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Pure Bollocks Issue 22_018
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* F E A T U R E S *
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Chaos Reigns in a wonderful world
Electronics has played an important role in one of the most profound
and exciting developments of the 1980s, perhaps of the century - a new branch
of science known as chaos.
Chaos is seen by some as rivalling in importance such fundamental
branches of science as quantum physics.
It consists of new mathematical ways of describing a huge variety of
phenomena and objects that all exhibit irregular, unstable patterns - from
clouds to rivers.
With conventional mathematics and physics, it was not possible to
describe or predict the formation and development patterns within such
systems. They were seen as randomly erratic; chaotic, infact.
The patterns in a fast flowing river, for example, have been until now
literally indescribable by conventional techniques. Such 'non linear
systems' could not be modelled mathematically.
The new science of chaos is now providing theories that can deal with
non linearity, showing that within apparent randomness there is order and
pattern, of a kind. A universal constant of chaos has been discovered that
describes the emergence of these irregular but patterned phenomena in many
different areas. But it has also been shown that chaotic systems will
always be inherently unpredictable.
Chaos is founded on abstruse esoteric mathematics, but despite that there
have already been practical applications, such as improved designs for
machines to treat heart attack victims. Even something as practical as
the analysis of a country's economic performance may well be improved by
the techniques of chaos.
Computers, and therefore the electronics that built them, have played a
crucial part in the emergence of chaos, enabling mathematicians and
physicists literally to see on a terminal the behaviour of chaotic systems.
But electronics has played a more central role than merely making
high speed digital computers possible. Some of the foundation work for
chaos was done by Stephen Smale, a leading mathematician from the University
of California at Berkley.
Smale's work was essentially mathematical, concerning the behaviour
of all dynamical systems. But he was led to it by considering the
behaviour of oscillating electronic circuits.
These circuits had been studied as far back as the 1920s by Balthasar
van der Pol, a Dutch electrical engineer. He analysed the behaviour of an
electronic valve fed with varying signal levels. When van der Pol did
the original work, he had no oscilloscope to monitor the effects, and
instead listened to alterations in the tone of a telephone ring.
As the input varied, the tone would change in a series of frequency
jumps, locking into a particular frequency for a time before jumping to
the next. But sometimes irregularities occurred before the jumps,
which van der Pol noticed but discounted. These irregularities were
chaotic phenomena.
The other major contribution of electronics to the development of chaos
came appropriately from Japan.
Working at the Department of Electrical Engineering at Kyoto University,
Yoshisuke Ueda published a paper that was a pioneering step towards
the science of chaos.
It concerns random oscillations in a series resonance circuit containing
a saturable inductor under the impression of a sinosoidal voltage.
Ueda introduced his paper thus: "In physical phenomena,
uncertainties lie between causes and effects. When uncertain factors are
small, their effects may be neglected in most physical systems and
the phenomena under consideration are treated as deterministic ones.
Whereas in non linear systems on some conditions, however small uncertain
factors may be, they sometimes cause global changes."
This summarises one of the central principals of chaos, known as the
butterfly effect. This states that no matter how small a degree of
uncertainty exists about the state of a non linear system, the uncertainty
can be felt rapidly.
A vivid way of illustrating this is to say that a single flap of a
butterfly's wing in North America will affect the state of the weather in
China a few days later. The butterfly effect is known more technically as
'sensitivity to initial conditions', and this sensitivity is infinite. In
describing the initial conditions of a non-linear dynamic system , no matter
what degree of accuracy is achieved, there will always be uncertainties. No
matter how small they are, they will in a relatively short period of time come
to affect the system noticeably.
This means that there is an inherent unpredictability to non linear
systems, such as the weather, that cannot be removed , no matter how much
knowledge about it grows.
Ueda's work also concerned entities called strange attractors, which lie
at the heart of the mathematics of chaos. They describe patterns that
emerge in chaotic systems, which are in one sense stable in that they are of
similar types. But they are never repeated identically.
For example, a pendulum swinging through a full circle driven by an
energetic kick at regular intervals will display chaotic behaviour,
tracking out a series of orbits that are similar but which never revert back
precisely to a previous orbit.
Ueda demonstrated how the same thing happens with electronic circuits:
"The phenomenon should be called turbulence in electric circuits. Results
obtained disclose an important feature of non linear phenomena in general
physical systems."
His paper shows that the randomness displayed by the circuits is an
inherent feature of the system as a whole.
Another name for strange attractors is fractal attractors. These
were discovered by Beniot Mandelbrot, an IBM computer scientist. They
are mathematical entities which generate infinitely complex patterns,
repeating for ever according to a recognisable theme but which can be proved
will never revert back to any previously traced pattern.
Again, electronics played a role in Mandelbrot's work. He was led to it
by work on intermittent noise in digital communication systems.
Mandelbrot has been a pioneering figure in the development of chaos and
was helped in this by the fact that he had access to powerful computers at
IBM in the late 1970s, machines that most mathematicians did not then have
available to them.
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