Foreword Malcolm Longair; 1. Space-time and cosmology Roger Penrose; 2. The mysteries of quantum physics Roger Penrose; 3. Physics and the mind Roger Penrose; 4. On mentality, quantum mechanics and the actualization of potentialities Abner Shimony; 5. Why physics? Nancy Cartwright; 6. The objections of an unashamed reductionist Stephen Hawking; 7. Response Roger Penrose; Appendix I: Goodstein's theorm and mathematical thinking; Appendix II: Experiments to test gravitationally induced state reduction.