
Sleight of Mind
Description
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Paradox is a sophisticated kind of magic trick. A magician's purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn't require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction.
The journey begins with "a most ingenious paradox” from Gilbert and Sullivan's Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform "supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more.
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Content
- Intro
- Title Page
- Copyright
- Dedication
- Table of Contents
- Acknowledgments
- Introduction
- 1. Infinity
- 1.1. Hilbert's Grand Hotel
- 1.2. Hyperwebster
- 1.3. Crossing Dimensions
- 1.4. Banach-Tarski Paradox
- 1.5. Cantor's Paradox
- 2. Zeno's Paradoxes of Motion
- 2.1. Dichotomy
- 2.2. Achilles and the Tortoise
- 2.3. The Arrow
- 2.4. The Stadium
- 3. Supertasks
- 3.1. Thomson's Lamp
- 3.2. Ross-Littlewood Paradox
- 3.3. Laraudogoitia's Point Masses
- 4. Probability
- 4.1. Sleeping Beauty
- 4.2. St. Petersburg Paradox
- 4.3. Two Envelopes
- 4.4. Monty Hall Problem
- 4.5. Bertrand's Boxes
- 4.6. Two Children
- 4.7. Simpson's Paradox
- 5. Social Choice
- 5.1. Condorcet Paradox
- 5.2. Arrow's Impossibility Theorem
- 5.3. Gibbard-Satterthwaite Theorem
- 6. Game Theory
- 6.1. Bertrand Paradox
- 6.2. Braess's Paradox
- 6.3. Parrondo's Paradox
- 6.4. Rubinstein's Email Problem
- 7. Self-Reference
- 7.1. Russell's Paradox
- 7.2. The Liar Paradox Family
- 7.3. Berry's Paradox
- 7.4. Richard's Paradox
- 7.5. Burali-Forti Paradox
- 7.6. Curry's Paradox
- 7.7. Gödel's Incompleteness Theorems
- 7.8. Unexpected Hanging
- 8. Induction
- 8.1. All Horses Are the Same Color
- 8.2. Blue-Eyed Islanders
- 8.3. Bottle Imp
- 8.4. The Raven
- 9. Geometry
- 9.1. Fractional Dimensions
- 9.2. Aristotle's Wheels
- 9.3. Coin Rotation Paradox
- 9.4. Roly-Poly's Staircase
- 9.5. Block Stacking
- 9.6. The Ant's Elastic Adventure
- 10. Operations
- 10.1. Missing Dollar Riddle
- 10.2. A Paradox of Derivatives
- 10.3. Two Equals One
- 10.4. Summing a Divergent Series
- 10.5. Summing the Naturals
- 11. Classical Physics (by Nicholas Laurita)
- 11.1. Maxwell's Demon
- 11.2. Brownian Ratchet
- 11.3. Feynman Sprinkler
- 12. Special Relativity (by Aidan Chatwin-Davies)
- 12.1. Logical Implications
- 12.2. Relativity of Simultaneity
- 12.3. Twin Paradox
- 12.4. Barn-Pole Paradox
- 12.5. Dewan and Beran's Paradox (Bell's Spaceship)
- 12.6. Ehrenfest's Paradox
- 12.7. Supplee's Paradox
- 13. Quantum Mechanics (by Michael Coughlin, Matt Cook, and Aidan Chatwin-Davies)
- 13.1. Double Slit Experiment
- 13.2. Schrödinger's Cat
- 13.3. Turing Paradox (Quantum Zeno Effect)
- 13.4. Einstein-Podolsky-Rosen Paradox
- 14. Invented or Discovered?
- 14.1. Essay and Poem by Grant Sanderson
- Notation Guide
- About the Contributors
- Bibliography
- Index
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