Original subtitles

The natural world is beautiful...

...but complex.

The skies dance with colour.

Yay! Yes!

Shapes form...

...and disappear.

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.

A regular day in the snow.

But if you look carefully,

there's something deeper.

This is fun!

Every one...

...is perfect, pretty much.

It looks like they've been cut out of thin paper.

I got one.

Snowflakes are complex, intricate things.

They are 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 has 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 snow crystals stuck to the bubble.

Oh! Wow!

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 and her friends are about to pit themselves

against the force that shaped our planet.

These children are going into battle...

...with gravity.

Towns from across Catalonia...

...have gathered to enter into a fierce competition...

...to build a human tower as high as possible.

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.

The family put their trust

in the most experienced members of the team, like David Merit.

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.

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.

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

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 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,

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 is 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.

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 is 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,

of between 100 and 200km.

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 200km,

they're beautiful spheres,

and if their radius is less than about 200km,

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.

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

But when you're the size of a planet, spheres come naturally.

4.5 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 a 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 honeybee.

The largest species of honeybee on the planet.

And collecting honey from under their watchful compound eyes

is one of the most dangerous jobs you could imagine.

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

Min and his nephew Hira 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,

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.

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.

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 Hira, 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 is 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 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.

It's winter,

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

Due to cool temperatures Friday morning...

...for the manatee, it's deadly.

...very dangerous, in search of warmer aquatic environments.

Manatees, like this female, are vegetarians.

Basically, she is a 10ft long aquatic cow with no legs.

To stay warm, she has to consume up to 50kg of leaves and seagrass

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.

Looking good.

There's Doug.

Doug likes it up here now.

Researcher Wayne Hartley is doing this morning's headcount,

part of a manatee census.

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.

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

And they are so peaceful.

They are so calm.

Just watching manatees has got to be good for your blood pressure,

and 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.

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 the 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.

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

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 300km 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 is 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 shape of living things

without understanding their evolutionary history.

We are 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.

Mrs Chae and Miss Kim

are haenyeo, are women of the sea.

They've grown up collecting seafood along these shores.

And they still do.

The haenyeo are part of a dying tradition.

Not many youngsters are interested any more.

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

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 Chae 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 - 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 fast predators

and skittish, speedy prey.

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.

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 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.

You know, 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.

They are big, big, heavy objects.

Far bigger than anything that 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 oilfields

off the coast of Newfoundland.

This team are here to help protect

those multibillion 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 control,

then we take it in and 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 with the same cross-sectional area.

Yes, we've got some here.

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 can 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.

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.

We'll go over to some of those smaller pieces.

OK. OK.

Yes, Captain Manning, we are OK to put the diver...

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 berg.

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 compress 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.

I'll basically have a good look at one side of the berg

between the surface and 30 metres.

Tell them what I saw,

and it will mean that they can interpret the sonar

the data that comes back.

They will 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 will be this really loud thud,

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 wall of ice

going into the depths.

This has tiny little dimples on it.

It 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 helps 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 a 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 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 hydrogen 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 sixfold 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 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 hexagonal if you like,

and some bits a bit rough,

then water molecules are more likely to bind

to the rough bits than the flat bits.

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 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 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 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 and 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.

When you look at a snowflake, you see history...

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

Look 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 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!

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,

like 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?

♪ You are my lucky star

♪ You open heaven's portals

♪ Here on Earth for this poor mortal

♪ You're my lucky star. ♪