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The kind of systems with which most people are familiar are machine-like. They can be natural like a human being. They can be artificial like a computer or a motor car. Their functionality is effected by a set of permanently inter-linked organs like the brain and the heart, or devices like a CPU, a disk drive, an engine or a gearbox. They are all centrally controlled. They have a fixed structure. They are not scaleable. If you join them together you do not simply get a bigger one. If you chop one up into arbitrary pieces, you do not thereby create a lot of perfectly working smaller ones.
In their futile attempts to impose centralised control over society, governments create models of society which resemble machines. The results prove that society is definitely not a simple deterministic machine.
A complex dynamical system is fundamentally different. It is not machine-like. It does not have a fixed structure: it is fluid. Its total functionality is resident in its entirety within each of its minutest component parts. It does not possess functionally-dedicated organs or devices. It cannot be centrally controlled. It is infinitely scaleable right down to its basic parts. So however closely or distantly you look at it, it always looks - and indeed is - the same. Its structure is what is termed fractal.
Human society is much more like a complex dynamical system made up of the 6 billion human individuals who inhabit this planet. Its highly distributed control system is made up of 6 billion loosely connected 100-billion neurone human brains. Its power therefore pales into insignificance that of the largest corporate and government super-computers used to try to impose a bureaucratic superstructure upon society. But how does it work?
Probably the most familiar example of a complex dynamical system is the Earth's atmosphere, or more specifically the global weather system. Like any kind of system, a complex dynamical system needs a source of energy to drive it. Everything on Earth - especially anything which is of a global scale - is driven principally by the sun. The weather system is driven by the daily and annual cycles of solar heat and in addition by the gravity of the moon. It is thus driven by three different periodic energy sources. Through its subsequent motion it dissipates this energy. The weather therefore belongs to a particular class of complex dynamical systems which is both periodically driven and dissipative. This class of complex dynamical systems exhibits certain distinctive modes of behaviour.
A fleeting carousel of autumn leaves drifting along the pavement. The calming melody of a summer rain. The violence of an equatorial storm. The searing heat of a tropical desert. The still grip of an arctic winter. Each has a finite existence in time and space. Each is a different manifestation of the forces which continually converge and disperse within the atmosphere. They are just some of the wide variety of features which make up the normal mode of behaviour of our global weather system.
The weather follows an annual cycle yet never repeats exactly. In some situations it can be predicted accurately in the short-term. In others it is wholly unpredictable. It is chaos superimposed on regularity. Yet from breathless calm to raging storm, from icy stillness to churning heat, its parameters never violate their decreed bounds. No matter how complex its behaviour may be, it always exhibits order. I feel that the term chaos which has been coined to describe this complex form of motion is an unfortunate misnomer. It is never a case of 'anything goes' or 'no holds barred'. Though it may not be regular, it is never random or formless. It obeys mathematical rules. It is held within its decreed limits which can be seen taking shape on a computer screen as a butterfly shaped graph which has become known by mathematicians as its strange attractor.
It is now thought that even the ice ages, which sporadically envelop the temperate latitudes, are merely extreme excursions within the weather's normal mode of behaviour. As such, it is still held within the pull of the same strange attractor which has two or more limbs between which the climate's behaviour can flip. The weather is thus bound always to return from such wild excursions back to its long-term norm.
But this is not the only mode in which the Earth's climate could operate. To forecast the weather, meteorologists model its behaviour in terms of differential equations. While exploring the behaviour of these equations by computer, they discovered that, if the atmosphere were subjected to a large external jolt, the global climate could be flipped into an entirely different mode of behaviour. They called it the White Earth because in this mode, the whole earth would be covered with snow and the oceans would be surfaced with ice. The atmosphere would be thinner. Weather features such as storms would be much smaller. Life would be hard.
In White Earth mode, the climate would be held within the influence of a different strange attractor. So once the climate had been knocked into White Earth mode, it would require another large external jolt to knock it back to normal. Furthermore, the equations show that a White Earth may not be the only stable alternative to our present global climate.
A complete definition of the behaviour of a complex dynamical system like the global weather would therefore probably involve many possible modes of behaviour. Some modes may be trivial, for instance where the atmosphere remained completely still. Others may be active but unable to support life, for instance where all motion were simple and periodic. In this case, the absence of turbulence would not facilitate the rapid mixing and dispersal of gasses and moisture vital to life on this planet. Both the normal mode and the White Earth mode exhibit very complex motion.
Behaviour - however complex - is the effect of a cause upon a system. Any system converts a particular cause into its effect according to the dictates of the particular laws of physics which that system embodies.
In machine-like systems, the relationship between cause and effect can normally be observed and measured. The law relating cause and effect can then be written down mathematically and hopefully understood. In complex dynamical systems, however, the relationships between cause and effect cannot be determined directly. One must look at the system's smallest constituent parts. In the case of the weather, these parts are the molecules of gas and vapour which are found in the Earth's atmosphere.
These are tiny systems in their own right. They embody physical laws. Each produces a determinable effect when subjected to a given cause. For instance, the relation between cause and effect for the impact of a solar photon on an atmospheric molecule is of itself reasonably simple.
However, the composite behaviour of zillions of photons impacting on zillions of molecules which then go on to collide with zillions of other molecules in a never-ending interlacing cascade of action and reaction, is unfathomably complex and indeterminable. Thus the apparent chaos of the weather is merely the result of countless tiny machines engaged in simple interactions in endless iteration.
Yet in all the turmoil of our planet's weather system, neither the form nor functionality of these tiny machines is ever violated or destroyed. The atoms and molecules of the atmosphere collide, combine, separate, move on and then recombine according to prescribed laws - laws which govern how they interact and guarantee their individual preservation.
The integrity of each of these tiny natural machines is protected by an unassailable energy barrier. The preservation of each is assured by the fact that the energy needed to break the bonds which hold together its internal members is many orders of magnitude higher than the greatest energy unleashed by the weather. Earthly storms could never achieve the fury required to tear apart the elements of the atmosphere into their constituent fundamental particles and fuse them into heavy, dangerous radioactive elements which would wipe out all the life on the Earth. Such behaviour could occur only within the 'weather systems' of the stars. It is way beyond the limits set by our terrestrial weather system's strange attractor. The survival of each of its basic components is thus assured.
Shaped by the myriad interactions between countless tiny mechanisms according to simple physical laws, the complex-but-bounded behaviour of our global weather system is - barring external catastrophe - destined to continue to provide the ideal vessel for human life and civilization.