This work is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking. It is also an account of what makes the science of probalitity daunting in our own day. To acquire a (correct) intuition of chance is not easy to begin with, and moving from an intuitive sense to a formal notion of probability presents further problems. The author traces the path this process takes in an individual trying to come to grips with concepts of uncertainty and fairness, and also charts the parrallel path by which societies have developed ideas about chance. Why, from ancient to modern times have people resorted to chance in making decisions? Is a decision made by random choice "fair"? What role has gambling played in our understanding of chance? Why do some individuals and societies refuse to accept randomness at all? If understanding randomness is so important to probabilistic thinking, why do the experts disagree about what it really is? And why are our intuitions about chance almost always wrong?
Anyone who has puzzled over a probability conundrum is struck by the paradoxes and counterintuitive results that occur at a relatively simple level. Why this should be, and how it has been the case through the ages, is the lesson of this book.
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Harvard University Press
Publisher: Harvard University Press
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US Kirkus Review »
Probabilities and statistics dominate our lives, yet few of us really understand them; here's an attempt to shed some light. Bennett (Mathematics/Jersey City State Coll.) uses practical examples to convey the history and nature of her subject. Ancient societies used dice or bones not only for gambling but to decide matters of life and death - on the theory that a random mechanism made the divine will known, without human bias. Old Testament Hebrews drew lots to divide an inheritance - hence the term "lot" for a parcel of land. The I Ching is a more elaborate method of using randomizers (tossed coins or counted yarrow stalks) to solicit divine guidance. A more scientific approach to probability began with the Renaissance; Galileo's writings about dice show awareness of the concept of equal probability. Bennett spends some time demonstrating the need for careful enumeration of all the possible outcomes in estimating probability. By the 18th century, the concept of random error led to scientists adopting the mean of a series of measurements as the best approach to accuracy. Laplace was the first to formulate the famous bell curve to describe the likely distribution of random events, a model rapidly adopted throughout the sciences. As the science of statistics matured, random numbers were generated as a tool for analyzing the randomness of natural phenomena. Eventually these investigations, often based on "randomly" chosen data such as the heights of convicts, yielded such statistical tools as the chi-square relationship, which often showed that the data were not as random as originally believed. It was not until the 20th century that the notion that yet undiscovered laws would allow exact prediction of all natural phenomena was abandoned by science and true randomness embraced - most strikingly in the form of quantum mechanics and chaos theory. A clear and detailed examination of the role of pure chance, with fascinating historical asides. (Kirkus Reviews)
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Author Biography - Deborah J. Bennett
Deborah J. Bennett is Associate Professor of Mathematics, Jersey City State College, New Jersey.