Chaos Theory
The word "chaos" is sometimes taken to mean
the opposite of "cosmos", in that the latter
term has connotations of "order". Until the
last few decades, chaotic systems have not
been studied nearly as much as ordered systems,
perhaps because chaotic systems are far more
difficult to understand...
What is a chaotic system?
Looking at the rising smoke from a
cigarette illustrates some of the differences
between ordered and chaotic systems. Initially
the smoke rises in a smooth upward flow (laminar
flow), which breaks down a few inches
above the tip of the cigarette into
a disordered, turbulent motion(turbulent flow).
This is an example of a transition from an ordered
system into a chaotic one. A stream of water flowing
out of an appropriately adjusted faucet exhibits
similar behaviour, which is ubiquitous in a host of
phenonomena, both man-made and natural.
The weather systems of the atmosphere (which
are intertwined with the heat and mass flows
in the oceans) are chaotic. A system of more
than two bodies orbiting under each other under
their mutual gravitational attraction is also chaotic,
by extension the entire solar system is a chaotic!
One non-technical definition of a chaotic system
goes as follows: A chaotic system is one in which
a tiny change can have a huge effect. Thus the oft
heard statement that a butterfly in China can cause
a hurricane in the Atlantic. What makes the situation
even more difficult is that we have only recently
begun to forge the mathematical tools necessary
to study these problems. As usual, some of the seminal
works on chaos were performed by physicists of the
former USSR, whose work received scant attention
until recently; although today, chaotic systems
are being extensively studied both experimentally
and theoretically.