Screen LibraryThe fate of Schrodinger's cat : using math and computers to explore the counterintuitive /
Can we correctly predict the flip of a fair coin more than half the time -- or the decay of a single radioactive atom? Our intuition, based on a lifetime of experience, tells us that we cannot, as these are classic examples of what are known to be 50-50 guesses.But mathematics is filled with counter...
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| Main Authors: | |
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| Published: |
World Scientific,
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| Publisher Address: | New Jersey : |
| Publication Dates: | [2020] |
| Literature type: | Book |
| Language: | English |
| Series: |
Problem solving in mathematics and beyond,
volume 17 |
| Subjects: | |
| Summary: |
Can we correctly predict the flip of a fair coin more than half the time -- or the decay of a single radioactive atom? Our intuition, based on a lifetime of experience, tells us that we cannot, as these are classic examples of what are known to be 50-50 guesses.But mathematics is filled with counterintuitive results -- and this book discusses some surprising and entertaining examples. It is possible to devise experiments in which a flipped coin lands heads completely at random half the time, but we can also correctly predict when it will land heads more than half the time. The Fate of Schrodinger's Cat shows how high-school algebra and basic probability theory, with the invaluable assistance of computer simulations, can be used to investigate both the intuitive and the counterintuitive.This book explores fascinating and controversial questions involving prediction, decision-making, and statistical analysis in a number of diverse areas, ranging from whether there is such a thing as a 'hot hand' in shooting a basketball, to how we can successfully predict, more than half the time, the decay of the radioactive atom that determines the fate of Schrodinger's Cat--Publisher's description. |
| Carrier Form: | xii, 158 pages : illustrations, forms ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 147-156) and index. |
| ISBN: |
9789811218637 9811218633 9789811218156 9811218153 |
| Index Number: | QA273 |
| CLC: | O211 |
| Call Number: | O211/S819 |
| Contents: |
Introduction: Mathematics, intuition, and computers -- The Realm of the Counterintuitive. The Monty Hall problem -- How probabilistic entanglement connects almost everything -- Blackwell's bet -- A stop at Willoughby : mathematics in the twilight zone -- The fate of Schrodinger's cat -- Coins and camels -- The Monday Morning Quarterback. The joy of simulation -- Numbed by numbers -- Losing the battle, winning the war -- Getting It Right; A Synergy of Mathematics, Intuition and Computers. The hot hand -- The bent coin and the hot hand -- The Last Hurrah. Using combinatorics to improve advertising : for everyone -- Appendices: Basic probability theory ; Computational rules for probability ; Conditional probability ; Independent events ; Expected value (a.k.a. expectation) ; Bernoulli trials ; Means and medians. Introduction: Mathematics, intuition, and computers -- The Realm of the Counterintuitive. The Monty Hall problem : The Monty Hall problem ; Looking at an extreme case ; A trickier Monty Hall problem ; Just one look -- How probabilistic entanglement connects almost everything : Is everything connected? ; Quantum entanglement ; Probabilistic entanglement ; Benefitting from a coin flip ; Flipism ; Multiple observations from a single group ; An odd number of trials ; Comparing means of unrelated groups ; How fundamental is probability? -- Blackwell's bet : Wunch with Wenny ; Unexpected expectations ; Can Blackwell's bet help you beat the line at sports betting? ; Applying Blackwell's bet to sample and population statistics -- A stop at Willoughby : mathematics in the twilight zone : Can you predict the flip of the coin? ; Random walks ; Next stop : Willoughby ; An actual coin flip prediction ; A magical mystery tour ; Are we predicting the future? -- The fate of Schrodinger's cat : Blackwell's bet redux ; More about Bernoulli trials ; Creating a predictable Schrodinger's cat experiment ; Would this experiment fool Erwin Schrodinger? ; The Schrodinger switcheroo ; Why science is difficult ; The solar neutrino deficit ; Hidden variables ; Non-predictable Bernoulli trials ; Time travel and predictability paradoxes ; Of time and third avenue ; Checking out the Schrodinger's cat experiment in your home -- Coins and camels : Distinguishing similar Bernoulli trials ; The problem of the 17 camels ; Doing the math ; A slightly different problem ; When one door closes : how mathematicians find problems to investigate -- The Monday Morning Quarterback. The joy of simulation : Random number generators ; Chi-square tests; Karl Pearson ; Simulations in contemporary science and engineering ; Simulation in fantasy sports ; Why educators should teach simulation rather than algebra ; Simulation in the electoral college ; Why are Tennis' Big Three so dominant? -- Numbed by numbers : A really, really, REALLY bad statistic ; The year of the unbeatens ; Simulating the NFL ; Integrating the real world with education -- Losing the battle, winning the war : The post-season ; The Gibbard-Satterthwaite theorem ; Dumping for future advantage -- Getting It Right; A Synergy of Mathematics, Intuition and Computers. The hot hand : Can the "hot hand" be exploited to win at betting sports? ; The "hot hand" in a wider context -- The bent coin and the hot hand : Binomial trials and tribulations ; Binomial trials and flipping a coin just once ; A different approach ; The probability of the probability of probabilities ; More simulations ; The hot hand redux ; Jensen's inequality ; Doing better than average -- The Last Hurrah. Using combinatorics to improve advertising : for everyone : A brief history of advertising ; What we hate about advertising ; The element of surprise ; Combinatorial commercials -- Appendices: Basic probability theory ; Computational rules for probability ; Conditional probability ; Independent events ; Expected value (a.k.a. expectation) ; Bernoulli trials ; Means and medians. |