Brian Cox: How Universal Laws Shape Nature's Forms

Unveiling Nature's Underlying Laws

• 💡 The seemingly infinite complexity and beauty of the natural world are merely a shadow of deeper, underlying laws of nature.
• 🧠 These universal laws are not only beautiful but also explain diverse phenomena, from the formation of snowflakes to the structure of stars.
• 🔍 By carefully observing naturally occurring shapes, we can glimpse the deep structure of nature itself and understand the principles that govern the universe.

Gravity's Sculpting Power

• 🌍 Planets like Earth are near-perfect spheres because gravity pulls mass equally in all directions, compacting material until it forms a round shape.
• 🥔 The concept of the "potato radius" explains that objects smaller than 100-200 kilometers lack sufficient gravity to overcome material strength, resulting in irregular, potato-like forms.
• ⚖️ Human towers demonstrate how geometry and collective force can temporarily defy gravity, but the relentless pull of gravity ultimately shapes all objects towards the Earth's center.

Mathematical Efficiency in Nature

• 🐝 Himalayan honeybees construct exquisitely engineered hexagonal honeycombs, which are a vivid solution to a deep mathematical problem.
• 📐 The honeycomb conjecture proves that hexagons are the most efficient shape for dividing a volume with the minimum amount of material, crucial for bees conserving wax.
• 💬 While mathematicians took millennia to prove this, bees instinctively (or through physical processes) utilize this mathematical law to store honey efficiently.

Physics of Form and Function

• ❄️ Icebergs float because the hexagonal structure of water molecules in solid ice makes it less dense than liquid water, a unique property among common solids.
• 💧 The water molecule's structure, with its hydrogen bonds, creates an open crystal lattice, which is reflected in the six-fold symmetry of snowflakes.
• 🌊 Manatees are notably round, as a spherical shape offers the smallest surface area to volume ratio, maximizing heat retention in cold waters, a key survival adaptation.

Evolution and Symmetry

• 🧬 The shapes of living things are sculpted by both basic physics and evolution by natural selection, which has had billions of years to adapt organisms to their environments.
• 🚶‍♀️ Bilateral symmetry, characterized by a left and right side, provides agility and orientation, conferring a significant survival advantage for mobile animals, especially predators.
• 👤 From early ocean life to humans, this fundamental body plan has been selected for, explaining why all animals with brains exhibit bilateral 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, The natural world is beautiful but complex. The skies dance with color. 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. A regular day in the snow. But if you look carefully, there's something deeper. Everyone is perfect. Pretty much 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 granny's? 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. 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. We look Carla and her friends are about to pit themselves against the force that shaped our planet. Fore! Foreign! Foreign! My knowcheech. 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. Mom and dad are here with their daughters, Mariana and Carla, to represent the town of Villa Frankie. 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 Meritt. There's the photo. 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 pushed inwards with equal force in all directions, butressing 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. foreign. Heat. Heat. Heat up 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 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. You can see why. because things uh that are too small for gravity to be strong enough to sculpt them look like they're 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 was 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 km, they're beautiful spheres. And if the radius is less than about 200 km, 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. 4 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 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 it's the first time for one of the young villagers. Min and his nephew Hero 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 Gurong people head into the mountains to exploit the bee's secret. Because it's Hera's first time, this trip will be particularly challenging. Yeah. The bees make their hives as inaccessible as possible to protect them from predators. Hey, 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 g of honey. So they benefit from building efficiently using as little wax as possible. Prime. Hey, hey, hey, hey. 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. Fore speech. Hey, hold on. Hey, there For Hira, this is all about keeping the Gurong 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? So 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. Huge paper, pages and pages of complex mathematics. And it turns out that hexagon is the most efficient shape. The bees knew what human mathematicians didn't know for thousands of years. Actually 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. 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 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 manity. 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 hurting some. It's winter and if the water temperature here drops below 20° for the manity, it's deadly. Very dangerous in warmer. Manatees like this female are vegetarians. Basically, she's a 10-ft long aquatic cow with no legs. To stay warm, she has to consume up to 50 kg of leaves and seaggrass 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, warmer reef. It's looking good. There's Doug. Doug likes it up here. Now, researcher Wayne Hartley is doing this morning's head count. Part of the manity 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, it's got to be good for your blood pressure or anything else that may aail you. biologist Amy Teg is working with Wayne to do a health check on the families. Well, he's just sort of hanging around checking things out. U manatees are very docile uh gentle creatures. Um 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°. Manity 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 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 manity 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 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 manity's natural habitat is shrinking, and they need to find warmth elsewhere. This power station helps provide energy for around 9 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 manity 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 molds 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. Fore speech. We're all the product of our experiences, our history, our culture, our lives make an indelible impression, 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. Chay and Miss Kim a henyo are women of the sea. They've grown up collecting seafood along these shores and they still do. The henyo are part of a dying tradition. Not many youngsters are interested anymore. It's hard work, especially if you're in your 70s. Right now the women are catching cunchch 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. All right, let's go. For Mrs. Chay 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. Welcome. 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. This body plant 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. 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 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 behaviors. ice. 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 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 Newf Finland 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 Newf Finland. 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. Okay. And if we lose patrol, 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. Yeah, we got some palms over here. So, you could be sailing along and doing very good seammanship looking at your radar and there's the thing all of a sudden and you're up on 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 over to some of those smaller pieces, please. Okay. Okay. Yes. Captain Manning, are we okay to put the diary? 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 ft. And we were just pinging 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 fully apart. Yeah. These giant frozen mountains are born from the most innocent beginnings, snowflakes. Over thousands of years, they're compressed to form glacias that then break off to form icebergs. An average one weighs 200,000 tons. 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 firsthand observations. basically have a good look at one side of the bed between the surface and 30 mters. 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 heart in the center of your chest where the iceberg is 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 there's even more of that uh anticipation and excitement that goes on in the in the lower part of your belly. So you swim in and you begin to see the details. You begin to realize that this is not a a flat wall of ice going into the depths. This has tiny little dimples on it, which it's 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 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 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 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. 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 bond into that leg. So you can see you build up 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 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 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 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 sightes 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 if 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 that starlike sharp structures on snowflakes. But then here 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. 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. I mean 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 atomic nuclei of oxygen together. And then you need to understand about symmetry and symmetry breaking. All the fundamental ideas that underly modern physics uh 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, 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.```