By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems. Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.

We can survive for weeks without food, but only days without water: it is the essential element of life. Yet many millions of us live in parched deserts around the world. In the second episode of Human Planet, we discover how the eternal quest for water brings huge challenges - and ingenious solutions - in the driest places on Earth. Battling through a sand storm in Mali, Mamadou must get his cows to a remote lake but desert elephants have arrived first. Can he find a safe way through the elephant blockade? Alone for weeks on end, Tubu women and children navigate the endless dunes of the Sahara. How does young Shede know where to find the last oasis, three days walk across the sea of sand? At the height of the drought we witness a spectacular frenzy: two thousand men rushing into Antogo Lake to catch the fish trapped by the evaporating water. When the rain finally arrives in the desert it's a time for flowering and jubilation - and love. The Wodaabe men of Niger put on make-up for an intoxicating courtship dance and beauty contest.

The oceans define the earth. They are crucial to life and we used to think that they were unique to our blue planet. But we were wrong. It has recently been discovered that there are oceans all over our solar system, and they are very similar to our own. And now scientists are going on an epic journey in search of new life in places that never seemed possible. Nasa is even planning to dive to the depths of a strange, distant ocean in a remarkable submarine. Discover that the hunt for oceans in space is marking the dawn of a new era in the search for alien life.

Originally a Prisoner of War camp for Soviet soldiers, SS Commander Rudolf Hoss oversaw the transition of Auschwitz from a political camp to a place to murder thousands of people. In the Autumn of 1941,the Nazis were about to embark on the most crucial few months in the planning of what they called 'The Final Solution' - the extermination of the Jews.

There is a contest each year that can change a young skater's life. There are no pros with million dollar endorsement deals here, just real kids with real lives and everything on the line. This is the story of a few of the best, from France, Brazil and the USA, as they risk everything for a chance of a lifetime. Motivation 3: The Next Generation is a proper follow-up to The Motivation but this time the stakes are so much higher. We're in deep with real kids escaping poverty and violence, crashing in skate-houses or still living with mom. For all of these kids a win at Tampa Am could mean a way out and an opportunity to do what they love for a living-skate.

Michael Wood tells the tale of China's first great international age under the Tang Dynasty (618-907). From the picturesque old city of Luoyang, he travels along the Silk Road to the bazaars of central Asia and into India on the track of the Chinese monk who brought Buddhism back to China. This tale is still loved by the Chinese today and is brought to life by storytellers, films and shadow puppet plays. Then in the backstreets and markets of Xi'an, Michael meets descendants of the traders from central Asia and Persia who came into China on the Silk Road. He talks to Chinese Muslims in the Great Mosque and across town hears the amazing story of the first reception of Christianity in 635. Moving south, Michael sees the beginnings of China as an economic giant. On the Grand Canal, a lock built in 605 still handles 800 barges every day! The film tracks the rise of the silk industry and the world's favourite drink - tea. Michael looks too at the spread of Chinese script, language and culture across east Asia. 'China's influence on the East was as profound as Rome on the Latin West', he says, 'and still is today'. Finally, the film tells the intense drama of the fall of the Tang. Among the eyewitnesses were China's greatest poets. In a secondary school in a dusty village, where the Chinese Shakespeare - Du Fu - is buried in the grounds, the pupils take Michael through one famous poem about loss and longing as the dynasty falls. And in that ordinary classroom, there is a sense of the amazing drama and the deep-rooted continuities of Chinese culture.