Books about Probability from Amazon.com

Amazon Guest Review: Stephen Hawking
Published in 1988, Stephen Hawking's A Brief History of Time became perhaps one of the unlikeliest bestsellers in history: a not-so-dumbed-down exploration of physics and the universe that occupied the London Sunday Times bestseller list for 237 weeks. Later successes include 1995's A Briefer History of Time, The Universe in a Nutshell, and God Created the Integers: The Mathematical Breakthroughs that Changed History. Stephen Hawking is Lucasian Professor of Mathematics at the University of Cambridge.

In The Drunkard's Walk Leonard Mlodinow provides readers with a wonderfully readable guide to how the mathematical laws of randomness affect our lives. With insight he shows how the hallmarks of chance are apparent in the course of events all around us. The understanding of randomness has brought about profound changes in the way we view our surroundings, and our universe. I am pleased that Leonard has skillfully explained this important branch of mathematics. --Stephen Hawking

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Price: $14.00 [Notify me when price goes down.]

Bestselling author Nassim Nicholas Taleb continues his exploration of randomness in his fascinating new book, The Black Swan, in which he examines the influence of highly improbable and unpredictable events that have massive impact. Engaging and enlightening, The Black Swan is a book that may change the way you think about the world, a book that Chris Anderson calls, "a delightful romp through history, economics, and the frailties of human nature." See Anderson's entire guest review below.

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Guest Reviewer: Chris Anderson

Chris Anderson is editor-in-chief of Wired magazine and the author of The Long Tail: Why the Future of Business Is Selling Less of More.

Four hundred years ago, Francis Bacon warned that our minds are wired to deceive us. "Beware the fallacies into which undisciplined thinkers most easily fall--they are the real distorting prisms of human nature." Chief among them: "Assuming more order than exists in chaotic nature." Now consider the typical stock market report: "Today investors bid shares down out of concern over Iranian oil production." Sigh. We're still doing it.

Our brains are wired for narrative, not statistical uncertainty. And so we tell ourselves simple stories to explain complex thing we don't--and, most importantly, can't--know. The truth is that we have no idea why stock markets go up or down on any given day, and whatever reason we give is sure to be grossly simplified, if not flat out wrong.

Nassim Nicholas Taleb first made this argument in Fooled by Randomness, an engaging look at the history and reasons for our predilection for self-deception when it comes to statistics. Now, in The Black Swan: the Impact of the Highly Improbable, he focuses on that most dismal of sciences, predicting the future. Forecasting is not just at the heart of Wall Street, but it's something each of us does every time we make an insurance payment or strap on a seat belt.

The problem, Nassim explains, is that we place too much weight on the odds that past events will repeat (diligently trying to follow the path of the "millionaire next door," when unrepeatable chance is a better explanation). Instead, the really important events are rare and unpredictable. He calls them Black Swans, which is a reference to a 17th century philosophical thought experiment. In Europe all anyone had ever seen were white swans; indeed, "all swans are white" had long been used as the standard example of a scientific truth. So what was the chance of seeing a black one? Impossible to calculate, or at least they were until 1697, when explorers found Cygnus atratus in Australia.

Nassim argues that most of the really big events in our world are rare and unpredictable, and thus trying to extract generalizable stories to explain them may be emotionally satisfying, but it's practically useless. September 11th is one such example, and stock market crashes are another. Or, as he puts it, "History does not crawl, it jumps." Our assumptions grow out of the bell-curve predictability of what he calls "Mediocristan," while our world is really shaped by the wild powerlaw swings of "Extremistan."

In full disclosure, I'm a long admirer of Taleb's work and a few of my comments on drafts found their way into the book. I, too, look at the world through the powerlaw lens, and I too find that it reveals how many of our assumptions are wrong. But Taleb takes this to a new level with a delightful romp through history, economics, and the frailties of human nature. --Chris Anderson

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Price: $15.48 [Notify me when price goes down.]

A timeless classic in how complex information should be presented graphically. The Strunk & White of visual design. Should occupy a place of honor--within arm's reach--of everyone attempting to understand or depict numerical data graphically. The design of the book is an exemplar of the principles it espouses: elegant typography and layout, and seamless integration of lucid text and perfectly chosen graphical examples. Very Highly Recommended..
Price: $27.88 [Notify me when price goes down.]

Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.

The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan

Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence..
Price: $11.93 [Notify me when price goes down.]

"There is terror in numbers," writes Darrell Huff in How to Lie with Statistics. And nowhere does this terror translate to blind acceptance of authority more than in the slippery world of averages, correlations, graphs, and trends. Huff sought to break through "the daze that follows the collision of statistics with the human mind" with this slim volume, first published in 1954. The book remains relevant as a wake-up call for people unaccustomed to examining the endless flow of numbers pouring from Wall Street, Madison Avenue, and everywhere else someone has an axe to grind, a point to prove, or a product to sell. "The secret language of statistics, so appealing in a fact-minded culture, is employed to sensationalize, inflate, confuse, and oversimplify," warns Huff.

Although many of the examples used in the book are charmingly dated, the cautions are timeless. Statistics are rife with opportunities for misuse, from "gee-whiz graphs" that add nonexistent drama to trends, to "results" detached from their method and meaning, to statistics' ultimate bugaboo--faulty cause-and-effect reasoning. Huff's tone is tolerant and amused, but no-nonsense. Like a lecturing father, he expects you to learn something useful from the book, and start applying it every day. Never be a sucker again, he cries!

Even if you can't find a source of demonstrable bias, allow yourself some degree of skepticism about the results as long as there is a possibility of bias somewhere. There always is.

Read How to Lie with Statistics. Whether you encounter statistics at work, at school, or in advertising, you'll remember its simple lessons. Don't be terrorized by numbers, Huff implores. "The fact is that, despite its mathematical base, statistics is as much an art as it is a science." --Therese Littleton.
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With the stock market breaking records almost daily, leaving longtime market analysts shaking their heads and revising their forecasts, a study of the concept of risk seems quite timely. Peter Bernstein has written a comprehensive history of man's efforts to understand risk and probability, beginning with early gamblers in ancient Greece, continuing through the 17th-century French mathematicians Pascal and Fermat and up to modern chaos theory. Along the way he demonstrates that understanding risk underlies everything from game theory to bridge-building to winemaking. .
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In the numbers explosion all around us in our modern-day dealings, the buzzword is data, as in, “Do you have any data to support your claim?” “The data supported the original hypothesis that . . .” and “The data bear this out. . . .” But the field of statistics is not just about data. Statistics is the entire process involved in gathering evidence to answer questions about the world, in cases where that evidence happens to be numerical data.

Statistics For Dummies is for everyone who wants to sort through and evaluate the incredible amount of statistical information that comes to them on a daily basis. (You know the stuff: charts, graphs, tables, as well as headlines that talk about the results of the latest poll, survey, experiment, or other scientific study.) This book arms you with the ability to decipher and make important decisions about statistical results, being ever aware of the ways in which people can mislead you with statistics. Get the inside scoop on number-crunching nuances, plus insight into how you can

• Determine the odds
• Calculate a standard score
• Find the margin of error
• Recognize the impact of polls
• Establish criteria for a good survey
• Make informed decisions about experiments

This down-to-earth reference is chock-full of real examples from real sources that are relevant to your everyday life: from the latest medical breakthroughs, crime studies, and population trends to surveys on Internet dating, cell phone use, and the worst cars of the millennium. Statistics For Dummies departs from traditional statistics texts, references, supplement books, and study guides in the following ways:

• Practical and intuitive explanations of statistical concepts, ideas, techniques, formulas, and calculations.
• Clear and concise step-by-step procedures that intuitively explain how to work through statistics problems.
• Upfront and honest answers to your questions like, “What does this really mean?” and “When and how I will ever use this?”

Chances are, Statistics For Dummies will be your No. 1 resource for discovering how numerical data figures into your corner of the universe..
Price: $9.89 [Notify me when price goes down.]

If you have ever looked for P-values by shopping at P mart, tried to watch the Bernoulli Trails on "People's Court," or think that the standard deviation is a criminal offense in six states, then you need The Cartoon Guide to Statistics to put you on the road to statistical literacy.

The Cartoon Guide to Statistics covers all the central ideas of modern statistics: the summary and display of data, probability in gambling and medicine, random variables, Bernoulli Trails, the Central Limit Theorem, hypothesis testing, confidence interval estimation, and much more--all explained in simple, clear, and yes, funny illustrations. Never again will you order the Poisson Distribution in a French restaurant!.
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Why would a casino try and stop you from losing? How can a mathematical formula find your future spouse? Would you know if a statistical analysis blackballed you from a job you wanted?

Today, number crunching affects your life in ways you might never imagine. In this lively and groundbreaking new book, economist Ian Ayres shows how today's best and brightest organizations are analyzing massive databases at lightening speed to provide greater insights into human behavior. They are the Super Crunchers. From internet sites like Google and Amazon that know your tastes better than you do, to a physician's diagnosis and your child's education, to boardrooms and government agencies, this new breed of decision makers are calling the shots. And they are delivering staggeringly accurate results. How can a football coach evaluate a player without ever seeing him play? Want to know whether the price of an airline ticket will go up or down before you buy? How can a formula outpredict wine experts in determining the best vintages? Super crunchers have the answers. In this brave new world of equation versus expertise, Ayres shows us the benefits and risks, who loses and who wins, and how super crunching can be used to help, not manipulate us.

Gone are the days of solely relying on intuition to make decisions. No businessperson, consumer, or student who wants to stay ahead of the curve should make another keystroke without reading Super Crunchers..
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