Shadows of the Mind. A Search for the Missing Science of Consciousness ROGER PENROSE. Rouse Ball Professor of Mathematics University of Oxford

Transcription

1 Shadows of the Mind A Search for the Missing Science of Consciousness ROGER PENROSE Rouse Ball Professor of Mathematics University of Oxford Oxford New York Melbourne OXFORD UNIVERSITY PRESS 1994

2 CONTENTS Notes to the reader xv Prologue 1 Part I: Why We Need New Physics to Understand the Mind The Non-Computability of Conscious Thought 1 Consciousness and computation Mind and science Can robots save this troubled world? The s/, ЗЙ, <, 3> of computation and conscious thinking Physicalism vs. mentalism Computation: top-down and bottom-up procedures Does viewpoint < violate the Church-Turing thesis? Chaos Analogue computation What kind of action could be non-computational? What of the future? Can computers have rights or responsibilities? 'Awareness', 'understanding', 'consciousness', 'intelligence' John Searle's argument Some difficulties with the computational model Do limitations of present-day AI provide a case for <^? The argument from Gödel's theorem Platonism or mysticism? What is the relevance of mathematical understanding? 51

3 Xll Contents i 1.19 What has Gödel's theorem to do with common-sense behaviour? Mental visualization and virtual reality Is mathematical imagination non-computational? 59 2 The Gödelian case Gödel's theorem and Turing machines Computations Non-stopping computations How do we decide that some computations do not stop? Families of computations; the Gödel-Turing conclusion ^ Possible technical objections to 'S Some deeper mathematical considerations The condition of co-consistency Formal systems and algorithmic proof Further possible technical objections to ^ 95 Appendix A: An explicit Gödelizing Turing machine The case for non-computability in mathematical thought What did Gödel and Turing think? Could an unsound algorithm knowably simulate mathematical understanding? Could a knowable algorithm unknowably simulate mathematical understanding? Do mathematicians unwittingly use an unsound algorithm? Can an algorithm be unknowable? Natural selection or an act of God? One algorithm or many? Natural selection of unworldly esoteric mathematicians Learning algorithms May the environment provide a non-algorithmic external factor? How can a robot learn? Can a robot attain 'firm mathematical beliefs'? Mechanisms underlying robot mathematics The basic contradiction Ways that the contradiction might be averted Does the robot need to believe in M? Robot errors and robot 'meanings'? How to incorporate randomness ensembles of robot activity The removal of erroneous -fr-assertions Only finitely many ^-assertions need be considered Adequacy of safeguards? 176

4 Contents хш 3.22 Can chaos save the computational model of mind? Reductio ad absurdum a fantasy dialogue Have we been using paradoxical reasoning? Complication in mathematical proofs Computational breaking of loops Top-down or bottom-up computational mathematics? Conclusions 201 Part II: What New Physics We Need to Understand the Mind The Quest for a Non-Computational Physics of Mind 4 Does mind have a place in classical physics? The mind and physical laws Computability and chaos in'the physics of today Consciousness: new physics or 'emergent phenomenon'? The Einstein tilt Computation and physics Structure of the quantum world Quantum theory: puzzle and paradox The Elitzur-Vaidman bomb-testing problem Magic dodecahedra Experimental status of EPR-type Z-mysteries Quantum theory's bedrock: a history extraordinary The basic rules of quantum theory Unitary evolution U State-vector reduction R Solution of the Elitzur-Vaidman bomb-testing problem Quantum theory of spin; the Riemann sphere Position and momentum of a particle Hubert space The Hilbert-space description of R Commuting measurements The quantum-mechanical 'and' Orthogonality of product states Quantum entanglement The magic dodecahedra explained 296 Appendix B: The non-colourability of the dodecahedron 300 Appendix C: Orthogonality between general spin states Quantum theory and reality Is R a real process? Many-worlds-type viewpoints 310

5 XIV Contents 6.3 Not taking \ф} seriously 6.4 The density matrix 6.5 Density matrices for EPR pairs 6.6 A FAPP explanation of R? 6.7 Does FAPP explain the squared modulus rule? 6.8 Is it consciousness that reduces the state vector? 6.9 Taking \ф} really seriously 6.10 Gravitationally induced state-vector reduction? 6.11 Absolute units 6.12 The new criterion 7 Quantum theory and the brain 7.1 Large-scale quantum action in brain function? 7.2 Neurons, synapses, and computers 7.3 Quantum computation 7.4 Cytoskeletons and microtubules 7.5 Quantum coherence within microtubules? 7.6 Microtubules and consciousness 7.7 A model for a mind? 7.8 Non-computability in quantum gravity: Oracle machines and physical laws 7.10 Non-computability in quantum gravity: Time and conscious perceptions 7.12 EPR and time: need for a new world-view 8 Implications? 8.1 Intelligent artificial 'devices' 8.2 Things that computers do well or badly 8.3 Aesthetics, etc. 8.4 Some dangers inherent in computer technology 8.5 The puzzling election 8.6 The physical phenomenon of consciousness? 8.7 Three worlds and three mysteries Epilogue Bibliography Index