These are exciting times for mathematics, science, and technology.
One of the fields that has been receiving great attention is Chaos
Theory. Actually, this is not a single discipline, but a potpourri
of nonlinear dynamics, nonequilibrium thermodynamics, information
theory, and fractal geometry. In the less than two decades that
Chaos Theory has become a major part of mathematics and physics, it
has become evident that the old paradigm of determinism is
insufficient if we are to understand - and perhaps solve - real
life problems. Curiously, many of these problems are deterministic,
but they are intertwined with randomness and chance. Thus the
deterministic laws of physics coexist with the laws of probability.
Consequently, uncertainty arises and unpredictability occurs,
characteristic of complex systems. In its short lifetime Chaos
Theory has already helped us gain insights into problems that in
the past we found intractable. Examples of such problems include
weather, turbulence, cardiological and neurophysiological episodes,
economic restructuring, financial transactions, policy analysis,
and decision making. Admittedly, we can as yet solve only
relatively simple problems, but much progress has been made and we
are now able to observe complex problems from new vantage points
that provide us with numerous benefits. One such benefit is the
universality of Chaos Theory in its applicability to different
situations, which enables us to look at communal problems in an
interdisciplinary manner, so that persons of different backgrounds
can communicate with one another. Chaos Theory also enables us to
reason in a holistic manner, rather than being constrained by
simplistic reductionism.Finally, it is gratifying that the
mathematics is not intimidating, and one can accomplish much with a
personal computer or even a handheld calculator.
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