The Emperor's New Mind · Concerning Computers, Minds, and the Laws of Physics (Popular Science) by Penrose, Roger -- Read -- Imperial Library of Trantor

Index

Title Page Copyright Page Note the Reader Acknowledgments Figure Acknowledgments Foreword Preface Contents Prologue 1 Can A Computer Have A Mind?

Introduction The Turing test Artificial intelligence An AI approach to ‘pleasure’ and ‘pain’ Strong AI and Searle’s Chinese room Hardware and software

2 Algorithms And Turing Machines

Background to the algorithm concept Turing’s concept Binary coding of numerical data The Church—Turing Thesis Numbers other than natural numbers The universal Turing machine The insolubility of Hilbert’s problem How to outdo an algorithm Church’s lambda calculus

3 Mathematics And Reality

The land of Tor’Bled-Nam Real numbers How many real numbers are there? ‘Reality’ of real numbers Complex numbers Construction of the Mandelbrot set Platonic reality of mathematical concepts?

4 Truth, Proof, And Insight

Hilbert’s programme for mathematics Formal mathematical systems Gödel’s theorem Mathematical insight Platonism or intuitionism? Gödel-type theorems from Turing’s result Recursively enumerable sets Is the Mandelbrot set recursive? Some examples of non-recursive mathematics Is the Mandelbrot set like non-recursive mathematics? Complexity theory Complexity and computability in physical things

5 The Classical World

The status of physical theory Euclidean geometry The dynamics of Galileo and Newton The mechanistic world of Newtonian dynamics Is life in the billiard-ball world computable? Hamiltonian mechanics Phase space Maxwell’s electromagnetic theory Computability and the wave equation The Lorentz equation of motion; runaway particles The special relativity of Einstein and Poincaré Einstein’s general relativity Relativistic causality and determinism Computability in classical physics: where do we stand? Mass, matter, and reality

6 Quantum Magic And Quantum Mystery

Do philosophers need quantum theory? Problems with classical theory The beginnings of quantum theory The two-slit experiment Probability amplitudes The quantum state of a particle The uncertainty principle The evolution procedures U and R Particles in two places at once? Hilbert space Measurements Spin and the Riemann sphere of states Objectivity and measurability of quantum states Copying a quantum state Photon spin Objects with large Spin Many-particle systems The ‘paradox’ of Einstein, Podolsky, and Rosen Experiments with photons: a problem for relativity? Schrödinger’s equation; Dirac’s equation Quantum field theory Schrödinger’s cat Various attitudes in existing quantum theory Where does all this leave us?

7 Cosmology And The Arrow Of Time

The flow of time The inexorable increase of entropy What is entropy? The second law in action The origin of low entropy in the universe Cosmology and the big bang The primordial fireball Does the big bang explain the second law? Black holes The structure of space-time singularities How special was the big bang?

8 In Search Of Quantum Gravity

Why quantum gravity? What lies behind the Weyl curvature hypothesis? Time-asymmetry in state-vector reduction Hawking’s box: a link with the Weyl curvature hypothesis? When does the state-vector reduce?

9 Real Brains And Model Brains

What are brains actually like? Where is the seat of consciousness? Split-brain experiments Blindsight Information processing in the visual cortex How do nerve signals work? Computer models Brain plasticity Parallel computers and the ‘oneness’ of consciousness Is there a role for quantum mechanics in brain activity? Quantum computers Beyond quantum theory?

10 Where Lies The Physics Of Mind?

What are minds for? What does consciousness actually do? Natural selection of algorithms? The non-algorithmic nature of mathematical insight Inspiration, insight, and originality Non-verbality of thought Animal consciousness? Contact with Plato’s world A view of physical reality Determinism and strong determinism The anthropic principle Tilings and quasicrystals Possible relevance to brain plasticity The time-delays of consciousness The strange role of time in conscious perception Conclusion: a child’s view

Epilogue References Index Footnotes