Patricia Fara, Stephen Pumfrey and Rhodri Lewis join Melvyn Bragg to discuss the Jacobean lawyer, political fixer and alleged founder of modern science Francis Bacon.In the introduction to Thomas Spratt's History of the Royal Society, there is a poem about man called Francis Bacon which declares 'Bacon, like Moses, led us forth at last, The barren wilderness he past, Did on the very border stand Of the blest promis'd land, And from the mountain's top of his exalted wit, Saw it himself, and shew'd us it'.Francis Bacon was a lawyer and political schemer who climbed the greasy pole of Jacobean politics and then fell down it again. But he is most famous for developing an idea of how science should be done - a method that he hoped would slough off the husk of ancient thinking and usher in a new age. It is called Baconian Method and it has influenced and inspired scientists from Bacon's own time to the present day.

Melvyn Bragg and guests discuss The School of Athens – the fresco painted by the Italian Renaissance painter, Raphael, for Pope Julius II’s private library in the Vatican. The fresco depicts some of the most famous philosophers of ancient times, including Aristotle and Plato, engaged in discussion amidst the splendour of a classical Renaissance chamber. It is considered to be one of the greatest images in Western art not only because of Raphael’s skill as a painter, but also his ability to have created an enduring image that continues to inspire philosophical debate today. Raphael captured something essential about the philosophies of these two men, but he also revealed much about his own time. That such a pagan pair could be found beside a Pope in private tells of the complexity of intellectual life at the time when classical learning was reborn in what we now call the Renaissance.With Angie Hobbs, Associate Professor in Philosophy at the University of Warwick; Valery Rees, Renaissance scholar and senior member of the Language Department at the School of Economic Science; Jill Kraye, Professor of the History of Renaissance Philosophy and Librarian at the Warburg Institute at the University of London

In the hot summer of 1900, Peking, the capital of China, was under heavy siege. But the surrounding forces were not foreign, they were Chinese. This was the Boxer Rebellion, the moment when the 'Society of Righteous and Harmonious Fists', known as the boxers, purged China of foreign merchants and missionaries. The Boxers had came out of the northern provinces, they claimed their fists were stronger than fire and they were invincible to bullets. But they were also desperate and starving and they blamed foreigners for their plight. In the end, the Boxer rebellion failed but it changed China and, more than a hundred years later, the spirit of the Boxer Rebellion lives on. They may have lost their battles but they may have won their war.

Melvyn Bragg and guests discuss the Library at Alexandria. Founded by King Ptolemy in the 3rd century BC the library was the first attempt to collect all the knowledge of the ancient world in one place. Scholars including Archimedes and Euclid came to study its grand array of papyri. the legacy of the library is with us today, not just in the ideas it stored and the ideas it seeded but also in the way it organised knowledge and the tools developed for dealing with it. It still influences the things we know and the way we know them to this day.With Simon Goldhill, Professor of Greek at the University of Cambridge; Matthew Nicholls, Lecturer in Classics at the University of Reading; Serafina Cuomo, Reader in Roman History at Birkbeck College, University of London.

Melvyn Bragg and guests discuss one of the deepest problems in contemporary physics. It’s called the measurement problem and it emerged from the flurry of activity in the early 20th century that gave rise to Quantum Mechanics. If the most famous fruit in physics is an apple, the most famous animal in physics is a cat. Schrödinger’s cat is named after Edwin Schrödinger, a theoretical physicist who in the early 20th century helped to develop the radical theories of Quantum Mechanics. The cat does not actually exist – it is the subject of a thought experiment – in which the rules of quantum mechanics make it appear both dead and alive at the same time.The problem of a cat that is both dead and alive illustrates the challenges of quantum physics and at the heart of this apparent absurdity is a thing called the measurement problem.The measurement problem arises because we don’t really understand how the atoms that constitute our world behave. They are fundamentally mysterious to us, even shocking, and they defy our attempts to measure and make sense of them. Possible solutions range from the existence of multiple realities to the rather more mundane possibility of an error in our mathematics - but a solution, if found, could transform our understanding of reality. With Basil Hiley, Emeritus Professor of Physics at Birkbeck, University of London, Simon Saunders, Reader in Philosophy of Physics and University Lecturer in Philosophy of Science at the University of Oxford; Roger Penrose, Emeritus Rouse Ball Professor of Mathematics at the University of Oxford

Melvyn Bragg and guests, including Steve Connor and Lawrence Rainey, discuss TS Eliot's seminal poem The Waste Land and its ambivalence to the modern world of technology, democracy and capitalism that was being forged around it.

Melvyn Bragg and guests discuss the Observatory in Jaipur with its vast and beautiful instruments built to make astronomical measurements of the stars. Commissioned in the early 18th century by the Rajput prince and child prodigy, Jai Singh, it was at the centre of attempts to marry hundreds of years of Indian and Persian astronomical tradition. The Observatory was also at the very centre of the city which was laid out according to astrological principles. Jai Singh’s observatory was the cutting edge of Indian astronomy but also a repository for aeons of Hindu and Islamic intellectual life. The instruments were extraordinarily accurate for the time but used no lenses and were built of masonry, not metal. They helped to develop astrological tables, immensely important in Hindu Society, and come down to us as a record of Indian astronomy on the cusp of colonialism. With Chandrika Kaul, Lecturer in Modern History at the University of St Andrews; David Arnold, Professor of Asian and Global History at the University of Warwick; Chris Minkowski, Professor in Sanskrit at the University of Oxford

Melvyn Bragg and guests discuss the Destruction of Carthage. The North African city of Carthage was rich and powerful, but in the second century BC it suffered a terrible fate. The Greek historian Appian wrote about it: “Then came new scenes of horror. As the fire spread and carried everything down, the soldiers did not wait to destroy the buildings little by little, but all in a heap. So the crashing grew louder, and many corpses fell with the stones into the midst. Others were seen still living, especially old men, women, and young children who had hidden in the inmost nooks of the houses, some of them wounded, some more or less burned, and uttering piteous cries.”When the Romans finally conquered their great enemy in 146 BC, they razed it to the ground, sold off its library and tried to destroy not merely the city but the civilisation based upon it. Carthage was removed from history with such effect that it’s hard to know the city save through Roman eyes.It was a pivotal moment in world history that left Rome as the supreme power in the Mediterranean but after it was gone the ghosts of Carthage haunted Rome and seemed to hint at Rome’s own fate. With Mary Beard, Professor of Classics at the University of Cambridge; Jo Quinn, Lecturer in Ancient History at the University of Oxford and Ellen O’Gorman, Senior Lecturer in Classics at the University of Bristol

Melvyn Bragg discusses the fairy tales of the Brothers Grimm with Juliette Wood, Marina Warner and Tony Phelan. The German siblings who in 1812 published a collection of fairy tales including Rapunzel, Hansel and Gretel, Cinderella and Rumpelstiltskin. But the Grimm versions are surprisingly, sometimes shockingly, different. Cinderella has no fairy godmother, her ugly sisters are not ugly but they do have their eyes pecked out by pigeons. Sleeping Beauty does not have an evil stepmother, Rapunzel is pregnant and Frog Princes do not get kissed but thrown against walls. They may not be the fairy tales as we know them, but without the Brothers Grimm we might not know them at all. But why did two respectable German linguists go chasing after fairy stories, what do the stories tell us about German culture and romantic nationalism at the time and why do these ever-evolving tales of horror, wonder and fantasy continue to hold us in thrall?With Juliette Wood, Associate Lecturer in Folklore at Cardiff University; Marina Warner, Professor in the Department of Literature, Film and Theatre Studies at the University of Essex; Tony Phelan, Professor in German at Keble College, Oxford.

Melvyn Bragg and guests discuss one of the most brilliant and shocking satires ever written in English – Jonathan Swift’s A Modest Proposal. Masquerading as an attempt to end poverty in Ireland once and for all, a Modest Proposal is a short pamphlet that draws the reader into a scheme for economic and industrial horror. Published anonymously but written by Jonathan Swift, A Modest Proposal lays bare the cruel presumptions, unchecked prejudice, the politics and the poverty of the 18th century, but it also reveals, perhaps more than anything else, the character and the mind of Swift himself.With John Mullan, Professor of English at University College London; Judith Hawley, Professor of 18th Century Literature at Royal Holloway, University of London and Ian McBride, Senior Lecturer in the History Department at King’s College London.