Showing papers by "Roger Penrose published in 2021"
Book•
01 Mar 2021TL;DR: In this paper, eminent physicist Roger Penrose argues that there are facets of human thinking, of human imagination, that can never be emulated by a machine, and demonstrates that laws even more wondrously complex than those of quantum mechanics are essential for the operation of a mind.
Abstract: From the Publisher:
In The Emporer's New Mind, eminent physicist Roger Penrose argues that there are facets of human thinking, of human imagination, that can never be emulated by a machine. Exploring a dazzling array of topics--complex numbers, black holes, entropy, quasicrystals, the structure of the brain, and the physical processes of consciousness--Penrose demonstrates that laws even more wondrously complex than those of quantum mechanics are essential for the operation of a mind.
1,213 citations
Book•
09 Jun 2021
TL;DR: The Road to Reality as discussed by the authors provides a comprehensive account of our present understanding of the physical universe, and the essentials of its underlying mathematical theory, and provides a feeling for the deep beauty and philosophical connotations of the subject, as well as of its intricate logical interconnections.
Abstract: The Road to Reality, some 1000 pages long, aims to provide a comprehensive account of our present understanding of the physical universe, and the essentials of its underlying mathematical theory. No particular mathematical knowledge on the part of the reader is assumed - the early chapters providing the essential mathematical background for the physical theories described in the remainder of the book. The aim is to convey something of an overall understanding - a feeling for the deep beauty and philosophical connotations of the subject, as well as of its intricate logical interconnections. Clearly, a work of this nature is challenging, but there is enough descriptive material to carry the less mathematically inclined reader through, as well as some 450-500, mostly hand-drawn, figures. The book provides a feeling for all the key issues and deep current controversies, and counters the common complaint that cutting-edge science is fundamentally inaccessible. The topics covered in this book include: the roles of different kinds of numbers and of geometry in physics; the ideas - and magic - of calculus and of modern geometry; notions of infinity; the physics and mathematics of relativity theory; the foundations and controversies of quantum mechanics; the standard model of particle physics; cosmology; the big bang; black holes; the profound challenge of the second law of thermodynamics; string and M theory; loop quantum gravity; twistors; fashions in science; and new directions.
46 citations
TL;DR: In this article, a general procedure based on Gerstenhaber-Schack complexes for extending the Donaldson-Friedman gluing of twistor spaces via deformation theory of singular spaces is described.
Abstract:
We describe a general procedure, based on Gerstenhaber–Schack complexes, for extending to quantized twistor spaces the Donaldson–Friedman gluing of twistor spaces via deformation theory of singular spaces. We consider in particular various possible quantizations of twistor spaces that leave the underlying spacetime manifold classical, including the geometric quantization of twistor spaces originally constructed by the second author, as well as some variants based on non-commutative geometry. We discuss specific aspects of the gluing construction for these different quantization procedures.
1 citations