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E-raamat: Fate Of Schrodinger's Cat, The: Using Math And Computers To Explore The Counterintuitive

(California State University, Long Beach, Usa)
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"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-intuitive 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 counter-intuitive. 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"--
Preface v
Introduction -- Mathematics, Intuition, and Computers 1(2)
Section I The Realm of the Counterintuitive
3(66)
Chapter 1 The Monty Hall Problem
7(6)
1.1 The Monty Hall Problem
7(1)
1.2 Looking at an Extreme Case
8(1)
1.3 A Trickier Monty Hall Problem
9(2)
1.4 Just One Look
11(2)
Chapter 2 How Probabilistic Entanglement Connects Almost Everything
13(10)
2.1 Is Everything Connected?
13(1)
2.2 Quantum Entanglement
13(1)
2.3 Probabilistic Entanglement
14(1)
2.4 Benefitting from a Coin Flip
15(2)
2.5 Flipism
17(1)
2.6 Multiple Observations from a Single Group
17(1)
2.7 An Odd Number of Trials
18(2)
2.8 Comparing Means of Unrelated Groups
20(2)
2.9 How Fundamental Is Probability?
22(1)
Chapter 3 Blackwell's Bet
23(10)
3.1 Wunch with Wenny
24(1)
3.2 Unexpected Expectations
25(2)
3.3 Can Blackwell's Bet Help You Beat the Line at Sports Betting?
27(1)
3.4 Applying Blackwell's Bet to Sample and Population Statistics
28(5)
Chapter 4 A Stop at Willoughby -- Mathematics in the Twilight Zone
33(10)
4.1 Can You Predict the Flip of a Coin?
33(1)
4.2 Random Walks
34(1)
4.3 Next Stop -- Willoughby
35(1)
4.4 An Actual Coin Flip Prediction
36(2)
4.5 A Magical Mystery Tour
38(2)
4.6 Are We Predicting the Future?
40(3)
Chapter 5 The Fate of Schrodinger's Cat
43(18)
5.1 Blackwell's Bet Redux
45(2)
5.2 More About Bernoulli Trials
47(1)
5.3 Creating a Predictable Schrodinger's Cat Experiment
48(3)
5.4 Would This Experiment Fool Erwin Schrodinger?
51(1)
5.5 The Schrodinger Switcheroo
52(2)
5.6 Why Science Is Difficult
54(1)
5.7 The Solar Neutrino Deficit
55(1)
5.8 Hidden Variables
56(1)
5.9 Non-Predictable Bernoulli Trials
57(1)
5.10 Time Travel and Predictability Paradoxes
58(1)
5.11 Of Time and Third Avenue
59(1)
5.12 Checking Out the Schrodinger's Cat Experiment in Your Home
60(1)
Chapter 6 Coins and Camels
61(8)
6.1 Distinguishing Similar Bernoulli Trials
61(1)
6.2 The Problem of the 17 Camels
62(1)
6.3 Doing the Math
63(3)
6.4 A Slightly Different Problem
66(1)
6.5 When One Door Closes -- How Mathematicians Find Problems to Investigate
66(3)
Section II The Monday Morning Quarterback
69(38)
Chapter 7 The Joy of Simulation
71(14)
7.1 Random Number Generators
73(1)
7.2 Chi-Square Tests; Karl Pearson
73(5)
7.3 Simulations in Contemporary Science and Engineering
78(1)
7.4 Simulation in Fantasy Sports
79(2)
7.5 Why Educators Should Teach Simulation Rather than Algebra
81(1)
7.6 Simulation in the Electoral College
81(1)
7.7 Why are Tennis' Big Three so Dominant?
82(3)
Chapter 8 Numbed by Numbers
85(10)
8.1 A Really, Really, REALLY Bad Statistic
85(3)
8.2 The Year of the Unbeatens
88(2)
8.3 Simulating the NFL
90(3)
8.4 Integrating the Real World with Education
93(2)
Chapter 9 Losing the Battle, Winning the War
95(12)
9.1 The Post-Season
97(4)
9.2 The Gibbard-Satterthwaite Theorem
101(3)
9.3 Dumping for Future Advantage
104(3)
Section III Getting It Right; A Synergy of Mathematics, Intuition and Computers
107(24)
Chapter 10 The Hot Hand
109(8)
10.1 Can the "Hot Hand/' Be Exploited to Win at Betting Sports?
112(2)
10.2 The "Hot Hand" in a Wider Context
114(3)
Chapter 11 The Bent Coin and the Hot Hand
117(14)
11.1 Binomial Trials and Tribulations
117(1)
11.2 Binomial Trials and Flipping a Coin Just Once
118(1)
11.3 A Different Approach
119(1)
11.4 The Probability of the Probability of Probabilities
120(4)
11.5 More Simulations
124(1)
11.6 The Hot Hand Redux
125(2)
11.7 Jensen's Inequality
127(1)
11.8 Doing Better than Average
128(3)
Section IV The Last Hurrah
131(8)
Chapter 12 Using Combinatorics to Improve Advertising -- For Everyone
133(6)
12.1 A Brief History of Advertising
133(1)
12.2 What We Hate about Advertising
133(2)
12.3 The Element of Surprise
135(1)
12.4 Combinatorial Commercials
136(3)
Appendix -- Basic Probability Theory
139(8)
A.1 Computational Rules for Probability
140(1)
A.2 Conditional Probability
141(1)
A.3 Independent Events
141(1)
A.4 Expected Value (a.k.a. Expectation)
142(1)
A.5 Bernoulli Trials
143(1)
A.6 Means and Medians
144(3)
Annotated Bibliography 147(10)
Index 157