Completed second draft of this book

PDF version of this book

Contents

• List of Figures
• List of Tables
• Preface
• Structure and essence
  • Essence and chemistry
  • Essence as a Platonic ideal
  • Structure in computing and mathematics
  • Gödel and unfathomable complexity
  
  
• What is
  • Unifying external and internal reality
  • Universal consciousness
  • Defining bessense
  • All that exists is finite
  • Boundaries
  • Extensions of consciousness
  
  
• Mathematical structure
  • Mathematics and consciousness
  • Logically determined unsolvable problems
  • Formal logic
  • Formal mathematics
  • Axioms of Set Theory
    • Axiom of extensionality
    • Axiom of the empty set
    • Axiom of unordered pairs
    • Axiom of union
    • Axiom of infinity
  • Infinity
  • Cardinal numbers
  • Gödel's Incompleteness Theorem
  • The Halting Problem
  
  
• Creative mathematics
  • Arithmetical Hierarchy
  • Ordinal induction
  • Axiom scheme of replacement
  • Ordinal numbers
  • Searching all possible paths
  • Power set axiom
  • Trees of trees
  • Extending mathematics
  • Is the cardinality of the reals 0 or ?
  • A philosophy of mathematical truth
  
  
• Digital physics
  • Time and distance scales
  • Waves, particles and events
  • Interpretations of quantum mechanics
  • Discretizing the wave equation
  • Unique properties of discrete models
  • Einstein's approach to physics
  • Special Relativity
  • General Relativity
  • Quantum Mechanics
  • The uncertainty principle
  • Quantum Entanglement
  • The real line and configuration space
  
  
• Relativity plus quantum mechanics
  • Locality and quantum mechanics
  • Realistic theories and randomness
  • Polarized light
  • Bell's theorem simple limited proof
  • Bell's theorem general proof
  • Experimental tests of Bell's inequality
  • Exploring discretized wave equations
  • The structure of the universe
  
  
• Bibliography
• About this document ...