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 Victor
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A History
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Chaos and Complexity Complexity Theory and Chaos Theory, which is a part of Complexity Theory, have taken off with the advent of the computer, since it can undertake the massive numbers of calculations required to investigate complex phenomena. It is a new area of science which some people have said could change our lives as much as Michael Faraday's discovery of electricity and its properties. Professor Stephen Hawking has said, "Complexity will be the science of the 21st Century." Although the bulk of the development has been in the last 30 years or so, there are people whose work foreshadowed the understandings we are now developing. Back around 1870 the King of Sweden announced a mathematical competition offering a prize for the person who could calculate the three body problem. When two celestial bodies are in motion with one in orbit around the other, we simply need to use Newton's Laws of motion to understand and predict their motion. When a third body is added, so one body orbits around a central body and the third body orbits the second body as in the case of the moon, earth and sun, then calculated where the bodies will be becomes far more complicated. Newton's Laws have been sufficient to enable us to get humans to the moon, but a fully accurate solution to the three body problem is not as straight forward. 
In fact,
Henri Poincaré (1854 -1912) was able to prove that the three
body
problem could in fact not be solved. As soon as the earth moves, it
changes the distances between the other bodies, which alters the
gravitational forces. All three bodies interact with each other in
such complicated ways as to defy calculation. If we cannot even
calculate the motions of three bodies, how can we possibly
predict the outcome of systems we see about us everyday with millions,
trillions or more of intensely
interacting parts?In the
1940's the field of cybernetics developed. Louis
Kauffmann, President of the American Society for Cybernetics, defined
Cybernetics as the study of systems and processes that interact with
themselves and produce themselves from themselves.
 Cybernetics
linked together many areas of study from control systems to electrical
network theory to evolutionary biology. Norbert Wiener and W.
Ross Ashby were important pioneers in the field of cybernetics. John van
Neumann was also influential through his early work on cellular
automataCybernetics has waxed and waned in popularity over the years. Since it linked so many different areas of knowledge, it has often been superceded by other developing areas. Complexity Theory has been one of those disciplines that has taken inspiration from it, but conitnued to develop in it's own way.  Ludwig van
Bertalanffy was one of the prime movers of General Systems Theory,
which developed arounf the same time. He emphasised the fact that
the traditional closed system could not explain the types of systems
that are found about us in our world. his work influenced cybernetics
and obviously points to the work done on dissipative systems. General
Systems theory emphasises holism over reductionisms and organism over
mechanism. Van Bertalanffy saw his work as particularly relevant to
social systems and has been used in the fileds of anthropology,
economics, political science and psychology. Margaret Mead and Gregory
Bateson helped develop General Systems Theory in the social sciences.  In the 1960s
Meteorologist Ed
Lorenz was using an early
computer to run a
simulation of the weather. One day, when he was rushed for time, he set
the
computer to round off the numbers to be calculated so a result would be
found sooner. He was expecting that the rounding off would have little
or no effect on the final results. However, surprisingly, what he found was
that the final results were dramatically different. He found small
changes in the state of a system can cause major changes in the final
output
(sensitivity to initial conditions). We had been used to thinking large
changes need large forces. He found that small forces could have large
effects. This has become known as the butterfly effect. It has been
said
(although it is an exaggeration) that a butterfly flapping its wings in
Hong Kong could cause a tornado in Texas. The picture above is the
mathematical depiction of the attractor he found investigating the
weather and is known as the butterfly attractor.If small changes
in the initial state of a complex system can
drastically alter the final outcome, then long-term weather prediction
is impossible as there is no way to perfectly measure and describe the
weather at any one point in time. There is always a further level of
accuracy to be measured.
 In
the early 1970s, Robert May was working on
how insect birthrates varied according to levels of food supply and
came up with results similar to those of Ed Lorenz. He found that at
critical values, the system took
twice as long to settle back into a stable pattern. After several
period
doubling cycles the system became unpredictable. Period doubling proved
to be an important concept in many branches of complexity.In 1971, David
Ruelle and Floris Takens discovered strange attractors
(also known as chaotic attractors) They mapped these mathematically
onto a phase space, where each dimension corresponds to a variable of
the system. This enabled accurate mapping of a system and its dynamics.
  In
the 1980s, Benoit
Mandelbrot used a home
computer to mathematically create what he was to call fractals. He
found the Mandelbrot Set (seen right)
in 1980. A fractal is a shape that is self similar, that is that
repeats the same basic shape at smaller levels within the same
structure. for example look at a fern and you will find that the sub
branches have the same basic shape as the whole fern and the sub
branches off the sub branches also have the same basic shape. Illya
Prigogine worked in the area of
dissipative systems. He won the Nobel Prize for his work in this area.
A
dissipative system is one that maintains
an ongoing shape or identity because a flow of energy through the
system is maintained. Our human body is a dissipative system because it
is maintained by a number of energy flows, such as food, water,
air, and even
environmental stimuli and cognitive processes. Dissipative systems
operate
far from equilibrium and not at an equilibrium point as had been
thought.
Prigogine found chemical dissipative systems that could exhibit strange
behaviour such as a chemical changing colour rhythmically. How do the
molecules in the mix know when it is time to change colour? Mitchel Feigenbaum was working in
the late 1970s looking at period doubling. He showed that this was the
normal way for order to break down into chaos. He found recurring
ratios in the period doubling, now called Feigenbaum Numbers. It was
found for example that the Feigenbaum Numbers were found in the the
period doubling that leads to heart attacks. Rene
Thom developed Catastrophe Theory based
on how a complex system bifurcates or branches out. The system will
reach a critical point through period doubling and must either collapse
into chaos or self organise to a new level of complexity. Thom examined
the lapse into chaos and the conditions under which it happens. The Santa Fe Institute was
founded in 1984 as a private and independent research and education
center, which has remained in the forefront of
research into chaos and complexity. Two of its prominent members were:Chris Langton did much research regarding the Edge of Chaos, the point where systems have enough order to maintain an ongoing identity, while also having enough chaos to allow for novelty and learning. At the Edge of Chaos self organisation and emergence can appear.  Stuart
Kauffman: Stuart
Kauffmann worked on connected networks of automata made up of
small computer programmes. When they interacted in the network, some
unexpected results were seen. Often the results were reasonably
predictable, but at critical levels the systems optimised their
effectiveness through co-adaption . His work has had particular
importance in the field of evolutionary biology.more detail of the history of the SFI   Stephen Wolfram is
developing a complexity based approach to mathematics as outlined on
his book, A New Kind of Science and much work is being done developing
complexity based mathematical simulations of real world situations
using techniques such as genetic algorithms.Chaos and Complexity continues to develop and slowly but surely is making inroads into mainstream scientific study. New areas of study are opening up. Previous Tutorial Next Victor's Home Page |
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