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The self-proclaimed 'Islamic State' is a jihadi militia active in the north and east of Syria, and in the west of Iraq, which has shocked the world with its cinematic staging of horrific acts of violence and its unexpected advances towards statehood. But why could IS expand so rapidly?

The Nazca Lines of Peru have been an important part of the Ancient Astronaut theory since its beginning. Originally Von Daniken claimed that the lines were kind of a UFO runway, or a type of alien airport, where the alien craft landed and took off. The idea that it was an airport makes no logical sense, and the symbols and rituals which were a huge part of the Nazcan culture more than explain the so called Nazca lines.

Professor Jim Al-Khalili investigates one of the most important concepts in the world today - information. He discovers how we harnessed the power of symbols, everything from the first alphabet to the electric telegraph through to the modern digital age. But on this journey he learns that information isn't just about human communication, it's woven very profoundly into the fabric of reality.

The second episode is about how plants gain their sustenance. Sunlight is one of the essential requirements if a seed is to germinate, and Attenborough highlights the cheese plant as an example whose young shoots head for the nearest tree trunk and then climb to the top of the forest canopy, developing its leaves en route. Using sunshine, air, water and a few minerals, the leaves are, in effect, the "factories" that produce food. However, some, such as the begonia, can thrive without much light. To gain moisture, plants typically use their roots to probe underground. Trees pump water up pipes that run inside their trunks, and Attenborough observes that a sycamore can do this at the rate of 450 litres an hour — in total silence. Too much rainfall can clog up a leaf's pores, and many have specially designed 'gutters' to cope with it. However, their biggest threat is from animals, and some require extreme methods of defence, such as spines, camouflage, or poison. Some can move quickly to deter predators: the mimosa can fold its leaves instantly when touched, and the Venus flytrap eats insects by closing its leaves around its prey when triggered. Another carnivorous plant is the trumpet pitcher that snares insects when they fall into its tubular leaves. Attenborough visits Borneo to see the largest pitcher of them all, Nepenthes rajah, whose traps contain up to two litres of water and have been known to kill small rodents.

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.

A visit to arguably the most famous archipelago on Earth, the Galapagos. It's home to a myriad of bizarre and unique creatures, endemic to these islands - but how did they get here and what is the key to these extraordinary islands that allows them to thrive? The programme reveals that this key holds not just the secret to life here, but also to how Darwin was able to leave with the ideas that would revolutionise biology.