Introduction

While

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

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

Effects

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

This

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.

However,

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

Conclusion

This

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).