Mind Tools -The Mathematics of Information

Rudolf Rucker000-000-000-0

Table of contents :
MIND TOOLS……Page 1
About the Author……Page 3
Dedication……Page 7
Contents……Page 9
00| INTRODUCTION — The Five Modes of Thought……Page 11
Mathematics as Information……Page 13
Number and Space……Page 15
Logic and Infinity……Page 20
Psychological Roots of Mathematical Concepts……Page 24
Information and Communication……Page 35
A History of Ideas……Page 41
01| NUMBER……Page 46
Zero and One……Page 48
Numbers and Logs……Page 49
Number Patterns……Page 58
Numerology, Numberskulls, and Crowds……Page 81
The Mind Reckoner……Page 86
Words as Numbers……Page 92
The Limits of Knowledge……Page 99
02| SPACE……Page 106
Math Space and Real Space……Page 108
Tiles, Cells, Pixels, and Grids……Page 112
Algebraic Curves……Page 128
Wiggles and Whorls……Page 150
Endless Complexity……Page 165
Fractals……Page 170
Life Is a Fractal in Hilbert Space……Page 187
Hilbert Space……Page 192
03| LOGIC……Page 204
The Laws of Thought……Page 206
The Syllogism……Page 209
Symbolic Logic……Page 216
Exploring Logical Space……Page 222
Godel's Theorem……Page 218
Turing Machines……Page 235
Unsolvable Problems……Page 245
The Ocean of Truth……Page 252
04| INFINITY AND INFORMATION……Page 258
How Big Is Infinity?……Page 260
Information and the Continuum Problem……Page 270
Infinitesimals in Perspective……Page 276
Algorithmic Complexity……Page 288
Inconceivability……Page 299
Runtime……Page 310
Everything is Information……Page 315
INDEX……Page 324
Back Page……Page 339