This collection has been inspired by the work of Roger Penrose. It gives an overview of current work on the interaction between geometry and physics, from which many important developments in research have emerged. This volume collects together the contributions of many important researchers, including Sir Roger himself, and gives an overview of the many applications of geometrical ideas and techniques across mathematics and the physical sciences. From the area of pure mathematics papers are included on the topics of classical differential geometry and non-commutative geometry, knot invariants, and the applications of gauge theory. Contributions from applied mathematics cover the topics of integrable systems and general relativity. Current research in experimental and theoretical physics inspired chapters on string theory, quantum gravity, the foundations of quantum mechanics, quasi-crystals and astrophysics. The collection also includes articles on quantum computation, quantum cryptography and the possible role of micro-tubules in a theory of consciousness.
Review
"Internationally renowned theoretical physicist Penrose invented twistor theory, a radical new approach to space-time where geometric points no longer enter the theory as primitives. More recently, he has stirred controversy with two books that invoke modern physics to plumb the nature of human consciousness. This festschrift honoring Penrose on his 65th birthday contains survey articles by some of the most eminent mathematicians (Atiyah, Donaldson, Connes, et al.) and physicists (Hawking, Astekar, Veneziano, among others) of our time. Besides browsing the most formidable contributions, undergraduates may particularly benefit from Artur Ekert's introduction to quantum cryptography, Paul Steinhardt's new approach to Penrose tilings, and particularly, biologist Stuart Hameroff's defense of Penrose's theories of consciousness from the charge of merely constituting a 'minimization of mysteries.' Highly recommended. Undergraduates through faculty."-- Choice
"This book grew out of a symposium ... honoring Roger Penrose (b. 1931) at the age of 65. Even at an early age, it was noted about Penrose that he 'thinks geometrically.' His geometrical thinking led him, in 1974, to a solution of a problem that had eluded Johannes Kepler and Albrecht Dürer, that is, how to cover a surface with motifs of pentagonal symmetry without gaps and overlaps, the Penrose tiling. ... In this volume, Paul Steinhardt ... revisits the Penrose tiling and quasicrystals, reports recent results in modeling, and points out the still unresolved problems. ... The Penrose tiling was an inadvertent discovery, a result of almost idle doodling. The main areas of Penrose's research include time-space, quantum theory, and the workings of the mind ... [and m]ost of the 32 contributions in this book, including Penrose's own Afterword, concern Penrose's main activities. The book is introduced by a brief and charming Laudatio by John A. Wheeler."-- The Chemical Intelligencer
About the Author
Mathematical Institute, 24-29 St Giles', OXFORD, OX1 3LB. Tel: +44 1865 273525; fax: +44 1865 273583
This collection has been inspired by the work of Roger Penrose. It gives an overview of current work on the interaction between geometry and physics, from which many important developments in research have emerged. This volume collects together the contributions of many important researchers, including Sir Roger himself, and gives an overview of the many applications of geometrical ideas and techniques across mathematics and the physical sciences. From the area of pure mathematics papers are included on the topics of classical differential geometry and non-commutative geometry, knot invariants, and the applications of gauge theory. Contributions from applied mathematics cover the topics of integrable systems and general relativity. Current research in experimental and theoretical physics inspired chapters on string theory, quantum gravity, the foundations of quantum mechanics, quasi-crystals and astrophysics. The collection also includes articles on quantum computation,
quantum cryptography and the possible role of micro-tubules in a theory of consciousness.
Review
"Internationally renowned theoretical physicist Penrose invented twistor theory, a radical new approach to space-time where geometric points no longer enter the theory as primitives. More recently, he has stirred controversy with two books that invoke modern physics to plumb the nature of human consciousness. This festschrift honoring Penrose on his 65th birthday contains survey articles by some of the most eminent mathematicians (Atiyah, Donaldson, Connes, et al.) and physicists (Hawking, Astekar, Veneziano, among others) of our time. Besides browsing the most formidable contributions, undergraduates may particularly benefit from Artur Ekert's introduction to quantum cryptography, Paul Steinhardt's new approach to Penrose tilings, and particularly, biologist Stuart Hameroff's defense of Penrose's theories of consciousness from the charge of merely constituting a 'minimization of mysteries.' Highly recommended. Undergraduates through faculty."-- Choice
"This book grew out of a symposium ... honoring Roger Penrose (b. 1931) at the age of 65. Even at an early age, it was noted about Penrose that he 'thinks geometrically.' His geometrical thinking led him, in 1974, to a solution of a problem that had eluded Johannes Kepler and Albrecht Dürer, that is, how to cover a surface with motifs of pentagonal symmetry without gaps and overlaps, the Penrose tiling. ... In this volume, Paul Steinhardt ... revisits the Penrose tiling and quasicrystals, reports recent results in modeling, and points out the still unresolved problems. ... The Penrose tiling was an inadvertent discovery, a result of almost idle doodling. The main areas of Penrose's research include time-space, quantum theory, and the workings of the mind ... [and m]ost of the 32 contributions in this book, including Penrose's own Afterword, concern Penrose's main activities. The book is introduced by a brief and charming Laudatio by John A. Wheeler."-- The Chemical Intelligencer
About the Author
Mathematical Institute, 24-29 St Giles', OXFORD, OX1 3LB. Tel: +44 1865 273525; fax: +44 1865 273583