Book: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