3 The Forgetting of Chaos Through Scientific Reductionism.
One of the difficulties encountered when trying to comprehend infinity
is that there are no reference points. Imagine a boat on an ocean. It is
night and the sky is clouded over. As far as can be seen there is nothing
but water. Without reference points, it is impossible to gain any understanding
of where we are. Therefore, humans add reference points, or attempt to
create order out of the ocean of chaos. Through reductionism, science has
taken this to the extreme, and in so doing, the mythological link humankind
had with chaos has become nullified.
"The psychologist, anthropologist, and critic René Girard
has observed that we humans have a great need to interpret the disorder
in myths from the point of view of order. ‘Even the word ‘dis-order’ suggests
the precedence and pre-eminence of order,’ he says. ‘We are always improving
on mythology in the sense that we suppress its disorder more and more.’
"
The same holds true in science, and with the birth of the modern scientific
method in Greece, chaos began to be forgotten.
3.1 The
Birth of Modern Science in Greece.
Despite strong ideas of chaos in their mythology, the Greeks were among
the first to attempt to understand their surroundings through reductionism.
In other words, they broke things down into their smallest possible components,
tried to understand them individually, and then added them up again in
order to comprehend the whole.
"Rationalism, for whatever its value, appears to have emerged from
mythology with the Greeks… There was a feeling that the natural laws, when
found, would be comprehensible. This Greek optimism has never entirely
left the human race."
Many of the Greek areas of study reflect their desire to understand the
world by its smallest and most simple parts. For example, there was much
discussion regarding atoms and indivisibles, a concept that continues to
be relevant today.
"…that most influential concept of early Greek science, the atom.
The notion of atoms was offered as the bedrock of understanding, and its
properties seemed to symbolise the supposedly ultimate form of reasonable
questions that could be raised about the universe."
Through reductionism, the Greeks were also the first to encounter some
of the problems it raised. On the mathematical frontier, several of these
were later solved by calculus. This process of reductionism began with
the Greek philosophers, Thales, Anaximander, and Anaxagoras who took the
mythological idea of chaos as a creative force and applied it to science.
"[They]… proposed that a specific substance or energy – water or
air – had been in chaotic flux and from that substance the various forms
in the universe had congealed."
Thales, born in Miletus in 624 BC is credited by later Greeks as being
the founder of Greek science, mathematics, and philosophy. Thales’ mother
is believed to have been a Phoenician and this may be one of the reasons
why he received an Eastern education. Although many details about his life
are sketchy, it is certain that he spent time in Egypt and most probably
Babylonia and would have had a grounding in creation myths from these and
other lands.
"It may be that what seemed to the Greeks a multiplicity of achievement
was simply the lore of the more ancient peoples."
Thales took the knowledge of the East and brought it to the West. However,
in doing so, he made the important advance of turning such knowledge into
abstract studies. He was the first to attempt to prove mathematical statements
using a logical series of arguments. Importantly, he was also the first
to ask the question ‘of what is the Universe made?’ from a purely scientific
perspective without relying on mythological ideas.
In this way, Thales began changing previous notions of chaos and creation
into more rational scientific ideas. He proposed water as the fundamental
element of the universe, still showing parallels to the mythological idea
of the universe being created from a primordial and boundless ocean.
An example of science taking over mythology can be seen in a discovery
of Pythagoras regarding the morning star (then known as Phosphorus) and
the evening star, known as Hesperus. He proved that they were, in fact,
the same star, and consequently it was renamed Aphrodite (and subsequently
Venus by the Romans).
In the Pythagorean approach, we can see the beginnings of a reductionist
view of the world. They viewed the world through numbers and geometry.
"In their world view lines were derived from points or unit numbers,
from lines surfaces, from surfaces simple bodies, from these the elements
and the whole world."
"They also held truth, intelligibility, and certitude to be cognate
to numbers, which they contrasted with the erroneous world of the undefined,
uncounted, senseless, and irrational."
Aristotle moved further away from mythological ideas of chaos and order,
proposing that order was pervasive. That which appears chaotic merely has
a high complexity of order, too complex to be understood at present.
Nevertheless, some Greek philosophers proposed that eventually, the
universe would revert to a state of disorder from which a new universe
would arise.
3. 2 From
the Renaissance to the Present: Reductionism to Chaos.
Scientists continued the Greek method of reductionism for centuries.
If a system appeared chaotic and unpredictable, science attempted to reduce
it with the belief that, at a fundamental level, the system was ordered,
linear, and predictable. Driven by this idea, scientists developed theories
that became minimalistic. Since the time of the Greeks, science had been
working towards a complete understanding of the universe. Later, prominent
scientists and philosophers like Galileo, Descartes, and Newton made this
seem astonishingly close to being reality.
"Traditionally, scientists have looked for the simplest view of
the world around us."
The mathematician, astronomer, and physicist, Galileo (1564 – 1642), studied
pendulum motion with this objective in mind. He discovered that the time
it takes for a pendulum to complete a cycle is always the same, regardless
of the size of the swing. That is, the speed and the size of the swing
are always proportionately identical. After producing this hypothesis,
he tested it by asking his friends to count the swing over the course of
several hours. Although this is not the soundest method of confirming a
hypothesis, the theory is an elegant one, and became widely accepted.
Galileo is also famed for his observations on the then unexplained force
of gravity. In his experiments, he found that weight does not affect the
speed with which an object falls to the ground. Throughout his work, he
was simplifying the laws that govern the earth.
During the seventeenth century, Newton developed his theory of gravity
and, along with Leibniz, calculus. Through understanding these new, all
encompassing laws of physics, it seemed that it would not be long before
the entire workings of the world could be explained and calculated. During
the Napoleonic era, the French physicist Pierre Laplace, excited by this
possibility, envisaged a law that could explain every physical phenomenon
in the universe. With approximate knowledge of the present, he stated,
it would be possible to predict an equally approximate future.
Indeed, by 1980 it seemed that physics had come so far that the end
of unpredictability was in sight. The cosmologist, Stephen Hawking, occupant
of Newton’s chair at Cambridge University, spoke for most of physics when
he said during a lecture entitled ‘Is the End in Sight for Theoretical
Physics?’:
"We already know the physical laws that govern everything we experience
in everyday life… It is a tribute to how far we have come in theoretical
physics that it now takes enormous machines and a great deal of money to
perform an experiment whose results we cannot predict."
Despite Hawking’s confidence in the power of modern physics to predict
the future, many experiments considered simplistic by most physicists can,
in fact, display unpredictable behaviour, as in the example of pendulums.
"Students for generations have regarded pendulums as classical
examples of simple, regular motion. In fact, pendulums still hold great
surprises in store for us."
Thanks, primarily, to the work of John Miles of the University of California,
pendulums are now seen as a good example of ‘deterministic chaos’. David
Tritton, of the University of Newcastle upon Tyne, explains a relatively
simple experiment that demonstrates this. It involves a ball suspended
from a piece of string. The string is attached to a horizontally oscillating
crankshaft. The crankshaft drives the motion of the pendulum.
When the crankshaft is driving the pendulum slightly higher than its
natural (free-swinging) speed, the motion of the pendulum increases accordingly,
before developing a secondary movement that runs perpendicular to the drive.
This causes the pendulum to move in a circular path. Once the pendulum
has settled into this path, it will continue as long as the oscillation
of the crankshaft is maintained. Although this motion is predictable and
non-chaotic, it does contain an unpredictable element: the initial direction
of the pendulum (clockwise or anti-clockwise) is a random event. Once the
direction becomes established, however, the course of the pendulum is easily
predicted.
If the crankshaft is driving the pendulum slightly lower than its natural
speed, there are many possible outcomes to the pendulum’s movement, all
of them elliptical with successive orbits never being identical. Over longer
periods of time, significant change can be noticed. Not only is the motion
aperiodic, it also frequently changes between clockwise and anti-clockwise.
Experimental and theoretical work by Miles suggests that, indeed, there
is no pattern to the movement. It is entirely chaotic.
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