*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 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

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

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?

Schrodinger's equation; Dirac's equation

Quantum field theory

Schrodinger'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

BUndsight

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*