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Corals build themselves homes of limestone in the warm, clear, shallow seas of the tropics. Their reefs occupy less than one tenth of one per cent of the ocean floor, yet they are home to a quarter of all known marine species. The broad-club cuttlefish has found its place by using a hypnotic display that apparently mesmerizes its prey, causing it to let down its defences. On the Great Barrier Reef a remarkable grouper uses sign language, dubbed the headstand signal, to reach out to an entirely different creature, a reef octopus, to flush small fish out of their hiding holes and into the groupers waiting mouth.

The big blue is the world's greatest wilderness, far from shore and many kilometres deep. It's a vast marine desert where there is little to eat and nowhere to hide. Yet it's home to some of the biggest and most spectacular creatures on earth. This episode reveals what it takes to survive in this savage and forbidding world. We witness feats of incredible endurance, moments of high drama and extraordinary acts of heart-wrenching self-sacrifice. Every animal in the big blue must find their own unique way to survive. Sperm whales have the largest brains in the world. They live for 80 years, and we are only now beginning to learn the extraordinary complexity of their language of clicks - thought to coordinate the whole family in everything from childcare to hunting. With special pressure-proof cameras, we witness record-breaking feats of endurance as they hunt for squid a kilometre down into the abyss. Only recently have we begun to solve the mystery of where baby turtles disappear to in their early years. They leave the crowded waters of the coast and head to the open ocean, where they use floating debris like logs as life rafts. Here they remain until adulthood, adrift on the high seas in relative safety away from coastal predators. Over half of all animals in the open ocean drift in currents. Jellyfish cross entire oceans feeding on whatever happens to tangle with their tentacles. The jelly-like Portuguese man-of-war can harness sail power to fish with its deadly tentacles. Sometimes there is a brief explosion of food in this marine desert, but ocean hunters must be fast to make the best of this bonanza. We witness super pods of up to 5,000 spinner dolphins racing to herd vast shoals of lanternfish, briefly caught at the surface where it is thought they spawn. New aerial footage reveals, for the first time, the truth to a centuries-old sailors' legend of the 'boiling seas' - the spectacular feeding frenzy of 90kg tuna and dolphins smashing through the lantern fish shoals turning the sea white with foam.

A mighty army of dolphins, sharks, whales, seals and gannets hunt down the billions of sardines along South Africa's east coast each winter. This is the Sardine Run: an underwater Armageddon, the greatest gathering of predators anywhere on the planet, and the most spectacular event in the world's oceans. From intimate moments of the creatures caught up in the run, to the dramatic finale of this spectacular event, The Great Tide is an action-packed feeding-frenzy, filmed underwater, on the ocean's surface, and in the air.
However, in recent years the sardine run has become less predictable, perhaps due to the warming effects of climate change. If the sardine run does not happen, the lives of the animals caught up in the drama hang in the balance. Pioneering a unique boat stabilised camera mount for surface filming, Nature's Great Events crew capture all the high octane action as the predators compete for sardines, filmed with aerial, underwater and above water cameras. Super slow motion cameras also capture the very moment gannets plunge into the water, hitting it at sixty miles an hour.
A violent winter storm is the trigger for the sardines to begin their desperate dash. They are followed by a super-pod of 5,000 dolphins and further up the coast more predators gather. A shoal of sardines 15 miles long is pushed into the shallows and aerial shots show thousands of sharks gathering to feed on them. The climax to the sardine run is a spectacular feeding frenzy as the dolphins round the sardines up into balls on which all the predators feast. Gannets rain down in their thousands, sharks pile in scattering the fish and a Bryde's whale lunges in taking great mouthfuls of sardines.

Dr Hannah Fry travels down the fastest zip wire in the world to learn more about Newton's ideas on gravity. His discoveries revealed the movement of the planets was regular and predictable. James Clerk Maxwell unified the ideas of electricity and magnetism, and explained what light was. As if that wasn't enough, he also predicted the existence of radio waves. His tools of the trade were nothing more than pure mathematics. All strong evidence for maths being discovered.
But in the 19th century, maths is turned on its head when new types of geometry are invented. No longer is the kind of geometry we learned in school the final say on the subject. If maths is more like a game, albeit a complicated one, where we can change the rules, surely this points to maths being something we invent - a product of the human mind. To try and answer this question, Hannah travels to Halle in Germany on the trail of perhaps one of the greatest mathematicians of the 20th century, Georg Cantor. He showed that infinity, far from being infinitely big, actually comes in different sizes, some bigger than others. This increasingly weird world is feeling more and more like something we've invented. But if that's the case, why is maths so uncannily good at predicting the world around us? Invented or discovered, this question just got a lot harder to answer.

Far from land, where few of us ever venture, is the ocean beyond the boundary of any country. Largely ungoverned, wild, and lawless. Venture into the deep, dark and desolate oceans that are home to an abundance of beautiful - and downright strange - creatures.

Bob Clewell's helicopter crew comes under intense fire in one of the final operations of the war. Joe Galloway returns to Vietnam and in Washington, D.C., Barry Romo throws down his medals in protest. The last American troops return home and POW wife Anne Purcell awaits word of her husband's fate. The fall of Saigon brings the unification of Vietnam.