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A Beautiful Math (Siegfried, 2006)

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The Case for Using Probabilistic Knowledge in a Computer Chess Program (John L. Jerz)
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Review by By  SG (Washington, DC)
Brilliant .. expert storytelling, November 21, 2006

If you read or saw "A Beautiful Mind" and think there was drama in John Nash's creative madness, wait until you plunge into the work that drove him. Even without a background in (or any natural talent for) math, this story swept me up completely and, like previous reviewers, I had a hard time putting the book down. Siegfried expertly ushers the reader into the heart of a branch of mathematics that influences everything from pop culture to Nobel-winning science .. and does so in a way that leaves you feeling awed, inspired, and eager for more.

p.27 With most sciences, experts make pretty accurate predictions. Mix two chemicals, and a chemist can tell you ahead of time what you'll get. Ask an astronomer when the next total eclipse will be, and you'll get the date, time, and best viewing locations, even if the eclipse won't occur for decades.
  But mix people with money, and you generally get madness. And no economist really has any idea when you'll see the next total eclipse of the stock market. Yet many economists continue to believe that they will someday practice a sounder science. If fact, some would insist that they are already practicing a sounder science - by viewing the economy as basically just one gigantic game.
 
p.30 Utility is basically a measure of value, or preference... One of the more famous expositors of the idea was Jeremy Bentham, the British social philosopher and legal scholar. Utility, Bentham wrote in 1780, is "that property in any object, whereby it tends to produce benefit, advantage, pleasure, good,or happiness... or... to prevent the happening of mischief, pain, evil, or unhappiness."
 
p.31,32 the idea of utility - what you want to maximize - can sometimes get pretty complicated. But in many ordinary situations, utility is no mystery... Often your problem is not defining utility, but choosing a good strategy to maximize it. Game theory is all about figuring out which strategy is best.
 
p.40 there remained an important aspect to utility that von Neumann and Morgenstern had to address. Was it even possible, in the first place, to define utility in a numerical way, to make it susceptible to mathematical theory? ... Utility, or preference, can be thought of as just a rank ordering.
 
p.48 So you have to keep your opponent guessing.
 
p.211"When you need a prediction, a probability distribution won't do," said [physicist-mathematician David] Wolpert... you need to consider how much you have to lose (or gain) if your decision is wrong (or right).
  "If you predict X, but the truth is Y, how much are you hurt? Or conversely, how much do you benefit?"

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