Fate Of Schrodinger's Cat, The: Using Math And Computers To Explore The Counterintuitive скачать fb2

Can we correctly predict the flip of a fair coin more than half the time &#x2014; 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&#x2013;50 guesses.But mathematics is filled with counterintuitive results &#x2014; 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&apos;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 &apos;hot hand&apos; 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&apos;s Cat.<b>Contents:</b> <ul><li>Preface</li><li>Introduction &#x2014; Mathematics, Intuition, and Computers</li><li><b><i>The Realm of the Counterintuitive:</i></b><ul><li>The Monty Hall Problem</li><li>How Probabilistic Entanglement Connects Almost Everything</li><li>Blackwell&apos;s Bet</li><li>A Stop at Willoughby &#x2014; Mathematics in the Twilight Zone</li><li>The Fate of Schrodinger&apos;s Cat</li><li>Coins and Camels</li></ul></li><li><b><i>The Monday Morning Quarterback:</i></b><ul><li>The Joy of Simulation</li><li>Numbed by Numbers</li><li>Losing the Battle, Winning the War</li></ul></li><li><b><i>Getting It Right; A Synergy of Mathematics, Intuition and Computers:</i></b><ul><li>The Hot Hand</li><li>The Bent Coin and the Hot Hand</li></ul></li><li><b><i>The Last Hurrah:</i></b><ul><li>Using Combinatorics to Improve Advertising &#x2014; For Everyone</li></ul></li><li><b><i>Appendix &#x2014; Basic Probability Theory:</i></b><ul><li>Computational Rules for Probability</li><li>Conditional Probability</li><li>Independent Events</li><li>Expected Value (a.k.a. Expectation)</li><li>Bernoulli Trials</li><li>Means and Medians</li></ul></li><li>Annotated Bibliography</i></b><li>Index</i></b></ul><br><b>Readership:</b> General Public, undergraduate math teachers and students in mathematics, computer programming, quantum mechanics, sports or the advertising business.Computer Programming;Sports Betting;Advertising;Prediction;Mathematics;Statistics;Bernoulli Trials;Coin Flip;Expectation;Quantum Mechanics;Mathematical Model;Gambling;Hidden Variables;Random Walk;Random Variable;Math Education;Sports Statistics;Arrow&apos;s Impossibility Theorem;Radioactive Decay;50–50;Paradox;Random Number Generator;Intuition;Monty Hall Problem;Chaos Theory;lackwell&apos;s Bet;David Blackwell;Butterfly Effect;Connectedness;Postdiction;Blackjack;Sportsmanlike Dumping0<b>Key Features:</b><ul><li>Much of the material is either new or has not seen in a book of this type &#x2014; in some cases because it has only appeared in journals or books within the last year or so</li><li>It is a unique blend of probability, statistics, computer modeling, sports, decision-making, quantum mechanics and the advertising business</li></ul>

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