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Infinity and the Mind
The Science and Philosophy of the Infinite
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Rudolf V Rucker
Language:
English
Published/Copyright:
2019
About this book
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.
Author / Editor information
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.
Reviews
“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
“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
Topics
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Frontmatter
i -
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TABLE OF CONTENTS
v -
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Preface to the 2019 Edition
ix -
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Preface to the 2005 Edition
xv -
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Preface to the 1995 Paperback Edition
xxiii -
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Preface to the First Edition
xxv -
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Chapter One: Infinity
1 -
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Chapter Two: All the Numbers
53 -
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Chapter Three: The Unnameable
93 -
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Chapter Four: Robots and Souls
157 -
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Chapter Five: The One and the Many
189 -
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Excursion One: The Transfinite Cardinals
221 -
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Excursion Two: Gödel's Incompleteness Theorems
267 -
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Answers to the Puzzles and Paradoxes
295 -
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Notes
307 -
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Bibliography
329 -
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Index
339
Publishing information
Pages and Images/Illustrations in book
eBook published on:
July 23, 2019
eBook ISBN:
9780691191256
Pages and Images/Illustrations in book
Main content:
376
Other:
110 b/w illus.
eBook ISBN:
9780691191256
Keywords for this book
Natural number; Real number; Infinity and the Mind; Theorem; Mathematics; Set theory; Axiom; Theory; Transfinite; Infinitesimal; Gödel's incompleteness theorems; Transfinite number; Infinity; Summation; Continuum hypothesis; Axiom of infinity; Actual infinity; Mathematician; Instance (computer science); Quantum mechanics; Hyperreal number; Subset; Thought; Ultrafilter; Transcendental number; Hilbert's program; Superspace; Many-worlds interpretation; Mental space; Goldbach's conjecture; Berry paradox; Tetration; Zermelo–Fraenkel set theory; Prime number; Ordinal number; Cardinality; Infinite divisibility (probability); Infinity symbol; Inaccessible cardinal; Richard's paradox; Zeno's paradoxes; The Philosopher; Martin's axiom; Exponentiation; Burali-Forti paradox; Polynomial; Conjecture; Divergent series; Contradiction; Method of exhaustion; Time travel; Special relativity; Douglas Hofstadter; Number theory; Limit cardinal; Surreal number; Fermat's Last Theorem; Coefficient; Infinite monkey theorem; Monism; Cantor's theorem; Measurable cardinal; Parity (mathematics); Commutative property; Equation; Calculation; Space; Complete theory; Integer; Sign (mathematics)
Audience(s) for this book
College/higher education;Professional and scholarly;General/trade;
