Sleight of mind: 75 ingenious paradoxes in mathematics, physics, and philosophy
Exploring more than seventy-five well-known paradoxes in mathematics, philosophy, physics, and the social sciences showing how reason and logic can dispel the illusion of contradiction.Paradox is a sophisticated kind of magic trick. A magician's purpose is to create the appearance of impossibil...
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| Format: | Buch |
| Sprache: | English |
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Cambridge, Massachusetts ; London, England
The MIT Press
[2020]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Exploring more than seventy-five well-known paradoxes in mathematics, philosophy, physics, and the social sciences showing how reason and logic can dispel the illusion of contradiction.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 |
| Beschreibung: | 79 b&w illus |
| Beschreibung: | xii, 350 Seiten Illustrationen, Diagramme 229 mm |
| ISBN: | 9780262043465 |
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| adam_text | Contents Acknowledgments Introduction 1 Infinity 1.1 1.2 1.3 1.4 1.5 2 xi 1 7 Hilbert s Grand Hotel 12 Hyperwebster 14 Crossing Dimensions 17 Banach-Tarski Paradox 20 Cantor s Paradox 29 2.1 Dichotomy 34 2.2 Achilles and the Tortoise 2.3 The Arrow 40 2.4 The Stadium 42 3 33 Zeno s Paradoxes of Motion 38 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 Bertrand s Boxes 84 4.6 Two Children 85 4.7 Simpson s Paradox 88
Contents 5 93 Social Choice 5.1 Condorcet Paradox 96 5.2 Arrow s Impossibility Theorem 98 5.3 Gibbard-Satterthwaite Theorem 101 6 6.1 6.2 6.3 6.4 7 103 Game Theory Bertrand Paradox 110 Braess s Paradox 113 Parrondo s Paradox 116 Rubinstein s Email Problem Self-Reference 117 125 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 Buraii-Forti Paradox 154 7.6 Curry s Paradox 157 7.7 Gödel s Incompleteness Theorems 7.8 Unexpected Hanging 171 8 Induction 179 8.1 All Horses Are the Same Color 8.2 Blue-Eyed Islanders 188 8.3 Bottle Imp 193 8.4 The Raven 196 9 Geometry 184 203 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 226 159
Contents ix 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) 12.1 12.2 12.3 12.4 12.5 12.6 12.7 13 Logical Implications 259 Relativity of Simultaneity 265 Twin Paradox 271 Barn-Pole Paradox 274 Dewan and Beran s Paradox (Bell s Spaceship) Ehrenfest s Paradox 281 Supplee’s Paradox 285 277 Quantum Mechanics (by Michael Coughlin, Matt Cook, and Aidan Chatwin-Davies) 13.1 13.2 13.3 13.4 14 255 291 Double Slit Experiment 297 Schrödinger s Cat 303 Turing Paradox (Quantum Zeno Effect) 308 Einstein-Podolsky-Rosen Paradox 311 Invented or Discovered? 317 14.1 Essay and Poem by Grant Sanderson Notation Guide 327 About the Contributors Bibliography Index 345 335 333 320
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| adam_txt |
Contents Acknowledgments Introduction 1 Infinity 1.1 1.2 1.3 1.4 1.5 2 xi 1 7 Hilbert's Grand Hotel 12 Hyperwebster 14 Crossing Dimensions 17 Banach-Tarski Paradox 20 Cantor's Paradox 29 2.1 Dichotomy 34 2.2 Achilles and the Tortoise 2.3 The Arrow 40 2.4 The Stadium 42 3 33 Zeno's Paradoxes of Motion 38 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 Bertrand's Boxes 84 4.6 Two Children 85 4.7 Simpson's Paradox 88
Contents 5 93 Social Choice 5.1 Condorcet Paradox 96 5.2 Arrow's Impossibility Theorem 98 5.3 Gibbard-Satterthwaite Theorem 101 6 6.1 6.2 6.3 6.4 7 103 Game Theory Bertrand Paradox 110 Braess's Paradox 113 Parrondo's Paradox 116 Rubinstein's Email Problem Self-Reference 117 125 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 Buraii-Forti Paradox 154 7.6 Curry's Paradox 157 7.7 Gödel's Incompleteness Theorems 7.8 Unexpected Hanging 171 8 Induction 179 8.1 All Horses Are the Same Color 8.2 Blue-Eyed Islanders 188 8.3 Bottle Imp 193 8.4 The Raven 196 9 Geometry 184 203 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 226 159
Contents ix 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) 12.1 12.2 12.3 12.4 12.5 12.6 12.7 13 Logical Implications 259 Relativity of Simultaneity 265 Twin Paradox 271 Barn-Pole Paradox 274 Dewan and Beran's Paradox (Bell's Spaceship) Ehrenfest's Paradox 281 Supplee’s Paradox 285 277 Quantum Mechanics (by Michael Coughlin, Matt Cook, and Aidan Chatwin-Davies) 13.1 13.2 13.3 13.4 14 255 291 Double Slit Experiment 297 Schrödinger's Cat 303 Turing Paradox (Quantum Zeno Effect) 308 Einstein-Podolsky-Rosen Paradox 311 Invented or Discovered? 317 14.1 Essay and Poem by Grant Sanderson Notation Guide 327 About the Contributors Bibliography Index 345 335 333 320 |
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| spelling | Cook, Matt Verfasser (DE-588)1151544256 aut Sleight of mind 75 ingenious paradoxes in mathematics, physics, and philosophy Cambridge, Massachusetts ; London, England The MIT Press [2020] © 2020 xii, 350 Seiten Illustrationen, Diagramme 229 mm txt rdacontent n rdamedia nc rdacarrier 79 b&w illus Exploring more than seventy-five well-known paradoxes in mathematics, philosophy, physics, and the social sciences showing how reason and logic can dispel the illusion of contradiction.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 bicssc bisacsh Mathematik (DE-588)4037944-9 gnd rswk-swf Paradoxon (DE-588)4044593-8 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Paradoxon (DE-588)4044593-8 s Mathematik (DE-588)4037944-9 s Physik (DE-588)4045956-1 s Philosophie (DE-588)4045791-6 s DE-604 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032032237&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Sleight of mind 75 ingenious paradoxes in mathematics, physics, and philosophy |
| title_auth | Sleight of mind 75 ingenious paradoxes in mathematics, physics, and philosophy |
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| title_full_unstemmed | Sleight of mind 75 ingenious paradoxes in mathematics, physics, and philosophy |
| title_short | Sleight of mind |
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