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How has computer science changed mathematical
thinking? In this first ever comprehensive survey of the
subject for popular science readers, Arturo Sangalli explains
how computers have brought a new practicality to mathematics
and mathematical applications. By using fuzzy logic and
related concepts, programmers have been able to sidestep
the traditional and often cumbersome search for perfect
mathematical solutions to embrace instead solutions that
are "good enough." If mathematicians want their
work to be relevant to the problems of the modern world,
Sangalli shows, they must increasingly recognize "the
importance of being fuzzy."
As Sangalli explains, fuzzy logic is a technique
that allows computers to work with imprecise terms -- to
answer questions with "maybe" rather than just
"yes" and "no." The practical implications
of this flexible type of mathematical thinking are remarkable.
Japanese programmers have used fuzzy logic to develop the
city of Sendai's unusually energy-efficient and smooth-running
subway system -- one that does not even require drivers.
Similar techniques have been used in fields as diverse as
medical diagnosis, image understanding by robots, the engineering
of automatic transmissions, and the forecasting of currency
exchange rates. Sangalli also explores in his characteristically
clear and engaging manner the limits of classical computing,
reviewing many of the central ideas of Turing and Godel.
He shows us how "genetic algorithms" can solve
problems by an evolutionary process in which chance plays
a fundamental role. He introduces us to "neural networks,"
which recognize ill-defined patterns without an explicit
set of rules -- much as a dog can be trained to scent drugs
without ever having an exact definition of "drug."
Sangalli argues that even though "fuzziness" and
related concepts are often compared to human thinking, they
can be understood only through mathematics -- but the math
he uses in the book is straightforward and easy to grasp.
Of equal appeal to specialists and the general reader, The
Importance of Being Fuzzy reveals how computer science
is changing both the nature of mathematical practice and
the shape of the world around us.
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