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Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics
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Randomness (Paperback, New Ed)
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Randomness (Paperback, New Ed)
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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)
From the ancients' first readings of the innards of birds to your
neighbor's last bout with the state lottery, humankind has put
itself into the hands of chance. Today life itself may be at stake
when probability comes into play--in the chance of a false negative
in a medical test, in the reliability of DNA findings as legal
evidence, or in the likelihood of passing on a deadly congenital
disease--yet as few people as ever understand the odds. This book
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, Randomness is also a
skillful account of what makes the science of probability so
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. Author
Deborah Bennett traces the path this process takes in an individual
trying to come to grips with concepts of uncertainty and fairness,
and also charts the parallel 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 dead 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, for bumblers and
brilliant mathematicians alike, is the entertaining and
enlightening lesson of Randomness.
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