Penrose, Roger, 1989-, The Emperor’s New Mind

Spis z PDF 6–7 sprawdzono wizualnie. Odtworzono tytuły z zachowanego spisu przeskładanej kopii, rozdzielając scalone wiersze; usunięto wtrącone żywe paginy XVII–XXI. Numery zachowano tylko tam, gdzie są widoczne. Nie uzupełniano brakującej paginacji rozdziałów 4–6 i 9–10 ani części podrozdziałów na podstawie innych wydań.

Prologue — 1

1 CAN A COMPUTER HAVE A MIND? — 3
Introduction — 3
The Turing test — 6
Artificial intelligence — 14
An AI approach to ‘pleasure’ and ‘pain’ — 17
Strong AI and Searle’s Chinese room — 21
Hardware and software — 30

2 ALGORITHMS AND TURING MACHINES — 40
Background to the algorithm concept — 40
Turing’s concept — 46
Binary coding of numerical data — 56
The Church Turing Thesis — 61
Numbers other than natural numbers — 65
The universal Turing machine — 67
The insolubility of Hilbert’s problem — 75
How to outdo an algorithm — 83
Church’s lambda calculus — 86

3 MATHEMATICS AND REALITY — 98
The land of Tor’Bled-Nam — 98
Real numbers — 105
How many real numbers are there? — 108
‘Reality’ of real numbers — 112
Complex numbers — 114
Construction of the Mandelbrot set
Platonic reality of mathematical concepts?

4 TRUTH, PROOF, AND INSIGHT
Hilbert’s programme for mathematics
Formal mathematical systems
Godel’s theorem
Mathematical insight
Platonism or intuitionism?
Godel-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 Poincare
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 — 299
Probability amplitudes — 306
The quantum state of a particle — 314
The uncertainty principle — 321
The evolution procedures U and R — 323
Particles in two places at once? — 325
Hilbert space — 332
Measurements — 336
Spin and the Riemann sphere of states — 341
Objectivity and measurability of quantum states — 346
Copying a quantum state — 348
Photon spin — 349
Objects with large spin — 353
Many-particle systems — 355
The ‘paradox’ of Einstein, Podolsky, and Rosen — 361
Experiments with photons: a problem for relativity? — 369
Schrodinger’s equation; Dirac’s equation — 372
Quantum field theory — 374
Schrodinger’s cat — 375
Various attitudes in existing quantum theory — 379
Where does all this leave us? — 383

7 COSMOLOGY AND THE ARROW OF TIME — 391
The flow of time — 391
The inexorable increase of entropy — 394
What is entropy? — 400
The second law in action — 407
The origin of low entropy in the universe — 411
Cosmology and the big bang — 417
The primordial fireball — 423
Does the big bang explain the second law? — 426
Black holes — 427
The structure of space-time singularities — 435
How special was the big bang? — 440

8 IN SEARCH OF QUANTUM GRAVITY — 450
Why quantum gravity? — 450
What lies behind the Weyl curvature hypothesis? — 453
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 quasi crystals
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 — 584
Index — 596