1 CAN A COMPUTER HAVE A MIND?
The Turing test
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 Hubert'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
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 and computability in physical things
5 THE CLASSICAL WORLD
The status of physical theory
The dynamics of Galileo and Newton
The mechanistic world of Newtonian dynamics
Is life in the billiard-ball world computable?
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
The quantum state of a particle
The uncertainty principle
The evolution procedures U and R
Particles in two places at once?
Spin and the Riemann sphere of states
Objectivity and measurability of quantum states
Copying a quantum state
Objects with large spin
The 'paradox' of Einstein, Podolsky, and Rosen
Experiments with photons: a problem for relativity?
Schrodinger's equation; Dirac's equation
Quantum field theory
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?
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?
Information processing in the visual cortex
How do nerve signals work?
Parallel computers and the 'oneness' of consciousness
Is there a role for quantum mechanics in brain activity?
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
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