Cargando…
Infinity and the Mind : the Science and Philosophy of the Infinite /
A dynamic exploration of infinityIn 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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2019.
|
| Colección: | Princeton science library ;
86. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; TABLE OF CONTENTS; Preface to the 2019 Edition; Preface to the 2005 Edition; Preface to the 1995 Paperback Edition; Preface to the First Edition; Chapter One: Infinity; A Short History of Infinity; Physical Infinities; Temporal Infinities; Spatial Infinities; Infinities in the Small; Conclusion; Infinities in the Mindscape; The Absolute Infinite; Connections; Puzzles and Paradoxes; Chapter Two: All the Numbers; From Pythagoreanism to Cantorism; Transfinite Numbers; From Omega to Epsilon-Zero; The Alefs; Infinitesimals and Surreal Numbers; Higher Physical Infinities
- Puzzles and ParadoxesChapter Three: The Unnameable; The Berry Paradox; Naming Numbers; Understanding Names; Random Reals; Constructing Reals; The Library of Babel; Richard's Paradox; Coding the World; What is Truth?; Conclusion; Puzzles and Paradoxes; Chapter Four: Robots and Souls; Gödel's Incompleteness Theorem; Conversations with Gödel; Towards Robot Consciousness; Formal Systems and Machines; The Liar Paradox and the Non-Mechanizability of Mathematics; Artificial Intelligence via Evolutionary Processes; Robot Consciousness; Beyond Mechanism?; Puzzles and Paradoxes
- Chapter Five: The One and the ManyThe Classical One/Many Problem; What is a Set?; The Universe of Set Theory; Pure Sets and the Physical Universe; Proper Classes and Metaphysical Absolutes; Interface Enlightenment; One/Many in Logic and Set Theory; Mysticism and Rationality; Satori; Puzzles and Paradoxes; Excursion One: The Transfinite Cardinals; On and Alef-One; Cardinality; The Continuum; Large Cardinals; Excursion Two: Gödel's Incompleteness Theorems; Formal Systems; Self-Reference; Gödel's Proof; A Technical Note on Man-Machine Equivalence; Answers to the Puzzles and Paradoxes; Notes