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