Chaos Theory

To those who professionally study the Chaos theory, it is a fundemental way
of perceiving the world around them. However, for the rest of us it seems to be a
mystery, one that boggles minds while simotaniously stimulating them to great
extents. For someone to understand the theory could prove quite revolutionary, as
the chaos theory is not obvious at first, rather it is somewhat abstract.
Understanding this emmensly complex notion will vastly improve a persons ability
to fully comprehend- and appriciate - the universe, which is after all, the main goal
of science.

An extremely vital concept of this theory is the “butterfly effect.” A man by
the name of Edward Lorenz discovered this on his weather simulating computer.
Keep in mind that this was in the 1970’s and the power of computers at the time was
relatively minute compared to their power today... On this computer he could graph
the weather patterns (in his computer generated universe) months in advance. The
computer read out for the patterns went to four decimal places, a fairly accurate and
precise measurement for the time, however when the program was actually operating
it would use many more. One day he decided to check the accuracy of his program.
Now, Lorenz had great faith in his creation but, as anyone with an anaylitical mind, he
wanted to prove to himself just how close to perfection his computer was. He
decided to collect a set of data representing all of the current conditions of his
“world” and ran the program. Then, when he attempted a repeat of the weather cycle
he was very surprised at the results. At first, the graphs of both patterns were very
closely related but as more and more time went by, they gradually became more and
more different, thus causing the graphs to become more and more dissimilar.
Remember how the computer only remembered conditions to four decimal places?
This was the cause of the chaos that he experienced. Although the initial conditions
in the repeated experiment were exact to one ten-thousandth of one, as the amount
of time increased so did the difference in the graphs. This effect came to be known
as the butterfly effect. To apply the butterfly effect to a hypothetical situation: Say
that something as small as a thunderstorm occurs . In the very distant future, perhaps
even thousands of years, the world wide weather will be severely different than it
would be had the storm never transpired (remember the word of advice: if you go
back in time, don’t touch anything). Even in ancient folklore, the butterfly effect is
portrayed:

For want of a nail, the shoe was lost;

For want of a shoe, the horse was lost;

For want of a horse, the rider was lost;

For want of a rider, the battle was lost;

For want of a battle, the kingdom was lost;

After deriving this butterfly effect, Edward Lorenz decided to look for chaos
in other places than simply his computer world. This lead him to convection. He
took a liquid in a container and place it on a stove, then he turned the heat on. Very
early in the experiment the liquid began to boil (this was expected), and by boiling
the liquid began to swirl in one direction (this was also expected). As the heat
intensified and the liquid approached higher and higher temperatures the boiling
liquid went into a frenzy with extreme palpatations and the swirling became faster. A
few minutes later as the heat reached even higher levels he noticed that the swirling
began to slow down. This surprised him, but not as much as what was to come.
Eventually the liquid stopped swirling, this only lasted for a few moments however
as the most chaotic action quickly occurred. The liquid began to spin in the opposite
direction. The graph of that liquid convection became rather famous in the world of
chaos and is known as the Lorenz Attractor. This graph appears to have intersecting
lines, however they do not intercept each other due to the fact that it is a three-
dimensional graph and the seemingly intersecting lines are actually at different
altitudes. This graph was made by using the following variables: rate of spin and the
height of the palpatations. This experiment was the first of many to follow, in a way,
it was the chaos theory summed up in a graph.

Next, it is important to understand the fractal. These are infinitely iterated
geometric series, or infinitely self repeating structures in a finite area. They are yet
another way of representing chaos without words. When you see a fractal, at first it
may appear to be very confusing and completely random. However, upon further
anyilization you will notice that there is organization to it. And, as with everything
dealing with chaos, fractals can be seen quite often in nature. For example, in trees,
fractals exist in many places. Next time you see a tree, closely examine its
branches, notice that each individual branch seems to closely assimilates the one
preceding it thus forming one giant fractal. The root system of a tree also follows
this same pattern. Even in the leaves of a tree, fractals are frequently found.
Another example in a slightly different way would be a rock. As you zoom more and
more closely to the surface of a rock, you will eventually notice a very distinctive
arrangement of the surface. This you may notice is infinitely self repeating, one of
the main aspects of a fractal.

This theory of chaos, an oxymoron in and of itself is a very complicated and
confusing idea. However, when broken down into easier terms to understand,
anything, including this theory can be addequately understood.