Melvyn Bragg and guests Jim Al-Khalili, Frank Close and Frank James discuss the history of the discovery of radiation.Today the word 'radiation' conjures up images of destruction. But in physics, it simply describes the emission, transmission and absorption of energy, and the discovery of how radiation works has allowed us to identify new chemical elements, treat cancer and work out what the stars are made of.Over the course of the 19th century, physicists from Thomas Young, through Michael Faraday to Henri Becquerel made discovery after discovery, gradually piecing together a radically new picture of reality. They explored the light beyond the visible spectrum, connected electricity and magnetism, and eventually showed that heat, light, radio and mysterious new phenomena like 'X-rays' were all forms of 'electromagnetic wave'. In the early 20th century, with the discovery of radioactivity, scientists like Max Planck and Ernest Rutherford completed the picture of the 'electromagnetic spectrum'. This was a cumulative achievement that transformed our vision of the physical world, and what we could do in it.Jim Al-Khalili is Professor of Theoretical Physics and Chair in the Public Engagement in Science at the University of Surrey; Frank Close is Professor of Physics at Exeter College, University of Oxford; Frank James is Professor of the History of Science at the Royal Institution.

Melvyn Bragg and guests Richard Corfield, Jane Francis and Sanjeev Gupta discuss the geological formation of Britain.Around 600 million years ago the island that we now call Britain was in two parts, far to the south of the Equator. Scotland and north-western Ireland were part of a continent (Laurentia) that also included what is now North America. To the south-east, near the Antarctic Circle, meanwhile, you would have found southern Ireland, England and Wales. They formed a mini-continent (Avalonia) with what is now Newfoundland.Over the course of hundreds of millions of years, as they inched their way north, the two parts came together - first as part of a vast unitary continent (Pangaea), later as a promontory on the edge of Europe, and eventually, as sea levels rose, as an island. The story of how Britain came to be where it is now, in its current shape - from the separation of North America and Europe to the carving out of the English Channel - is still being uncovered today.Richard Corfield is Visiting Senior Resarch Fellow at Oxford University; Jane Francis is Professor of Palaeoclimatology at the University of Leeds; Sanjeev Gupta is a Royal Society-Leverhulme Trust Research Fellow at Imperial College London.

Melvyn Bragg discusses the epic feud between Sir Isaac Newton and Gottfried Leibniz over who invented an astonishingly powerful new mathematical tool - calculus. Both claimed to have conceived it independently, but the argument soon descended into a bitter battle over priority, plagiarism and philosophy. Set against the backdrop of the Hanoverian succession to the English throne and the formation of the Royal Society, the fight pitted England against Europe, geometric notation against algebra. It was fundamental to the grounding of a mathematical system which is one of the keys to the modern world, allowing us to do everything from predicting the pressure building behind a dam to tracking the position of a space shuttle.Melvyn is joined by Simon Schaffer, Professor of History of Science at the University of Cambridge and Fellow of Darwin College; Patricia Fara, Senior Tutor at Clare College, University of Cambridge; and Jackie Stedall, Departmental Lecturer in History of Mathematics at the University of Oxford.

Melvyn Bragg and guests Martin Brasier, Richard Corfield and Rachel Wood discuss the Ediacara Biota, the Precambrian life forms which vanished 542 million years ago, and whose discovery proved Darwin right in a way he never imagined. Darwin was convinced that there must have been life before the Cambrian era, but he didn't think it was possible for fossils like the Ediacara to have been preserved. These sea-bed organisms were first unearthed in the 19th century, but were only recognised as Precambrian in the mid-20th century. This was an astonishing discovery. Ever since, scientists have been working to determine its significance. Were the Ediacara the earliest forms of animal life? Or were they a Darwinian dead end? Either way, it is argued, they reveal some of the secrets of the workings of evolution. Richard Corfield is Senior Lecturer in Earth Sciences at the Open University; Martin Brasier is Professor of Palaeobiology at the University of Oxford; Rachel Wood is Lecturer in Carbonate Geoscience at the University of Edinburgh.

Melvyn Bragg discusses Logical Positivism, the eye-wateringly radical early 20th century philosophical movement. The Logical Positivists argued that much previous philosophy was built on very shaky foundations, and they wanted to go right back to the drawing board. They insisted that philosophy - and science - had to be much more rigorous before it started making grand claims about the world. The movement began with the Vienna Circle, a group of philosophically-trained scientists and scientifically-trained philosophers, who met on Thursdays, in 'Red Vienna', in the years after the First World War. They were trying to remould philosophy in a world turned upside down not just by war, but by major advances in science. Their hero was not Descartes or Hegel but Albert Einstein. The group's new doctrine rejected great swathes of earlier philosophy, from meditations on the existence of God to declarations on the nature of History, as utterly meaningless. When the Nazis took power, they fled to England and America, where their ideas put down new roots, and went on to have a profound impact.Melvyn is joined by Barry Smith, Professor of Philosophy at the University of London; Nancy Cartwright, Professor of Philosophy at the London School of Economics; and Thomas Uebel, Professor of Philosophy at Manchester University.

Melvyn Bragg and guests Steve Jones, Bill Amos and Eleanor Weston discuss the evolutionary history of the whale. The ancestor of all whales alive today was a small, land-based mammal with cloven hoofs, perhaps like a pig or a big mole. How this creature developed into the celebrated leviathan of the deep is one of the more extraordinary stories in the canon of evolution. The whale has undergone vast changes in size, has moved from land to water, lost its legs and developed specialised features such as filter feeding and echo location. How it achieved this is an exemplar of how evolution works and how natural selection can impose extreme changes on the body shape and abilities of living things. How the story of the whales was pieced together also reveals the various forms of evidence - from fossils to molecules - that we now use to understand the ancestry of life on Earth.Steve Jones is Professor of Genetics at University College London; Eleanor Weston is a mammalian palaeontologist at the Natural History Museum, London; Bill Amos is Professor of Evolutionary Genetics at Cambridge University.

Melvyn Bragg and guests Frank Close, Jocelyn Bell Burnell and Ruth Gregory discuss the Vacuum of Space. The idea that there is a nothingness at the heart of nature has exercised philosophers and scientists for millennia, from Thales's belief that all matter was water to Newton's concept of the Ether and Einstein's idea of Space-Time. Recently, physicists have realised that the vacuum is not as empty as we thought and that the various vacuums of nature vibrate with forces and energies, waves and particles and the mysterious phenomena of the Higgs field and dark energy.

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 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