**Chapter 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**

**Chapter 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 Undo an Algorithm**

**Church's Lambda Calculus**

**Chapter 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 Mandlebrot Set**

**Platonic Reality of Mathematical Concepts**

**Chapter 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**

**Complexity Theory**

**Complexity and Computability in Physical Things**

**Chapter 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**

**Chapter 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 Space**

**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?**

**Chapter 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?**

**Chapter 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?**

**Chapter 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?**

**Chapter 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-Verbailty 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 Releance to Brain Plasticity**

**The Time-Delays of Consciousness**

**The Strange Role of Time in Conscious Perception**