What exactly is chaos? The name "chaos theory" comes from the fact that the
systems that the theory describes are apparently disordered, but chaos theory is
really about finding the underlying order in apparently random data.
When
was chaos first discovered? The first true experimenter in chaos was a
meteorologist, named Edward Lorenz. In 1960, he was working on the problem of
weather prediction. He had a computer set up, with a set of twelve equations to
model the weather. It didn't predict the weather itself. However this computer
program did theoretically predict what the weather might be.
One day
in 1961, he wanted to see a particular sequence again. To save time, he started
in the middle of the sequence, instead of the beginning. He entered the number
off his printout and left to let it run.
When he came back an hour later,
the sequence had evolved differently. Instead of the same pattern as before, it
diverged from the pattern, ending up wildly different from the original.
Eventually he figured out what happened. The computer stored the numbers to six
decimal places in its memory. To save paper, he only had it print out three
decimal places. In the original sequence, the number was .506127, and he had
only typed the first three digits, .506.
By all conventional ideas of the
time, it should have worked. He should have gotten a sequence very close to the
original sequence. A scientist considers himself lucky if he can get
measurements with accuracy to three decimal places. Surely the fourth and fifth,
impossible to measure using reasonable methods, can't have a huge effect on the
outcome of the experiment. Lorenz proved this idea wrong.
This effect
came to be known as the butterfly effect. The amount of difference in the
starting points of the two curves is so small that it is comparable to a
butterfly flapping its wings.
The flapping of a single butterfly's wing
today produces a tiny change in the state of the atmosphere. Over a period of
time, what the atmosphere actually does diverges from what it would have done.
So, in a month's time, a tornado that would have devastated the Indonesian coast
doesn't happen. Or maybe one that wasn't going to happen, does. (Ian Stewart,
Does God Play Dice? The Mathematics of Chaos, pg. 141)
This phenomenon,
common to chaos theory, is also known as sensitive dependence on initial
conditions. Just a small change in the initial conditions can drastically change
the long-term behavior of a system.
Now, flap your wings and ignite a spark.
Bea Rigsby-Kunz
