Melvyn Bragg and guests discuss the Cambrian period when there was an explosion of life on Earth. In the Selkirk Mountains of British Columbia in Canada, there is an outcrop of limestone shot through with a seam of fine dark shale. A sudden mudslide into shallow water some 550 million years ago means that a startling array of wonderful organisms has been preserved within it. Wide eyed creatures with tentacles below and spines on their backs, things like flattened rolls of carpet with a set of teeth at one end, squids with big lobster-like arms. There are thousands of them and they seem to testify to a time when evolution took a leap and life on this planet suddenly went from being small, simple and fairly rare to being large, complex, numerous and dizzyingly diverse. It happened in the Cambrian Period and it's known as the Cambrian Explosion.But if this is the great crucible of life on Earth, what could have caused it? How do the strange creatures relate to life as we see it now? And what does the Cambrian Explosion tell us about the nature of evolution?With Simon Conway Morris, Professor of Evolutionary Palaeobiology, Cambridge University; Richard Corfield, Visiting Senior Lecturer at the Centre for Earth, Planetary, Space and Astronomical Research, Open University; Jane Francis, Professor of Palaeoclimatology, University of Leeds.

Melvyn Bragg and guests discuss the mind/body problem in philosophy. At the start of René Descartes' Sixth Meditation he writes: "there is a great difference between mind and body, inasmuch as body is by nature always divisible, and mind is entirely indivisible. For when I consider the mind, or myself in so far as I am merely a thinking thing, I am unable to distinguish many parts within myself; I understand myself to be something quite single and complete. Although the whole mind seems to be united to the whole body, I recognize that if a foot or an arm or any other part of the body is cut off nothing has thereby been taken away from the mind".This thinking is the basis of what's known as 'Cartesian dualism', Descartes' attempt to address one of the central questions in philosophy, the mind/body problem: is the mind part of the body, or the body part of the mind? If they are distinct, then how do they interact? And which of the two is in charge?With Anthony Grayling, Reader in Philosophy at Birkbeck, University of London; Julian Baggini, editor of The Philosophers' Magazine; Sue James, Professor of Philosophy at Birkbeck, University of London.

Melvyn Bragg and guests discuss the Second Law of Thermodynamics which can be very simply stated like this: "Energy spontaneously tends to flow from being concentrated in one place to becoming diffused and spread out". It was first formulated – derived from ideas first put forward by Lord Kelvin - to explain how a steam engine worked, it can explain why a cup of tea goes cold if you don't drink it and how a pan of water can be heated to boil an egg.But its application has been found to be rather grander than this. The Second Law is now used to explain the big bang, the expansion of the cosmos and even suggests our inexorable passage through time towards the 'heat death' of the universe. It's been called the most fundamental law in all of science, and CP Snow in his Two Cultures wrote: "Not knowing the Second Law of Thermodynamics is like never having read a work of Shakespeare".What is the Second Law? What are its implications for time and energy in the universe, and does it tend to be refuted by the existence of life and the theory of evolution?With John Gribbin, Visiting Fellow in Astronomy at the University of Sussex; Peter Atkins, Professor of Chemistry at Oxford University; Monica Grady, Head of Petrology and Meteoritics at the Natural History Museum.

Melvyn Bragg and guests discuss the extraordinary mind of the psychiatrist Carl Gustav Jung. In 1907 Sigmund Freud met a young man and fell into a conversation that is reputed to have lasted for 13 hours. That man was the Swiss psychiatrist Carl Gustav Jung. Freud is celebrated as the great pioneer of the 20th century mind, but the idea that personality types can be 'introverted' or 'extroverted', that certain archetypal images and stories repeat themselves constantly across the collective history of mankind, and that personal individuation is the goal of life, all belong to Jung: "Your vision will become clear only when you look into your heart... Who looks outside, dreams. Who looks inside, awakens", he declared. And he also said "Show me a sane man and I will cure him for you".Who was Jung? What is the essence and influence of his thought? And how did he become such a controversial and, for many, such a beguiling figure?With Brett Kahr, Senior Clinical Research Fellow in Psychotherapy and Mental Health at the Centre for Child Mental Health in London and a practising Freudian; Ronald Hayman, writer and biographer of Jung; Andrew Samuels, Professor of Analytical Psychology at the University of Essex and a Jungian analyst in clinical practice.

Melvyn Bragg and guests discuss the Higgs Boson particle. One weekend in 1964 the Scottish scientist Peter Higgs was walking in the Cairngorm Mountains. On his return to his laboratory in Edinburgh the following Monday, he declared to his colleagues that he had just experienced his 'one big idea' and now had an answer to the mystery of how matter in the universe got its mass. That big idea took many years of refining, but it has now generated so much international interest and has such an important place in physics that well over one billion pounds is being spent in the hope that he was right. It's the biggest science project on Earth; the quest to find the 'Higgs Boson', a fundamental constituent of nature that - if it does exist - has such a central role in defining the universe that it's also known as the God Particle.What is the Higgs Boson? Why is it so important to scientists and how are they planning to find it?With Jim Al-Khalili, Senior Lecturer in Physics at the University of Surrey; David Wark, Professor of Experimental Physics at Imperial College London and the Rutherford Appleton Laboratory; Professor Roger Cashmore, former Research Director at CERN and now Principal of Brasenose College, Oxford.

Melvyn Bragg and guests discuss the dawn of the age of electricity. In Gulliver's Travels, published in 1726, Jonathan Swift satirised natural philosophers as trying to extract sunbeams from cucumbers. Perhaps he would have been surprised, or even horrified, by the sheer force of what these seemingly obscure experimentalists were about to unleash on society. Electricity soon reached into all areas of 18th century life, as Royal Society Fellows vied with showmen and charlatans to reveal its wonders to the world. It was, claimed one commentator, 'an entertainment for Angels rather than for Men'. Electricity also posed deep questions about the nature of life. For some it was the divine spark that animated all things, for others it represented a dangerous materialism that reduced humans to mere machines.But how did electricity develop in the 18th and 19th centuries? Why was it so politically contentious and how was it understood during the age in which it changed the world forever?With Simon Schaffer, Professor in History and Philosophy of Science at the University of Cambridge and a Fellow of Darwin College; Patricia Fara, historian of science and a Fellow of Clare College, Cambridge; Iwan Morus, Lecturer in the History of Science at Queen's University Belfast.

Melvyn Bragg and guests discuss the emergence of the world’s first organic matter nearly four billion years ago. Scientists have named 1.5 million species of living organism on the land, in the skies and in the oceans of planet Earth and a new one is classified every day.  Estimates of how many species remain to be discovered vary wildly, but science accepts one categorical point – all living matter on our planet, from the nematode to the elephant, from the bacterium to the blue whale, is derived from a single common ancestor. What was that ancestor?  Did it really emerge from a ‘primordial soup’? And what, in the explanation of evolutionary science, provided the catalyst to start turning the cycle of life?With Richard Dawkins, Charles Simonyi Professor of the Public Understanding of Science at Oxford University; Richard Corfield, Visiting Senior Lecturer at the Centre for Earth, Planetary, Space and Astronomical Research at the Open University; Linda Partridge, Biology and Biotechnology Research Council Professor at University College London.

Melvyn Bragg and guests discuss the history of the most detailed number in nature. In the Bible's description of Solomon's temple it comes out as three, Archimedes calculated it to the equivalent of 14 decimal places and today's super computers have defined it with an extraordinary degree of accuracy to its first 1.4 trillion digits. It is the longest number in nature and we only need its first 32 figures to calculate the size of the known universe within the accuracy of one proton. We are talking about Pi, 3.14159 etc, the number which describes the ratio of a circle's diameter to its circumference. How has something so commonplace in nature been such a challenge for maths? And what does the oddly ubiquitous nature of Pi tell us about the hidden complexities of our world? With Robert Kaplan, co-founder of the Maths Circle at Harvard University, Eleanor Robson, Lecturer in the Department of History and Philosophy of Science at Cambridge University; and Ian Stewart, Professor of Mathematics at the University of Warwick.

Melvyn Bragg and guests discuss Renaissance obsession with Magic. In 1461 one of the powerful Medici family’s many agents carried a mysterious manuscript into his master’s house in Florence. It purported to be the work of an ancient Egyptian priest-king and magician called Hermes Trismegistus. When Cosimo de Medici saw the new discovery, he ordered his translations of Plato to be stopped so that work could begin on the new discovery at once. Hermes promised secret knowledge to his initiates and claimed to have spoken with the spirits and turned base metal into gold. His ideas propelled natural magic into the mainstream of Renaissance intellectual thought, as scholars and magi vied to understand the ancient secrets that would bring statues to life and call the angels down from heaven.But why did magic appeal so strongly to the Renaissance mind? And how did the scholarly Magus, who became a feature of the period, manage to escape prosecution and relate his work to science and the Church?With Peter Forshaw, Lecturer in Renaissance Philosophies at Birkbeck, University of London; Valery Rees, Renaissance historian and a translator of Ficino’s letters; Jonathan Sawday, Professor of English Studies at the University of Strathclyde.

Melvyn Bragg and guests discuss our knowledge of the planets in both our and other solar systems. Tucked away in the outer Western Spiral arm of the Milky Way is a middle aged star, with nine, or possibly ten orbiting planets of hugely varying sizes. Roughly ninety-two million miles and third in line from that central star is our own planet Earth, in thrall to our Sun, just one of the several thousand million stars that make up the Galaxy.Ever since Galileo and Copernicus gave us a scientific model of our own solar system, we have assumed that somewhere amongst the myriad stars there must be other orbiting planets, but it took until 1995 to find one. ‘51 Pegasus A’ was discovered in the Pegasus constellation and was far bigger and far closer to its sun than any of our existing theories could have predicted. Since then 121 new planets have been found. And now it is thought there may be more planets in the skies than there are stars.What causes a planet to form? How do you track one down? And how likely is there to be another one out there with properties like the Earth’s?With Paul Murdin, Senior Fellow at the Institute of Astronomy in Cambridge; Hugh Jones, planet hunter and Reader in Astrophysics at Liverpool John Moores University; Carolin Crawford, Royal Society Research Fellow at the Institute of Astronomy in Cambridge.