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Tables of Contents for The Emperor's New Mind
Chapter/Section Title
Page #
Page Count
Prologue
1
3
Can a Computer Have a Mind?
3
37
Introduction
3
3
The Turing test
6
8
Artificial intelligence
14
3
An AI approach to `pleasure' and `pain'
17
4
Strong AI and Searle's Chinese room
21
9
Hardware and software
30
10
Algorithms and Turing Machines
40
58
Background to the algorithm concept
40
6
Turing's concept
46
10
Binary coding of numerical data
56
5
The Church--Turing Thesis
61
4
Numbers other than natural numbers
65
2
The universal Turing machine
67
8
The insolubility of Hilbert's problem
75
8
How to outdo an algorithm
83
3
Church's lambda calculus
86
12
Mathematics and Reality
98
31
The land of Tor'Bled-Nam
98
7
Real numbers
105
3
How many real numbers are there?
108
4
`Reality' of real numbers
112
2
Complex numbers
114
6
Construction of the Mandelbrot set
120
3
Platonic reality of mathematical concepts?
123
6
Truth, Proof, and Insight
129
64
Hilbert's programme for mathematics
129
4
Formal mathematical systems
133
5
Godel's theorem
138
3
Mathematical insight
141
5
Platonism or intuitionism?
146
5
Godel-type theorems from Turing's result
151
4
Recursively enumerable sets
155
6
Is the Mandelbrot set recursive?
161
7
Some examples of non-recursive mathematics
168
9
Is the Mandelbrot set like non-recursive mathematics?
177
4
Complexity theory
181
7
Complexity and computability in physical things
188
5
The Classical World
193
98
The status of physical theory
193
9
Euclidean geometry
202
7
The dynamics of Galileo and Newton
209
8
The mechanistic world of Newtonian dynamics
217
3
Is life in the billiard-ball world computable?
220
5
Hamiltonian mechanics
225
3
Phase space
228
10
Maxwell's electromagnetic theory
238
5
Computability and the wave equation
243
1
The Lorentz equation of motion; runaway particles
244
4
The special relativity of Einstein and Poincare
248
13
Einstein's general relativity
261
12
Relativistic causality and determinism
273
5
Computability in classical physics: where do we stand?
278
2
Mass, matter, and reality
280
11
Quantum Magic and Quantum Mystery
291
100
Do philosophers need quantum theory?
291
4
Problems with classical theory
295
2
The beginnings of quantum theory
297
2
The two-slit experiment
299
7
Probability amplitudes
306
8
The quantum state of a particle
314
7
The uncertainty principle
321
2
The evolution procedures U and R
323
2
Particles in two places at once?
325
7
Hilbert space
332
4
Measurements
336
5
Spin and the Riemann sphere of states
341
5
Objectivity and measurability of quantum states
346
2
Copying a quantum state
348
1
Photon spin
349
4
Objects with large spin
353
2
Many-particle systems
355
6
The `paradox' of Einstein, Podolsky, and Rosen
361
8
Experiments with photons: a problem for relativity?
369
3
Schrodinger's equation; Dirac's equation
372
2
Quantum field theory
374
1
Schrodinger's cat
375
4
Various attitudes in existing quantum theory
379
4
Where does all this leave us?
383
8
Cosmology and the Arrow of Time
391
59
The flow of time
391
3
The inexorable increase of entropy
394
6
What is entropy?
400
7
The second law in action
407
4
The origin of low entropy in the universe
411
6
Cosmology and the big bang
417
6
The primordial fireball
423
3
Does the big bang explain the second law?
426
1
Black holes
427
8
The structure of space-time singularities
435
5
How special was the big bang?
440
10
In Search of Quantum Gravity
450
33
Why quantum gravity?
450
3
What lies behind the Weyl curvature hypothesis?
453
5
Time-asymmetry in state-vector reduction
458
7
Hawking's box: a link with the Weyl curvature hypothesis?
465
10
When does the state-vector reduce?
475
8
Real Brains and Model Brains
483
40
What are brains actually like?
483
9
Where is the seat of consciousness?
492
4
Split-brain experiments
496
3
Blindsight
499
1
Information processing in the visual cortex
500
2
How do nerve signals work?
502
5
Computer models
507
5
Brain plasticity
512
2
Parallel computers and the `oneness' of consciousness
514
2
Is there a role for quantum mechanics in brain activity?
516
2
Quantum computers
518
2
Beyond quantum theory?
520
3
Where Lies the Physics of Mind?
523
60
What are minds for?
523
6
What does consciousness actually do?
529
5
Natural selection of algorithms?
534
4
The non-algorithmic nature of mathematical insight
538
3
Inspiration, insight, and originality
541
7
Non-verbality of thought
548
2
Animal consciousness?
550
2
Contact with Plato's world
552
3
A view of physical reality
555
3
Determinism and strong determinism
558
2
The anthropic principle
560
2
Tilings and quasicrystals
562
4
Possible relevance to brain plasticity
566
2
The time-delays of consciousness
568
5
The strange role of time in conscious perception
573
5
Conclusion: a child's view
578
5
Epilogue
583
1
References
584
12
Index
596