Just Announced: The Children's & YA Book Awards Winners Explore Now
Infinity and the Mind: The Science and Philosophy of the Infinite

Infinity and the Mind: The Science and Philosophy of the Infinite

by Rudolf V Rucker
Infinity and the Mind: The Science and Philosophy of the Infinite

Infinity and the Mind: The Science and Philosophy of the Infinite

by Rudolf V Rucker

Overview

A dynamic exploration of infinity

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.

Product Details

ISBN-13: 9780691191386
Publisher: Princeton University Press
Publication date: 07/23/2019
Series: Princeton Science Library , #63
Edition description: Reprint
Pages: 376
Sales rank: 442,536
Product dimensions: 5.50(w) x 8.40(h) x 0.80(d)

About the Author

Rudy Rucker is a mathematician, computer scientist, author, and one of the founders of the cyberpunk literary movement. His many books on mathematics and philosophy include Mind Tools and The Fourth Dimension, and his numerous works of science fiction include The Ware Tetralogy, Turing & Burroughs, and his novel of infinity, White Light.

Table of Contents

Preface to the Paperback Edition ix
Preface xi
Chapter One: Infinity 1
A Short History of Infinity 1
Physical Infinities 9
Temporal Infinities 10
Spatial Infinities 15
Infinities in the Small 24
Conclusion 34
Infinities in the Mindscape 35
The Absolute Infinite 44
Connections 49
Puzzles and Paradoxes 51
Chapter Two: All the Numbers 53
From Pythagoreanism to Cantorism 53
Transfinite Numbers 64
From Omega to Epsilon-Zero 65
The Alefs 73
lnfinitesimals and Surreal Numbers 78
Higher Physical Infinities 87
Puzzles and Paradoxes 91
Chapter Three: The Unnameable 93
The Berry Paradox 93
Naming Numbers 95
Understanding Names 100
Random Reals 107
Constructing Reals 108
The Library of Babel 120
Richard's Paradox 126
Coding the World 130
What is Truth? 143
Conclusion 152
Puzzles and Paradoxes 155
Chapter Four: Robots and Souls 157
Godel's incompleteness Theorem 157
Conversations with Godel 164
Towards Robot Consciousness 171
Formal Systems and Machines 172
The Liar Paradox and the Non-Mechanizability of Mathematics 175
Artificial Intelligence via Evolutionary Processes 180
Robot Consciousness 183
Beyond Mechanism? 185
Puzzles and Paradoxes 187
Chapter Five: The One and the Many 189
The Classical One/Many Problem 189
What is a Set? 191
The Universe of Set Theory 196
Pure Sets and the Physical Universe 196
Proper Classes and Metaphysical Absolutes 202
Interface Enlightenment 206
One/Many in Logic and Set Theory 207
Mysticism and Rationality 209
Satori 214
Puzzles and Paradoxes 219
ExcursionOne: The Transfinite Cardinals 221
On and Alef-One 221
Cardinality 226
The Continuum 238
Large Cardinals 253
Excursion Two: Godel's Incompleteness Theorems 267
Formal Systems 267
Self-Reference 280
Godel's Proof 285
A Technical Note on Man-Machine Equivalence 292
Answers to the Puzzles and Paradoxes 295
Notes 307
Bibliography 329
Index 339

What People are Saying About This

Martin Gardner

Informal, amusing, witty, profound. . . . In an extraordinary burst of creative energy, Rudy Rucker has managed to bring together every aspect of mathematical infinity. . . . A dizzying glimpse into that boundless region of blinding light where the mysteries of transcendence shatter the clarity of logic, set theory, proof theory, and contemporary physics.

Thomas Tymoczko

Infinity and the Mind can be read and enjoyed by experts and nonexperts alike. Rudy Rucker is a talented logician who draws on his talents as a science-fiction writer and cartoonist to convey his ideas. This makes for not only a solid, accurate, and informative book but also a good read.
— Thomas Tymoczko, Smith College

From the Publisher

“A terrific study with real mathematical depth.”—New Yorker

“Rucker leads his readers through these mental gymnastics in an easy, informal way.”—San Francisco Chronicle

“Infinity and the Mind is funny, provocative, entertaining, and profound.”—Joseph Shipman, Journal of Symbolic Logic

“Attempts to put Gödel’s theorems into sharper focus, or at least to explain them to the nonspecialist, abound. My personal favorite is Rudy Rucker’s Infinity and the Mind, which I recommend without reservation.”—Craig Smorynski, American Mathematical Monthly

“Informal, amusing, witty, profound. . . . In an extraordinary burst of creative energy, Rudy Rucker has managed to bring together every aspect of mathematical infinity.”—Martin Gardner

From the B&N Reads Blog
Page 1 of

Related Subjects

Philosophy
Science & Technology
Major Branches of Philosophical Study
Mathematics
Logic
Logic & Foundations of Mathematics
Mathematics - Sets, General Topology, & Categories
Philosophy
Science & Technology
Major Branches of Philosophical Study
Mathematics
Logic
Logic & Foundations of Mathematics
Mathematics - Sets, General Topology, & Categories

Customer Reviews