Sleight of Mind: 75 Ingenious Paradoxes in Mathematics, Physics, and Philosophy

by Matt Cook

Overview

This “fun, brain-twisting book . . . will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden).

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.

Product Details

ISBN-13:	9780262542296
Publisher:	MIT Press
Publication date:	08/03/2021
Series:	Mit Press
Pages:	368
Sales rank:	204,135
Product dimensions:	5.60(w) x 8.70(h) x 0.80(d)

About the Author

Matt Cook, PhD, is an economist, bestselling author, and magician. Among his works are the thriller novel Sabotage and entrepreneurial success book The Startup Star, which he wrote at Stanford University. Trained at the world-famous Magic Castle, he has performed across the globe and enjoys infusing talks and lectures with sleight of hand. He cofounded U.S. Common Sense, the country's premiere government data and transparency organization. For his support of the military, he was honored by President George W. Bush with the Call to Service Award. He is an accomplished pianist and musical composer, has executive produced for film, and earned his doctorate at the University of Pennsylvania.

Table of Contents

Acknowledgments xi

Introduction 1

1 Infinity 7

1.1 Hilbert's Grand Hotel 12

1.2 Hyperwebster 14

1.3 Crossing Dimensions 17

1.4 Banach-Tarski Paradox 20

1.5 Cantor's Paradox 29

2 Zeno's Paradoxes of Motion 33

2.1 Dichotomy 34

2.2 Achilles and the Tortoise 38

2.3 The Arrow 40

2.4 The Stadium 42

3 Supertasks 45

3.1 Thomson's Lamp 46

3.2 Ross-Littlewood Paradox 48

3.3 Laraudogoitia's Point Masses 52

4 Probability 57

4.1 Sleeping Beauty 63

4.2 St. Petersburg Paradox 69

4.3 Two Envelopes 74

4.4 Monty Hall Problem 83

4.5 Berrrand's Boxes 84

4.6 Two Children 85

4.7 Simpson's Paradox 88

5 Social Choice 93

5.1 Condorcet Paradox 96

5.2 Arrow's Impossibility Theorem 98

5.3 Gibbard-Satterthwaite Theorem 101

6 Game Theory 103

6.1 Bertrand Paradox 110

6.2 Braess's Paradox 113

6.3 Parrondo's Paradox 116

6.4 Rubinstein's Email Problem 117

7 Self-Reference 125

7.1 Russell's Paradox 129

7.2 The Liar Paradox Family 135

7.3 Berry's Paradox 151

7.4 Richard's Paradox 152

7.5 Burali-Ford Paradox 154

7.6 Curry's Paradox 157

7.7 Gödel's Incompleteness Theorems 159

7.8 Unexpected Hanging 171

8 Induction 179

8.1 All Horses Are the Same Color 184

8.2 Blue-Eyed Islanders 188

8.3 Bottle Imp 193

8.4 The Raven 196

9 Geometry 203

9.1 Fractional Dimensions 204

9.2 Aristotle's Wheels 213

9.3 Coin Rotation Paradox 214

9.4 Roly-Poly's Staircase 216

9.5 Block Stacking 218

9.6 The Ant's Elastic Adventure 220

10 Operations 223

10.1 Missing Dollar Riddle 224

10.2 A Paradox of Derivatives 225

10.3 Two Equals One 226

10.4 Summing a Divergent Series 227

10.5 Summing the Naturals 234

11 Classical Physics (by Nicholas Laurita) 239

11.1 Maxwell's Demon 245

11.2 Brownian Ratchet 249

11.3 Feynman Sprinkler 251

12 Special Relativity (by Aidan Chatwin-Davies) 255

12.1 Logical Implications 259

12.2 Relativity of Simultaneity 265

12.3 Twin Paradox 271

12.4 Barn-Pole Paradox 274

12.5 Dewan and Beran's Paradox (Bell's Spaceship) 277

12.6 Ehrenfest's Paradox 281

12.7 Supplee's Paradox 285

13 Quantum Mechanics (by Michael Coughlin, Matt Cook, and Aidan Chatwin-Davies) 291

13.1 Double Slit Experiment 297

13.2 Schrödinger's Cat 303

13.3 Turing Paradox (Quantum Zeno Effect) 308

13.4 Einstein-Podolsky-Rosen Paradox 311

14 Invented or Discovered? 317

14.1 Essay and Poem by Grant Sanderson 320

Notation Guide 327

About the Contributors 333

Bibliography 335

Index 345

What People are Saying About This

From the Publisher

“Nothing focuses the mind like a good paradox. In this fun, brain-twisting book, Matt Cook and collaborators examine an impressive list of apparently self-contradictory scenarios, only to explain away the puzzles using logic and science. Every chapter will make you think.”

—Sean Carroll, theoretical physicist and New York Times bestselling author of Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime

“A monumental achievement written so that it can be enjoyed as pure fun. Matt Cook takes us on a guided tour of some of the most vexing problems in logic, physics, math, and beyond. Full of brain teasers, if not brain breakers."

—Lee McIntyre, philosopher and author of Post-Truth andThe Scientific Attitude: Defending Science from Denial, Fraud, and Pseudoscience

“A delightful catalog of paradoxes in mathematics, social sciences, and physics. Intellectually curious readers will learn much about how far rational thinking can lead us in understanding the physical and social world and how counter-intuitive the consequences of logic sometimes can be. A most pleasurable trip of discovery!”

—Jesus Fernandez-Villaverde, Professor of Economics at the University of Pennsylvania