Nonlinear Systems - Global Complexity

Shifts in Scientific Thinking

All good things come to an end, and the supremacy of the linear paradigm—characterised by certainty and predictability—was no exception. Einstein (1879–1955), Bohr (1885–1962), Schrödinger (1887–1961), Heisenberg (1901–1976), and Dirac (1902–1984) played pivotal roles in advancing the natural sciences beyond the Newtonian limits that had defined them for centuries. Later scholars in the natural and life sciences demonstrated that uncertainty is an integral part of many phenomena, now described as nonlinear.

In a reversal of earlier trends at the beginning of the modern scientific era, discoveries in these sciences began to introduce a measure of realism to expectations about prediction and control of socio-economic events.

Nonlinear Phenomena

Nonlinear systems do not follow the familiar bell-shaped distribution of linear systems, where change is gradual, orderly, and measurements cluster around an average. Instead, as Mandelbrot and Gleick, among others, discovered, nonlinear systems display more random and less predictable behavior. They involve discontinuities, sudden shifts instead of smooth changes, and persistence, where low values do not necessarily follow high ones.

Complex Systems

Some nonlinear entities attracted particular interest. These systems are described as complex because they have numerous internal elements; dynamic, because global behavior is governed by local interactions; and dissipative, because they must exchange energy with other systems to maintain stable, self-organized global patterns. When stable patterns are capable of evolution, the systems are also referred to as adaptive.

Self-Organised Complexity

Linear systems are usually at or near equilibrium. A ball bearing on the rim of a bowl provides a classic example, as it quickly settles at the bottom and remains there. Nonlinear systems, by contrast, operate far from equilibrium.

Complex Adaptive Systems can maintain stable global patterns even under such conditions. The second law of thermodynamics states that when an organised system is left alone, it drifts steadily into disorder. A deserted building eventually collapses into rubble, and the wreckage itself may disappear. Any system cut off from external inputs will decline into a random equilibrium where little happens. Disorder is more probable than order.

For a system to remain organised, it must continuously exchange energy or matter with other systems. Without the nourishing energy of the Sun, the Earth would fall into equilibrium and become lifeless. Solar energy sustains activity far from equilibrium, driving local interactions that create stable global patterns known as life. Local chaotic activity is crucial for maintaining overall stability. Organised complexity emerges from a mix of chaos and order.

Two key features are central to understanding complexity:

A complex regime combines global order with local chaos.
As long as local interactions proceed suitably, the system avoids collapse and remains in a self-organised state.

Traits of Complex Adaptive Systems

Complex Adaptive Systems differ from other systems in several ways:

They contain large numbers of internal elements, lightly but not sparsely connected. Local interactions provide energy to sustain stable global patterns.
Internal elements generate enough variety for the system to adapt to unforeseen circumstances. Numerous local interactions create vast numbers of microstates, some of which will fit changing conditions.
Variations in conditions lead to numerous minor adaptations and occasional significant mutations, but specific outcomes cannot be predicted in advance.
Predictability is limited to global patterns. Specific causes cannot be linked to particular effects.

Evolution

Several features mark the way Complex Adaptive Systems evolve:

As Gell-Mann noted, “complexity can either increase or decrease,” but the most significant complexity tends to grow over time.
The average complexity of systems also tends to rise as evolution unfolds.
Evolution usually involves minor adaptations that accumulate slowly. There is no ideal end-state, only long-term survival.
Evolution follows a punctuated equilibrium path. Systems remain stable for long periods, then shift rapidly to new patterns.

Apparent inactivity is misleading. At the local level, systems constantly transition through many microstates within a single global pattern, or attractor. Occasionally, small events push the system into a new attractor. The change then becomes apparent, but stability soon returns in a new form. Variety and flexibility allow adaptation; without them, extinction replaces evolution.

Words of Caution

In this context, “complex” and “complexity” do not necessarily imply difficulty or complication. The terms describe systems fundamentally different from the linear systems of Newtonian physics. It is important to stress this point in anticipation of the natural question: why emphasise complexity when life already appears complex? The answer lies in the very different behaviours and implications of these systems.

Another caution is warranted. The field of Complexity has drawn many adherents from varied backgrounds. Some have made exaggerated claims. Complexity will not solve routine tasks or change the world order by itself. It offers instead a framework for a better understanding of phenomena that behave differently from mechanistic systems.