ground.

And he knows the secret to defying gravity

is geometry.

COX: To support David and eventually the kids,

the rest of the town all push inwards

with equal force in all directions

buttressing the tower from all sides.

And this results in the emergence of a symmetrical shape

a circle.

No other shape gives the tower such strength.

But gravity

is unforgiving.

Ana' that's a worry if your child is climbing to the top.

(SPEAKING OWN LANGUAGE)

(SPEAKING OWN LANGUAGE)

(CROWDS APPLAUDING)

(CROWD CHEERING)

COX: It's clear that the force of gravity

is unrelenting.

The collapsing towers

are shadows of the process that shaped our planet.

These people aren't just falling towards the ground,

they're falling towards the center of the Earth.

And the Earth's gravity pulls everything down

from people to snowflakes,

to the very rock that the Earth is made of.

And this is ultimately, why the Earth is spherical.

So why does gravity sculpt things into spheres?

Well, the first thing to say is that it doesn't, necessarily.

If I pick up a snowball,

it's not spherical, kind of an irregular shape.

But if I apply pressure to it

and squash it evenly in all directions,

then I can turn that into a sphere.

And that is what's happening with gravity.

As I start adding mass to it,

that gravitational pull becomes bigger.

So, I'll get to a point where this snowball,

if I kept adding mass to it,

will be so massive

that gravitational pull on its surface will be so strong

that it would start to squash the material out of which it's made.

In this case, snow,

or in the case of a planet or moon, the rock.

That pressure exerts on the surface equally in all directions,

because gravity works equally in all directions.

Well, you can ask the question, "How much matter do I need"

"for gravity to get strong enough"

"to start overcoming the strength of rock"

"and sculpting things into spheres?"

Well, that minimum size has got a name,

it's a brilliant name, it's called the Potato Radius.

You can see why, because things that are too small for gravity

to be strong enough to sculpt them look like misshapen potatoes.

The great thing is you don't even need to imagine it.

You can calculate it.

I did that this morning.

And I got an answer, just roughly between 100 and 200 kilometers.

The brilliant thing, the most beautiful thing

is if you look up into space

and look at the moons of Mars and Saturn and Jupiter

and objects out there in the solar system,

you'll find that, roughly speaking,

if their radius is bigger than about 200 kilometers,

they're beautiful spheres.

And if the radius is less than about 200 kilometers

they look more like misshapen potatoes.

So, you can calculate it.

COX: If you're small,

spheres don't come easily.

Even asteroids or moons don't quite manage it.

The potato shape might be as close as you can get.

But when you are the size of a planet,

spheres come naturally.

Four and a half billion years ago,

rocks circling the sun began sticking together

until they had sufficient mass for gravity to really get to work

turning potato shapes

into one very important sphere

suspended in space.

A universal law sculpted the familiar, elegant,

symmetrical shape of our planet.

But closer to the surface, it's littered with endless shapes and forms.

And in every one of these naturally occurring structures,

there are simple underlying laws waiting to be glimpsed.

Here in the Himalayas

there's a shape that's a shadow of a fundamental mathematical law.

It's guarded by the Himalayan honey bee,

the largest species of honey bee on the planet.

And collecting honey from under their watchful compound eyes

is one of the most dangerous jobs you could imagine.

(SPEAKING OWN LANGUAGE)

And today is the first time for one of the young villagers.

Min and his nephew, Hiro,

will be the ones leading the hunt for the precious honey.

It's prized for its medicinal properties and sells for a high price.

Hidden beneath the seething mass of bodies

sits a network of exquisitely engineered hexagons.

The bees appear to be master builders

preforming structural calculations with architectural precision.

The bees benefit from hidden mathematic law

that explains why they build hexagons to store their honey.

And twice a year, the Gurung people head into the mountains

to exploit the bees' secret.

Because it's Hiro's first time,

this trip will be particularity challenging.

The bees make their hives as inaccessible as possible

to protect them from predators.

(BELL CLANGING)

The hives the bees are defending contain a vivid visible solution

to a deep mathematic problem and a very practical one.

They need to store honey to sustain their colony

through the long winter months.

They build their hives out of wax.

But for every gram of wax a bee produces

it will have to consume more than six grams of honey.

So they benefit from building efficiently

using as little wax as possible.

Each sting is like a hypodermic needle.

After the bees sting, they die,

the ultimate sacrifice to guard the hexagons and the honey they hold.

For Hiro, this is all about keeping

the Gurung tradition of honey hunting alive.

And the hexagon is at the heart of it all.

So why do bees build hexagonal honeycombs?

Well, that is in fact a very good question.

It's actually a mathematical question.

The problem is how do I divide up a volume

into shapes of equal size using the minimum amount of stuff?

Now, why does that matter to a bee?

Because that stuff is wax and wax is extremely valuable to the bees.

So what shape should it be?

Should it be squares or should it be triangles?

You can see it can't be circles,

because circles, when you pack them together, leave gaps.

So they're not very efficient.

Or could it be that hexagons are the most efficient?

Well, that is actually a simple sounding question with a very complicated answer.

It's one of the oldest questions in mathematics.

It's got a name actually, it's called the Honeycomb Conjecture.

Mathematicians have worked on it for thousands and thousands of years,

and it's only recently that the Honeycomb Conjecture was proved.

Here's one of the proofs.

A huge paper,

pages and pages of complex mathematics,

and it turns out that the hexagon is the most efficient shape.

The bees knew what human mathematicians didn't know for thousands of years.

Actually, I'm using "know" in quite a loose sense there.

There's still a great deal of debate amongst biologists

as to how the bees actually do it.

Do they build hexagons from scratch

using some kind of instinctive behavior?

Or do they in fact build a simpler shape, perhaps circles,

and then because the wax heats up, it can deform,

and the laws of physics themselves change the circles into hexagons.

That's still not agreed upon.

But what is agreed upon by the mathematicians and the bees

is the hexagon is the most efficient shape.

That just shows you it's a beautiful thing.

Mathematics is the universal language.

I mean, when you look at a perfect honeycomb,

you see a shadow of that language of mathematics

made real by bees.

Perfect shapes reveal simple laws.

Whether it's spherical planets sculpted by gravity,

pulling us to the center of the Earth,

or the mathematically refined efficiency of hexagonal honeycombs,

simple laws underpin the shapes we can see,

and they're universal.

But the action of these simple laws

seems at odds with the complex shapes of life.

These shallow springs are home

to one of nature's seemingly less elegant shapes,

the manatee.

Like all marine animals, they're free from the effects of gravity.

No need for strong bones to support their weight,

but they don't have complete freedom from the laws of physics.

MAN: (ON RADIO) Several manatees...

COX: It's winter,

and if the water temperature here drops below 20 degrees...

WOMAN: (STATIC) Due to cold temperatures Friday morning...

COX: For the manatee, it's deadly.

WOMAN: (STATIC) Can be very dangerous...

In search of warmer aquatic environments...

COX: Manatees, like this female, are vegetarians.

Basically, she's a 10-foot-long aquatic cow with no legs.

To stay warm, she has to consume up to 50 kilograms

of leaves and sea grass every day.

And the females here are eating for others, too.

This one is suckling two young calves.

And the weather is only getting colder.

WAYNE HARTLEY: Ooh, Lemon...

Ruth.

Looking good.

Oh, there's Doug. Doug likes it up here now.

COX: Researcher Wayne Hartley is doing this morning's head count,

part of the manatee census.

HARTLEY: It's a special thing to come to work,

come down in the morning

and it's quiet.

The steam's coming off the water.

You can hear the manatees out there breathing. It's just "whoosh."

And they are so peaceful, they are so calm.

Just watching manatees has gotta be good for your blood pressure

or anything else that may ail you.

COX: Biologist Amy Teague is working with Wayne

to do a health check on the families.

AMY: He '5 just sort of hanging around, checking things out.

Er, manatees are very docile, uh, gentle creatures.

Uh, but they are very curious, anything new in their environment

they often like to come check out.

Uh, so he's probably just checking me out.

Yeah, he's just chewing on my flipper.

Got 23.5 degrees Celsius.

COX: Manatee families are drawn in from colder waters

because this is a hot spring.

And some make it just in time.

He is severely cold stressed.

HARTLEY: With the cold stress, they don't eat.

Their immune system shuts down.

AMY: They're here to keep themselves alive in the winter.

They... They really require warm water.

COX: It might look like these animals keep warm using blubber, like seals,

but they're not fat, they're round.

In terms of pure physics, the best way to stay warm is to be a sphere.

It has the smallest surface area-to-volume ratio of any shape,

less area for heat to escape from.

A beautiful example with a naturally occurring shape

reflecting a deeper mathematical law,

the manatee could well be the most spherical mammal on Earth.

What a wonderful thing to be.

Sorry, their breath stinks.

(LAUGHS)

HARTLEY: To me, it smells like the inside of a hot truck tire.

COX: But, of course, they're not perfect spheres.

There are many other competing factors that determine their shape.

Like all animals, they have to live, breathe, eat,

and move.

The manatee's natural habitat is shrinking,

and they need to find warmth elsewhere.

This power station helps provide energy for around nine million people.

And, in the process,

warms the water that keeps over half of Florida's manatees alive

through the winter.

The same families that Wayne and Amy study

can end up here, over 300 kilometers away,

where the mothers and calves can hold on to as much heat as possible

because of their round bodies.

To a physicist,

the perfect shape for a manatee would be a symmetrical sphere,

but biology complicates things.

Manatees can't just bob around waiting for food

or warmth to come to them.

They need fins and a tail to move around

whether that's to a hot spring or to a power station.

The forces of nature sculpts and restricts the shapes of all things,

the inanimate, like pebbles or rocks or cliffs,

or living things.

But, of course, basic physics is not the only force shaping life.

(BEES BUZZING)

Evolution by natural selection molds living things of a time

in response to their environment

and their interaction with other life forms,

and it's had billions of years to do it.

So, you can't understand the shape of living things

without understanding their evolutionary history.

(WOMAN SPEAKING KOREAN)

COX: We're all the product of our experiences.

Our history, our culture, our lives, make an indelible impression

and make us all different.

But we're also all similar,

not just to each other as human beings but to countless other animals on Earth.

We are obviously related.

Most obviously, through the symmetry of our bodies.

(WOMAN SPEAKING KOREAN)

(WOMAN SPEAKING KOREAN)

Mrs Chae and Miss Kim are Haenyo or Women of the Sea.

They've grown up collecting seafood along these shores,

and they still do.

(WOMAN SPEAKING KOREAN)

(LOCAL FOLK MUSIC PLAYING)

The Haenyo are part of a dying tradition,

not many youngsters are interested any more.

It's hard work, especially if you're in your 70s.

(MISS KIM SPEAKING KOREAN)

COX: Right now, the women are catching conch or sea snails.

It's a crucial time of year when they have a chance to make the most money.

The tradition of free diving for food

is part of these women's cultural history.

But the details of the human form itself,

in particular, its symmetry that allows them to dive, swim, and hunt

is part of their evolutionary history.

(SPEAKING KOREAN)

COX: For Mrs Chae and Miss Kim, this is all about the search for food,

and that's where the symmetrical structure of their bodies comes in,

their blueprint that started out here in the oceans

hundreds of millions of years ago.

Very few animals have steered clear of it.

(EXCLAIMS)

(WOMAN SPEAKING KOREAN)

COX: Life is, and always has been, a competition.

In a free-floating world,

life grew to adopt different types of symmetry

to get what it needed.

Some animals became round or radially symmetric

organizing their sensory organs around a central axis.

Rather than chasing down food, they waited for food to come to them.

But in order to really go after prey, you need to leave that strategy behind.

You need to be divided down the middle.

That gives you two sides, bilateral symmetry.

Basically, you have a left and a right.

And you can build on this plan,

with arms to grab and search and a head and a tail.

All this means you can orientate yourself

and really target your prey.

(SPEAKING KOREAN)

COX: This body plan has been selected for over hundreds of millions of years.

It confers a survival advantage.

And it turns out that all animals with brains are bilaterally symmetrical.

Bilateral symmetry provided the agility that drove a spiral

of cunning fast predators and skittish speedy prey.

(SPEAKING KOREAN)

COX: The beautiful symmetry of the human body, which we all take for granted,

is the product of a sweeping majestic story

stretching back to some of the earliest life on Earth.

COX: So we can understand the symmetry of organisms

by understanding their history.

You're essentially seeing the results of evolution by natural selection

over hundreds and millions, even billions of years.

But how do you understand the structure and symmetry of a snowflake?

There's no natural selection here.

There's no DNA to record and reproduce information.

These things arise spontaneously from basic laws of physics.

GIRL: Bingo! Bingo!

Oh, bingo!

COX: The intricate beauty of a snowflake is at first sight baffling,

given the simplicity of their story.

But in fact, it's a gift.

A gift of almost nothing.

One frozen moment

that can reveal how the underlying laws of nature

can lead to seemingly infinite complexity.

Because snowflakes form in minutes and they're made out of a single ingredient

with strange properties that give rise to a vast array

of naturally occurring forms of all shapes, sizes, and behaviors.

Ice.

(FOG HORN)

NEIL RIGGS: It's so mystical when you leave in the morning in the fog.

You're just looking around

and then you see these shapes that come out of the fog.

(FOG HORN)

DOUG ALLAN: They are big, big heavy objects,

far bigger than anything that we've created, floating on the sea.

(FOG HORN)

We've got to remember, it was an iceberg that sailed passed Newfoundland

which ended up sinking the Titanic.

COX: Doug Allan is here because it's iceberg season.

He's part of a scientific expedition.

Every summer, thousands of icebergs float south from the Arctic

into the shipping lanes and oil fields off the coast of Newfoundland.

This team are here to help protect those multi-billion-dollar industries

by trying to understand more about where the icebergs are heading.

The man leading the expedition is Neil Riggs.

So, we put it back in the water again, OK,

and if we lose control, then we take it in, we secure it.

And if that goes nowhere, we go home.

COX: The big problem with icebergs is simple.

They float.

RIGGS: Iceberg ice reflects radar 69 times less effectively

than a ship with the same cross-sectional area.

(INDISTINCT)

So, you could be sailing along and doing very good seamanship,

looking at your radar, and there's the thing, all of a sudden,

and you're upon it.

And it's still a massive piece of ice relative to your ship.

So, it could make a nice little hole.

COX: The team will have to understand the influence

of a large number of variables if they are to distinguish

between harmless icebergs and dangerous ones.

ALLAN: It's a complicated jigsaw.

It's a little bit... You could think of it as a crime scene

where you have the forensic people go in and they pick up little bits of clues,

and together, you make a bigger picture.

What I'm doing is just adding my little piece to the overall picture

and hopefully helping their mathematical models to be more real.

COX: Doug is a specialist cold-water diver.

It's his job to photograph the underside of the icebergs.

We'll go over to some of those

- smaller pieces. - OK.

OK.

Yes, Captain Manning, we are OK to put the divers in the water now...

COX: Rick Stanley is looking after safety.

RICK STANLEY: Who knows what's gonna happen.

There's so much pressure in this ice that it blows, it explodes.

But there's pressure in there that can blow a piece of iceberg off the ice

probably 15 or 20 feet.

(RUMBLING)

ALLAN: And we were just puttering around and suddenly,

with no warning at all, the whole thing split in half,

and it was almost like it was all falling into each other.

This might be a bit unstable.

- I'm not... - This is a huge berg.

I'd rather dive round one that wasn't falling apart.

Yeah.

COX: These giant frozen mountains

are born from the most innocent beginnings.

Snowflakes.

Over thousands of years, they're compressed to form glaciers

that then break off to form icebergs.

An average one weighs 200,000 tonnes.

And that, give or take, is around 100 trillion snowflakes

that form the structures that the expedition is trying to model,

using a combination of sonar robots and Doug's first-hand observations.

ALLAN: I basically have a good look at one side of the berg

between the surface and 30 meters.

Tell them what I saw and it will mean that they can interpret

the sonar data that comes back.

They'll get a better idea of it if I've seen it for myself.

It's quite eerie going down the side of the iceberg.

You're going down into the darkness, into the blue, into the green,

and very occasionally there'll be this really loud thump,

just like someone had hit you with the flat of their hand

in the center of your chest,

where the iceberg is banging on the bottom.

You really don't want to go too far down

because there is a real danger of being squished by the iceberg underneath.

Well, you always worry when divers are in the water. But iceberg diving

there's even more of that anticipation and excitement that goes on

in the lower part of your belly.

ALLAN: So you're swimming and you begin to see the details.

You begin to realize that this is not

a flat wall of ice going into the depths.

This has tiny little dimples on it. Which...

It almost looks like a giant golf ball.

COX: These features are added to the models

to understand how they affect the way the icebergs float

and travel over long distances and into the shipping lanes.

It's good to contribute to science at a basic level like this

when the science is still developing,

to come in, take some shots which help the scientists.

That's really useful.

COX: For all their unpredictability,

there is regularity in the behavior of icebergs

if you look carefully and ask the right questions,

which is what science is all about.

And the simplest question of all

is about the most obvious part of their behavior.

Why does ice float?

That's not a naive question

because no other commonly occurring solid floats on its own liquid.

The answer lies in the structure of the water molecule itself.

Think of what a molecule is. Take a water molecule, for example.

It's two hydrogen atoms stuck to an oxygen atom.

That's two hydrogen nuclei,

which have positive electric charge

sticking to an oxygen nucleus,

which has a positive electric charge.

And they are surrounded by negatively charged electrons.

That's what sticks the atoms together.

See, the negatively charged electrons

tend to cluster around the oxygen nucleus

leaving those two legs of hydrogen slightly positively charged.

That means those positive charges

can attract other negatively charged ends

of other water molecules.

So, an oxygen can come and orientate itself and bond to that leg.

The other side, another oxygen from another water molecule

will be attracted to the positive charge and bond to that leg.

On the top, you get a hydrogen in and bond into that leg.

So, you can see, you build up a structure.

An open crystal structure.

A shape which is actually hexagonal.

And it's that property, that open structure,

which is a reflection of the underlying structure

of the water molecule itself,

that leads to the solid ice being less dense than the liquid.

And that is why ice cubes and icebergs float on liquid water.

The hexagonal structure of ice

is a shadow of the forces of nature that hold molecules together.

Forces that shape every molecule of water

and that create the six-fold symmetry of snowflakes.

You can tell they're all the same thing. They're all six-sided.

And yet, you can also see, just by eye,

that every one is different, some are radically different.

It's very difficult to imagine how all this beauty and complexity

could emerge spontaneously from a few simple laws of nature.

As snowflakes fall through the sky,

they form and grow around a symmetrical framework.

So if you start with an ice crystal and some part of it has got a flat bit,

part of the hexagon, if you like, and some bits a bit rough,

then water molecules are more likely to bind

to the rough bit than the flat bit.

There are basically more ways for them, more sites for them to stick to.

So, that means that the rough bits

will accumulate more molecules than the flat bits,

and it will build up faster until it gets flat.

And then, it will slow down.

So, there's a tendency for the underlying structure

of the ice crystals themselves to get echoed into bigger and bigger units.

Then, there's a second process called branching or the branch instability.

That happens when the snowflake

goes into a particularly humid region in a cloud.

So, that's a region where there are lots of water molecules available.

So, you get a little bump on the flat surface.

That bump is more likely to have water molecules bind to it.

It's got more binding sites, if you like,

so it will grow quickly

if there are lots of water molecules available.

So, it will grow into a spike,

and then other bumps can appear, and they'll grow into spikes.

So that's how you get that star-like sharp structures on snowflakes.

But, then, if the snowflake drifts back into a region that's less humid,

so there are less water molecules available,

then the faceting takes over again.

And smooth edges, hexagonal structures start to form.

Then, it goes into a humid region,

and the branching takes over and you get the branches.

It's a wonderfully complex and intricate process.

And the thing I find most beautiful about it

is that when you look at a snowflake, then you can read its entire history.

You can see its history made solid.

Every individual snowflake has a different history.

Every snowflake

followed a slightly different path through the clouds onto the ground.

And that means every snowflake grew in a subtly different way.

And that's why no two snowflakes are ever alike,

because no two paths through time are ever alike.

COX: When you look at a snowflake, you see history

and the deep structure of nature condensed into a frozen moment.

CHILD: Look how many stars it is together.

WOMAN: You can see them so clearly.

You look.

COX: It is wonderful, you know, that when you think about it,

the whole universe, the whole of physics is contained in a snowflake.

To describe them, you need all four forces of nature.

You need gravity to allow the snowflake to fall down

through the clouds and onto the ground.

You need electro magnetism

to stick all those water molecules together

to form these beautiful crystals.

You need the nuclear forces to stick the atomic nuclei

of oxygen together.

And then you need to understand about symmetry

and symmetry breaking.

All the fundamental ideas that underline modern physics

can be thought of in the journey of a snowflake to the ground.

Oh, look, how many stars do you think there are?

Oh, wow!

COX: Every snowflake shares the same building blocks,

the same basic beautiful symmetric forces of nature

at their heart.

But because of their histories, because of the way they formed,

they're all different.

And so it is with solar systems, so it is with planets,

and so it is with people.

We're all made out of the same building blocks,

but we're all slightly and magnificently different

because of the history of our formation.

The structures we see in the universe, stars and planets

and trees and snowflakes

are shadows of something deeper.

They mask an underlying beauty and simplicity.

But isn't it a beautiful thought that our origin and evolution,

just like the structure of a snowflake

in a snow storm, can be explained

by a few simple natural laws.

And isn't it a wonderful idea

that that thought came from just looking carefully at nature

and trying to understand it.

(MUSIC PLAYING)