Documentary AreaSimply the best Documentaries

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.

Iain explores man's relationship with fire. He begins by embarking on an extraordinary encounter with this terrifying force of nature - a walk right through the heart of a raging fire. Fire has long been our main source of energy and Iain shows how this meant that the planet played a crucial role in Britain's industrial revolution, whilst holding China's development back. Along the way he dives in a mysterious lake in Oregon, climbs a glacier of salt, crawls through an extraordinary cave in Iran and takes a therapeutic bath in crude oil.

Twenty years on from the invention of the world wide web, this major new series takes stock of its profound impact – how, for better and for worse, the digital revolution is reshaping our lives. Dr Aleks Krotoski explores the meaning of a phenomenon that is transforming everything, from how we learn to how we shop, vote and make friends. With a quarter of the planet connected so far, this series examines what is in store for the remaining 75 per cent of the world's population as they come online." In the first part series, Aleks charts the extraordinary rise of blogs, Wikipedia and YouTube, and traces an ongoing clash between the freedom the technology offers us, and our innate human desire to control and profit. Dr Aleks Krotoski looks at how it is reshaping almost every aspect of our lives. Joined by some of the web's biggest names - including the founders of Facebook, Twitter, Amazon, Apple and Microsoft, and the web's inventor - she explores how far the web has lived up to its early promise.

In the third programme of the series, Aleks gives the lowdown on how, for better and for worse, commerce has colonized the web - and reveals how web users are paying for what appear to be 'free' sites and services in hidden ways. Joined by some of the most influential business leaders of today's web, including Eric Schmidt (CEO of Google), Chad Hurley (CEO of YouTube), Bill Gates, Martha Lane Fox and Reed Hastings (CEO of Netflix), Aleks traces how business, with varying degrees of success, has attempted to make money on the web. She tells the inside story of the gold rush years of the dotcom bubble and reveals how retailers such as Amazon learned the lessons. She also charts how, out of the ashes, Google forged the business model that has come to dominate today's web, offering a plethora of highly attractive, overtly free web services, including search, maps and video, that are in fact funded through a sophisticated and highly lucrative advertising system which trades on what we users look for. Aleks explores how web advertising is evolving further to become more targeted and relevant to individual consumers. Recommendation engines, pioneered by retailers such as Amazon, are also breaking down the barriers between commerce and consumer by marketing future purchases to us based on our previous choices. On the surface, the web appears to have brought about a revolution in convenience. But, as companies start to build up databases on our online habits and preferences, Aleks questions what this may mean for our notions of privacy and personal space in the 21st century

Dr Aleks Krotoski concludes her investigation of how the World Wide Web is transforming almost every aspect of our lives. Joined by Facebook founder Mark Zuckerberg, Bill Gates, Al Gore and the neuroscientist Susan Greenfield, Aleks examines the popularity of social networks such as Facebook and asks how they are changing our relationships. And, in a ground-breaking test at University College London, Aleks investigates how the Web may be distracting and overloading our brains.

Painted over five centuries ago, Filippo Lippi's nativity is like none other: it shows the birth of Christ in a dark, wooded wilderness. There are no shepherds, kings, ox, ass – there is no Joseph. Its beauty inspired Michelangelo, Leonardo da Vinci and Botticelli. But it also conceals a deeply personal story. It was painted for Cosimo de Medici, a wealthy banker who feared that his money was dragging him straight to hell. The artist's life was equally surprising. One of the most celebrated painters of his day, Filippo Lippi was also a Carmelite friar, but he was no stranger to the temptations of the flesh, to which he frequently yielded. Shortly before painting his Adoration, he caused uproar by seducing a twenty year-old nun. His paintings rejoice not only in divine beauty, but in the beauty of women. In later times, the Adoration's history was interwoven with that of rulers and dictators. It became a bargaining chip after Napoleon's allies seized twenty merchant ships. And in the 20th century, it was hidden by the Nazis in a potassium mine, where specialist american officers, known as Monuments Men, stumbled upon it. they were now told to get it ready to be shipped out. In an unprecedented turn of events they refused. This is the only known case in the whole of the Second World War of American officers refusing an order. It was sent to the National Gallery of Art, but in 1949 Lippi's Adoration was returned to Germany.