Original subtitles

The natural world is beautiful, but complex.

The skies dance with colour.

Shapes form...

..and disappear.

But this seemingly infinite complexity is just a shadow of something deeper.

The underlying laws.

The laws of nature.

The world is beautiful to look at, but it's even more beautiful to understand.

A regular day in the snow.

But if you look carefully, there's something deeper.

Everyone...

..is perfect, pretty much.

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

I got one!

Snowflakes are complex, intricate things.

But 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 tantalisingly 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 shape 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.

Wow, I can see a star.

It really looks like a snow crystal stuck in a bubble.

There's 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.

Carla, it's your turn now.

I want, I want, I want...

What's possible?

Carla and her friends are about to pit themselves

against the force that's shaped our planet.

Because it's the first time that I've gone to a hole.

And when it's nine o'clock in the morning, everyone is going to jump to the surface

Well, it's very exciting.

You get very nervous.

Very nervous for them, very nervous for everything to

go well, for them not to fall, for them not to get hurt.

What you feel is a beastly emotion, because you get goose bumps and sometimes

you are about to cry before starting to build castles.

These children are going into battle, with gravity.

Towns from across Catalonia have gathered to enter into a fierce competition,

to build a human capital.

A tower as high as possible.

Mum and dad are here with their daughters, Mariona

and Carla, to represent the town of Villafranca.

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.

There is a lot of nerves, because there are many people.

The family put their trust in the most experienced members of the team,

like David Miret.

Depression of the stage, right?

In addition, the Plaza de Braus has this circular shape, the sound is very loud and

it is a wave, a wave.

From the outside, it may seem that we are a group of people, that we climb up and

that we pile up in an anarchic way, totally, without any rigor.

The first one is the last one!

But no, not all structures have...

David feels the weight of everyone above him.

His gravity pulls them down to the ground.

And he knows the secret to defying gravity is geometry.

They are symmetrical below, they have their own line, they create concentric

lines towards that point, so that the forces go concentrically.

To support David, and eventually the kids, the rest of the town all pushed 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.

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

When Carla and Mariona climb up the castle, I have

to follow the castle from the bottom to the top.

I can't be without looking at the castle.

When I climb up the castle, I try not to fall.

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 down.

They're falling towards the ground.

They're falling towards the centre 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...

would be so massive...

that the gravitational pull on its surface would 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.

Now, you could 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.

And you 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 kilometres.

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 will find that, roughly speaking...

if their radius is bigger...

than about 200 kilometres...

they're beautiful spheres.

And if the radius is less... than about 200 kilometres...

they look more like misshapen potatoes.

So you can calculate it.

If you're small...

spheres don't come easily.

Even asteroids or moons... don't quite manage it.

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

But when you're 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.

But that's nothing...

for the young villagers.

Today... it's the first time... for one of the young villagers.

Min and his nephew Herah...

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

It's prized... for its medicinal properties...

and sells for a high price.

The local culture...

protects the whole place... by its magic.

Be careful...

when you are walking on... these roads...

Hidden beneath the seething mass of bodies sits

a network of exquisitely engineered hexagons.

The bees appear to be master builders, performing

structural calculations with architectural precision.

The bees benefit from a hidden mathematical 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 Hira's first time, this trip will be particularly challenging.

If you want to eat honey, you have to dig a hole.

This is the new honey that I learned from Niravani.

This is Hira's honey.

I don't know if it will work or not.

Uncle, let's start from the beginning.

Hey,

let's start from the beginning.

Hey, take it.

The bees make their hives as inaccessible as possible to protect them from predators.

The hives the bees are defending contain a vivid,

visible solution to a deep mathematical 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.

In the beginning, I was a little scared of primers.

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.

At first, I was a little scared.

But when I got to the bank, I realized that it's okay.

I have my own mind.

Before I started learning, I was a little scared.

I was afraid.

Maybe.

But it is a good thing, always.

When I see the honey, I start working on it.

For Hiro, this is all about keeping the Gurung tradition of honey hunting alive.

When the hexagon is at the heart of it all.

I just want the honey to keep on growing.

How 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 say, that the bees 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.

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 way.

There's 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 behaviour?

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.

And 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 centre 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.

Several manatees are hunting some mothers and cats.

There they are.

It's winter.

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

Do you think the temperature's Friday morning?

..for the manatee, it's deadly.

Very dangerous in terms of warmer and hotter environments.

Manatees, like this female, are vegetarians.

Basically, she's a ten-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.

Lemon?

On the roof?

No.

Looking good.

There's Doug.

Doug likes it up here now.

Researcher Wayne Hartley is doing this morning's

head count, part of the manatee census.

It's a special thing to come to work.

You 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, it's got to be good for your

blood pressure or anything else that may ail you.

Biologist Amy Tegg is working with Wayne to do a health check on the families.

Well, he's just sort of hanging around, checking things out.

Manatees are very docile, gentle creatures.

But they are very curious.

Anything new in their environment, they often like to come check out.

So he's probably just checking me out.

Yeah, he's just chewing on my flipper.

It's got 23.5 degrees Celsius.

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.

With the cold stress, they don't eat.

Their immune system shuts down.

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

They really require warm water.

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 of 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.

The manatee is a manatee.

Sorry, their breath stinks.

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

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 kilometres away.

Where their 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 sculpt and restrict 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.

Evolution by natural selection moulds living things over 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 shapes.

The shapes of living things.

Without understanding their evolutionary history.

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 are 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.

I'm Kim Sun-duk.

I'm 73.

Mrs. Choi and Ms. Kim, the Henyo, are women of the sea.

They've grown up collecting seafood along the shores.

But they still do.

The haenyeo are part of a dying tradition.

Not many youngsters are interested in one.

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

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 freediving 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.

For Mrs Choi, and Miss Kim, this is all about the search for food.

Calming sensation

For Mrs Choi and Miss Kim, this is all about the search for food.

And that's where the symmetrical structure of their bodies comes in.

A blueprint that started out here in the oceans, hundreds of millions of years ago.

Very few animals have steered clear of it.

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,

organising 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.

A 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.

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 and ingenuity.

And the ability to catch fast predators.

And skittish, speedy prey.

It's been a long time since we've had such strong waves.

I caught a lot today.

When I catch a lot, I feel good.

I feel like I'm going to fly.

But if I can't catch this, I feel bad.

I feel like I'm going to die.

I'm going to die.

I'm going to die.

I'm going to die.

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.

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 of 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.

Bingo!

Bingo!

Oh, bingo!

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 story, the underlying laws of

nature, can lead to seemingly infinite complexity.

Because snowflakes form in minutes and are 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 behaviours.

Ice.

涄 You know, it's so mystical when you leave in a morning in the fog.

You're just looking around.

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

They're big, big heavy objects.

Far bigger than anything we've created floating on the sea.

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

past Newfoundland, which ended up sinking the Titanic.

Doug Allen 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 you put it back in the water again, OK, and if we lose, well, then we take it

in, we secure it, and if that goes nowhere, we go home.

The big problem with icebergs is simple.

They float.

Iceberg ice reflects radar 69 times less effectively

than a ship of the same cross-sectional area.

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.

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.

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.

Doug is a specialist cold water diver.

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

Go on up to some of those smaller pieces, please.

Okay.

Okay.

Yes, Captain Manning, are we okay to put the divers on?

Rick Stanley is looking after safety.

Who knows what's going to 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.

And we were just pottering 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.

This is a huge bird.

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

Yeah.

These giant frozen mountains are born from the most innocent beginnings.

Snowflakes.

Over thousands of years, they're compressed to

form glaciers, but 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.

I basically have a good look at one side of

the bed between the surface and 30 metres.

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 centre 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.

So you swim in and you begin to see the details.

You begin to realise that this is not a flat boat.

This is a wall of ice going into the depths.

This has tiny little dimples on it which almost looks like a giant golf ball.

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.

For all their unpredictability, there is regularity in the behaviour 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 behaviour.

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're surrounded by negatively charged electrons.

That's what sticks the atoms together.

The negatively charged electrons tend to cluster around the oxygen nucleus,

leaving those two legs of hydrogen slightly positively charged.

That means that those positive charges can attract other There are other negatively

charged ends of other water molecules.

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

On 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 hydrogenate bonding to 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 a 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 everyone 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's 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 bit will accumulate more molecules than the flat

bit, and it'll build up faster until it gets flat.

And then it'll 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'll grow quickly.

There are lots of water molecules available.

So it'll 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 into 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.

When you look at a snowflake, you see history

and the deep structure of nature condensed.

Into a frozen moment.

How many stars it is together?

You can see them so clearly.

You look.

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 electromagnetism 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 underlie modern physics can

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

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 snowstorm, 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?