Introduction researcher for the Massachusetts Institute of Technology

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most branches of physics study predictable notions such as electricity or
classical mechanics, chaos theory refers to systems that are nonlinear and unpredictable.
That which is encompassed in chaos theory can be considered to be out of our
control, such as the weather, which was in fact how the discovery that led to
chaos theory occurred 1. Chaos theory refers to the behaviour of
systems that are highly sensitive to their initial conditions. This occurs
because we can never be sure of all of the initial conditions in a complex
system, therefore we cannot possibly be able to predict its fate. 2
The smallest errors in measurement will cause a drastic change in the outcome,
meaning that any predictions made would be useless. It was born from a phenomenon
discovered by Edward Lorenz in 1972 called the ‘butterfly effect’. This refers
to an idea that most systems that change over time, be that natural or
artificial, will differ if just the tiniest adjustment is made to their
starting point. A well noted quote demonstrating this was given by Philip
Merilees who said, “Does the flap of a butterfly’s wings in Brazil set off a
tornado in Texas?” 1 This question sparked the beginning of a
whole new field of research called chaos theory.


Discovery of Chaos Theory

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Lorenz was working as a researcher for the Massachusetts Institute of Technology
when he combined meteorology with mathematics and computing. He built a
processor with the intention of modelling a simple version of the weather. His breakthrough
regarding the butterfly effect happened as he put numbers into his computer to
rerun a simulation. The result he got was drastically different from what he expected
to see and when looking into any possible errors, he realised that all he had
done was rounded one of the values, using 0.506 instead of 0.506127. 1
It was here that Lorenz realised that small
changes can have large consequences, and this is what eventually came to be known as the butterfly effect. This
accidental discovery had a paramount corollary
which was that forecasting the future can be nearly impossible.

Lorenz’s work
was so ground-breaking because it challenged the classical understanding of
nature published in 1687 by Isaac Newton. He had suggested a predictable system
known as the “clockwork universe” 7, but Lorenz’s discovery
contradicted this. Not only did he spark a new theory of the way the universe
works, his discovery also became the founding principle of
chaos theory, which expanded rapidly and vastly during the 1970s and 1980s. It eventually
came to be extremely important in fields of science such as geology, biology
and meteorology. According to one of the professors of geophysics at the
Massachusetts Institute of Technology, “It became a wonderful instance of a
seemingly esoteric piece of mathematics that had experimentally verifiable
applications in the real world”. 7


and Uses of Chaos Theory

From this we noticed that chaos can be found everywhere you look. One
example of this is our solar system, this qualifies as a chaotic system because
it involves the interaction of more than two bodies. Considering that it
contains 8 planets, the sun, 181 known moons 3 and countless
asteroids and comets, our solar system is rather chaotic. But if our solar
system is as chaotic as it seems to be, how can we possibly hope to predict its
fate? The answer is that we simply can’t. It is impossible to predict the fate of our world
because the smallest error could cause a drastic change in the outcome. 4
However this does not mean that our solar system is fated for a violent
demise, in fact these chaotic orbits tend to be ‘bounded’ which means that they
move in cycles that never repeat identically, but are contained within a
limited volume of space. This limits the danger of collision. 1


Another example of a chaotic
system is a double pendulum, where two rods are joined insecurely and allowed
to swing freely. The unpredictability exhibited by this system illustrates the
random motion that we expect to see in a chaotic system. The bottom pendulum
traces a pattern containing loops. This is where the ‘strange attractor’ came
from. The most well-known example of a strange attractor is the Lorenz
attractor (shown in figure 1), this is a map of the movement of a chaotic
system in three dimensions 1. It illustrates the random motion of
a chaotic system as it shows that two points on the attractor that are near each other at
one time will be arbitrarily far apart later on. 5


phenomenon can be described using fractal mathematics. A fractal is a never-ending pattern, such as
the Lorenz attractor 2. Fractal properties can be found in a range
of naturally occurring bodies such as clouds, rivers and trees. This shows how
fractals can capture the infinite complexity of nature. An important characteristic
of fractals is that you can take a small fragment of the shape and it looks identical
to the shape as a whole. This is called self-similarity.
8 Fractals often represent images of dynamic systems, and
therefore illustrate chaos.


The fact
that these systems are bounded does not mean that they can’t have extreme
consequences. This is exhibited by the effect that the planets in our solar
system can have on each other. Although the orbits do not deviate
significantly, the chaotic motion has the possibility of causing a catastrophic
danger. For example, a tiny knock to Saturn from the particles in the solar
wind could make its orbit aperiodic. 1 This means that its path
will change each time it orbits the sun. This opens up the possibility that
Jupiter, Saturn and the Sun will align at some point. The combined gravitational
pull of this trio would be enough to pull rocks out of the asteroid belt that
lies between the orbits of Jupiter and Mars, causing an asteroid storm. Some scientists
believe that such an event preceded the asteroid impact that ended the age of
the dinosaurs, this shows the drastic effect that chaos could have on the Earth.


the possible effects of chaos theory aren’t all bad. Having an awareness of the fractal
nature of the world around us can provide a new insight into the way that
things work. For example, understanding the chaotic dynamics of the Earth’s atmosphere
means that we are able to “steer” hot air balloons. If we are able to understand the dynamic
systems in which we live, such as our ecosystems and social systems we can aim
to avoid actions which may cause damage to the long-term welfare of the
population. In fact, chaos theory has brought about a greater understanding of
certain illnesses and has therefore caused medical advances. The up and down
pattern of epidemics such as AIDS, measles and polio follows a chaotic trajectory,
meaning that it is sensitive to the tiniest variations; for example, an inoculation
programme. 1 Theorists call it ‘bifurcation’ which refers to the qualitative
change in the dynamics of a system produced by varying parameters. 6 The
introduction of an inoculation programme can cause the epidemic to be thrown
into a chaotic frenzy. This means that the short-term figures for the disease
may increase, however awareness of chaos allows medical researchers
to ignore the short-term issue and allow for a chaotic response. This response suggests
that it should be followed by a downward trajectory in the long term. 1


illustrates how an understanding of chaos theory can allow us to have a greater
understanding of the world around us, allowing us to positively influence the
outcome of certain situations by varying the most minute initial detail. Although
chaos can result in cataclysmic events similar to those previously described,
this is extremely unlikely. The benefits we have been able to gain from a
better understanding of chaos theory have enabled us to improve medical
knowledge and better control dynamic systems. This shows that chaos does not
necessarily mean danger, and therefore it does not always cause chaos (in the
general sense of the word).

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