ProofWiki:Books/Rudy Rucker/Mind Tools
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Rudy Rucker: Mind Tools: The Five Levels of Mathematical Reality
Published 1987, Houghton Mifflin Company.
ISBN 0-395-46810-8
Contents
- INTRODUCTION: THE FIVE MODES OF THOUGHT
- Mathematics as Information
- Number and Space
- Logic and Infinity
- Psychological Roots of Mathematical Concepts
- Information and Communication
- A History of Ideas
- 1 NUMBER
- Zero and One
- Numbers and Logs
- Number Patterns
- Numerology, Numberskulls, and Crowds
- The Mind Reckoner
- Words as Numbers
- The Limits of Knowledge
- 2 SPACE
- Math Space and Real Space
- Tiles, Cells, Pixels, and Grids
- Algebraic Curves
- Wiggles and Whorls
- Endless Complexity
- Fractals
- Life Is a Fractal in Hilbert Space
- Hilbert Space
- 3 LOGIC
- The Laws of Thought
- The Syllogism
- Symbolic logic
- Exploring Logical Space
- Godel's Theorem
- Turing Machines
- Unsolvable Problems
- The Ocean of Truth
- 4 INFINITY AND INFORMATION
- How Big Is Infinity?
- Information and the Continuum Problem
- Infinitesimals in Perspective
- Algorithmic Complexity
- Inconceivability
- Runtime
- Everything Is Information
- Index
