In Our Time: Science Folgen

Melvyn Bragg and guests discuss the problem of P versus NP, which has a bearing on online security. There is a $1,000,000 prize on offer from the Clay Mathematical Institute for the first person to come up with a complete solution. At its heart is the question "are there problems for which the answers can be checked by computers, but not found in a reasonable time?" If the answer to that is yes, then P does not equal NP. However, if all answers can be found easily as well as checked, if only we knew how, then P equals NP. The area has intrigued mathematicians and computer scientists since Alan Turing, in 1936, found that it's impossible to decide in general whether an algorithm will run forever on some problems. Resting on P versus NP is the security of all online transactions which are currently encrypted: if it transpires that P=NP, if answers could be found as easily as checked, computers could crack passwords in moments.With Colva Roney-Dougal Reader in Pure Mathematics at the University of St AndrewsTimothy Gowers Royal Society Research Professor in Mathematics at the University of CambridgeAnd Leslie Ann Goldberg Professor of Computer Science and Fellow of St Edmund Hall, University of OxfordProducer: Simon Tillotson.

Melvyn Bragg and guests discuss the rise of the idea of perpetual motion and its decline, in the 19th Century, with the Laws of Thermodynamics. For hundreds of years, some of the greatest names in science thought there might be machines that could power themselves endlessly. Leonardo Da Vinci tested the idea of a constantly-spinning wheel and Robert Boyle tried to recirculate water from a draining flask. Gottfried Leibniz supported a friend, Orffyreus, who claimed he had built an ever-rotating wheel. An increasing number of scientists voiced their doubts about perpetual motion, from the time of Galileo, but none could prove it was impossible. For scientists, the designs were a way of exploring the laws of nature. Others claimed their inventions actually worked, and promised a limitless supply of energy. It was not until the 19th Century that the picture became clearer, with the experiments of James Joule and Robert Mayer on the links between heat and work, and the establishment of the First and Second Laws of Thermodynamics.With Ruth Gregory Professor of Mathematics and Physics at Durham UniversityFrank Close Professor Emeritus of Physics at the University of OxfordandSteven Bramwell Professor of Physics and former Professor of Chemistry at University College LondonProducer: Simon Tillotson.

In 1977, scientists in the submersible "Alvin" were exploring the deep ocean bed off the Galapagos Islands. In the dark, they discovered hydrothermal vents, like chimneys, from which superheated water flowed. Around the vents there was an extraordinary variety of life, feeding on microbes which were thriving in the acidity and extreme temperature of the vents. While it was already known that some microbes are extremophiles, thriving in extreme conditions, such as the springs and geysers of Yellowstone Park (pictured), that had not prepared scientists for what they now found. Since the "Alvin" discovery, the increased study of extremophile microbes has revealed much about what is and is not needed to sustain life on Earth and given rise to new theories about how and where life began. It has also suggested forms and places in which life might be found elsewhere in the Universe. With Monica Grady Professor of Planetary and Space Sciences at the Open UniversityIan Crawford Professor of Planetary Science and Astrobiology at Birkbeck University of LondonAndNick Lane Reader in Evolutionary Biochemistry at University College LondonProducer: Simon Tillotson.