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In this book, Roger Penrose presents a masterly summary of those areas of physics in which he feels there are major unsolved problems. These ideas are then challenged by three distinguished experts from different backgrounds - Abner Shimony and Nancy Cartwright as Philosophers of science and Stephen Hawking as a theoretical physicist and cosmologist. Finally, Roger Penrose responds to their thought-provoking criticisms. This paperback edition has been updated to include a striking and easily accessible example of Goedel's theorem, and a ground-breaking proposal for a physical experiment designed to test some of Penrose's most novel ideas about quantum mechanics. Penrose's enthusiasm, insight and good humour shine through this accessible, illuminating, and brilliant account of 21st-century theoretical physics.