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In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

Sagan discusses the story of the Heike crab and artificial selection of crabs resembling samurai warriors, as an opening into a larger discussion of evolution through natural selection (and the pitfalls of intelligent design). Among the topics are the development of life on the Cosmic Calendar and the Cambrian explosion; the function of DNA in growth; genetic replication, repairs, and mutation; the common biochemistry of terrestrial organisms; the creation of the molecules of life in the Miller-Urey experiment; and speculation on alien life (such as life in Jupiter's clouds). In the Cosmos Update ten years later, Sagan remarks on RNA also controlling chemical reactions and reproducing itself and the different roles of comets (potentially carrying organic molecules or causing the Cretaceous–Paleogene extinction event).

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.

This illuminating ten-part series tells the story of World War ll through the ten most pivotal turning points in the conflict. Gripping story-telling illustrated with exquisitely restored and colourised archived films and supported by a global cast of stellar historians bring this crucially important era in history to life.
In the first chapter, Britain and France declare war when Hitler invades Poland. In May 1940 the Germans attack Holland and Belgium as a decoy. As the Wehrmacht comes through the Ardennes and the Luftwaffe strikes in force, French leaders are caught like rabbits in headlights. The Germans are on a drug called Pervitin, which beats off fatigue, and reach the Atlantic coast. There is a danger that the Germans will encircle the Allies and cut them off from the sea. But Hitler issues his Halt Order and some 340,000 Allies are evacuated.

Frequent security expos feature companies like Megvii and its facial- recognition technology. They show off cameras with A.I. that can track cars, and identify individuals by face, or just by the way they walk. In China it's been projected that over 600 million cameras will be deployed by 2020. Here, they may be used to discourage jaywalking, but they also serve to remind people that the state is watching. Matching with the most advanced artificial intelligence algorithm, they can actually use this data, real-time data, to pick up a face or pick up a action.
A.I. is a technology that can be used for good and for evil. So, how do governments limit themselves in, on the one hand, using this A.I. technology and the database to maintain a safe environment for its citizens, but not to encroach on a individual's rights and privacies?

Facebook is a company that has grown from nothing to be worth half a trillion dollars in just 15 years. Today nearly a third of all humans are using it, and yet we rarely get to see the people actually in charge of the biggest social network in the world.
The company has suffered a series of deepening scandals and intense media scrutiny. In 2018, their mission - to connect everyone on the planet - seemed to be going dramatically wrong. Data leaks, fake news and hacks on user security were threatening to destroy everything Mark Zuckerberg had built.
Yet throughout this difficult time, the company allowed the filmakers to follow key members of the team trying to fix the problems and secure the platform. This film goes behind the scenes and follows the teams inside Facebook. It tackles difficult questions, like how our data is used and what content should and shouldn’t be on the site, but also shows how Facebook works, what the teams are doing to secure it, and reveals a hidden technological playground, where some of the smartest engineers in the world are being hired to build systems and technology no one has built before.