In 1834, John Scott Russell observed a barge going along a canal when it suddenly stopped. A wave continued in front of the boat, but instead of dying away, continued down the canal for several miles. The phenomenon was noted elsewhere, and repeated experimentally, but was not explained until 1895. Even then, the phenomena had no obvious application, and were regarded as mere scientific curiosities. It was recognised as a nonlinear phenomenon, but mathematics was only at the time able to deal with linear equations. (Davies).

During the 1960’s, numerical experiments were carried out on computers to see what would happen if two solitary waves of different heights collided. They were expected to collapse. Instead, the two humps both emerged from the disturbance and travelled on serenely with their original speeds. (Davies)

The soliton has been recognised as the basis of superconductivity and is leading to revolutionary scientific and technological changes. In molecular biology, there is a long standing controversy about how energy is passed along long chain molecules like DNA. It is possible that this is not by chemical processes, but by soliton ripples in the structure of the molecule (Davies). Turbulent behaviour, like solitons, was also put aside, or bracketed outside of the explanatory framework.

This burgeoning study of nonlinear systems is causing a remarkable shift of emphasis away from inert “things” – lumpen matter responding to impressed forces and towards “systems” that contain elements of spontaneity and surprise. The old machine vocabulary of science is giving way to language more reminiscent of biology than physics – adaptation, coherence, organisation…In many cases the same basic nonlinear phenomena are manifesting themselves in systems that are not really material at all, including computer networks and economic models. Chaos. James Gleick, Penguin 1987. (Gleick 1988

An eerie type of chaos can lurk just behind a facade of order, and yet deep inside the chaos lurks an even eerier type of order. (Gleick 1988).

Order and pattern exists where formerly only the erratic, the unpredictable, the chaotic had been observed, and conversely, that which appears orderly and simple is in fact highly complex.

Laplace wrote:

Such an intelligence would embrace in the same formula the movements of the greatest bodies in the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.

There was always a small compromise. Measurement could never be perfect. It was given that, with an approximate knowledge of a system’s initial conditions and an understanding of the natural law, the approximate behaviour of the system can be calculated.

The basic idea of Western science is that you do not have to take into account the falling of a leaf on some planet in another galaxy when you are trying to account for the motion of a billiard ball on a pool table on earth. (Gleick 1988)

This belief is only justified because it works. The errors may stay small for millions of years, but they might not.

In the early nineteenth century, there was a difference of opinion between Goethe and Newton’s followers about the nature of colour. Goethe’s views were thought to be pseudo scientific meandering. He argued that colour is a matter of perception. He had repeated Newton’s famous experiment with a prism. A prism breaks a beam of white light into a rainbow. Newton proposed that colours must correspond to frequencies. Goethe only got colours when there was an imperfection; a spot or a cloud in the sky. He concluded it was the “interchange of light and shadow” that causes colour. Colour is “a degree of darkness, allied to shadow.

In the language of non linearity, colour comes from boundary conditions and singularities. Redness is not necessarily a bandwidth of light, it is a territory of a chaotic universe, and the boundaries of that territory are not easy to describe yet our minds find redness with regular and verifiable consistency. (Gleick 1988

A pendulum has not one, but two states of equilibrium. The first is obvious, the tick tock from side to side. The second solution to its equations of motion is when it is hanging straight down and not moving. Hiding within any particular system could be more than one stable solution. An observer could see one type of behaviour for a very long time, but a completely different kind of behaviour could be just as natural for the system. (Gleick 1988)

The snowflake is the essence of chaos; a delicate balance between forces of stability, surface tension, and instability, the diffusion of heat as water freezes. Traditionally, because the surface tension effects are so small, researchers assumed that for practical purposes they could be disregarded. The tiniest scales proved crucial; the surface effects proved infinitely sensitive to the molecular structure of a solidifying substance. The natural molecular structure of ice gives a built in preference for six directions of growth. The mixture of stability and instability amplifies this microscopic preference, creating the lace work of snowflakes. (Gleick 1988).

Sensitive dependence on initial conditions serves not to destroy, but create. A snowflake typically takes an hour or more to float to earth. The choices made by the branching tips at any moment depend on such things as temperature, humidity and impurities.

The final flake is for practical purposes, unique. (Gleick 1988).

When a child draws a tree, a green mass sits atop a brown trunk…..A child’s cloud is a smoothly rounded bulk ….. These are not the clouds we see. They are highly stylised forms ….. As children and adults we own a repertoire of such stylised images, like ideograms in Chinese painting. First they help us to see for without such templates, our minds are powerless to sift the welter of sensations that bombard our eyes and ears. But they hinder our seeing, too. (Gleick 1990)

Imagine a river ….. Inevitably and universally, we imagine a line, drawn with some curve or wiggle. When we speak of a river by name, we think of an entity flowing from one place to another, source to outlet, from a mountain spring to the sea. (Gleick 1990)

North America’s longest river is the Mississippi, or is it the Missouri, a tributary? A nomenclatural hybrid “Mississippi Missouri Jefferson Beaverhead Red Rock” is actually the longest, cascading and meandering from the Northwest Rockies to the Gulf of Mexico, flowing © according to our sense of the river’s essential, Platonic form in a line.

It is not so. Our imaginations mislead us. In reality, a river’s basic shape, repeated wherever nature empties the land of water is not a line, but a tree. A river… is a thing that branches. So are most plants, so is lightning. So is the human lung, a tree of ever smaller tubes: bronchi, bronchia, and bronchioles, intertwining with another tree, the network of blood vessels. (Gleick 1990).

North America’s longest river actually spans thirty-one American states and two Canadian provinces ….. Except in human perception and language, nothing separates its few wide and deep stretches from its many small and narrow ones. In the vernacular of a new science, it is fractal, its structure echoing itself on all scales, from river to stream to brook to creek to rivulet, branches too small to
name and too many to count. (Gleick 1990).

This is an open universe. We live with a multidimensional, open, interrelated universe. Life is constructed on these principles, as are our brains, and effects like water giving up latent heat when it freezes. The atom, the point, the electron, the straight line do not seem to exist.

Instead there are wave forms that we perceive according to our ability to construct a four dimensional universe out of a ten or more dimensional universe. These wave forms seem to take on the individual existence of an electron, or that of a wave, or both, depending on how we decide to look at or measure it.

“Imagine a skyful of starlings, or a million minnows changing direction. Studies have shown that the turning motion of a flock travels through it like a wave. It passes from bird to bird in a seventieth of a second, far faster than the birds reaction time.

Zoologists have seriously proposed there must be some thing like thought transference, or electromagnetic communication, assuming there must be a leader or group of leaders.” (Gleick 1990).

Chaos has provided a paradox. Order, as well as chaos, arises spontaneously from unplanned interactions. Complex behaviour emerges from the interactions of individuals following rules.

Computer simulations have produced lifelike flock behaviour. It is not programmed from the top down, rather each “bird” is given general rules. As if by magic the computer flock simulates the cooperative grace of a natural flock. (Gleick 1990).

Davies and Gribben comment on the holistic character of nonlinear systems. Would human societies be better structured from the bottom, with individuals following general principles, than by hierarchical top down structures? If nature achieves the grace and precision of the turning motion without leaders, why cannot humans?

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