## Complexity

We often refer to something complex as something that is intricate, complicated or difficult to understand.

The following is a study of a different type of complexity: *physical *complexity.

Physical complexity is a universal natural phenomenon found from molecules, organisms and neural networks to some social organisations; yet, it is something that we hardly understand.

**Definition**

There are many different types of systems in nature and not all of them are complex. Systems are very diverse. They can be small, like atoms and molecules or large like planetary systems. They can be simple like a pendulum or complicated like a computer network. They can be coherent like an organism or chaotic like a gas. And they can be local like an ecosystem or global like the climate.

Complex systems are a particular type of systems. All systems are formed multiple elements interacting with each other. But complex systems are characterised by the high degree of *integration* and *differentiation* among the constituting parts. The integration of the system depends on a high interconnectivity and interaction between constituting parts. And the degree of differentiation is given by their degree of multiplicity and diversity.

Complexity then, is characterised by both qualities: integration *and *differentiation. Systems with either a low degree of integration or differentiation don’t behave like complex systems.

**The relativity of complexity**

Not all systems are equally complex. Complexity is relative and it depends on the degree of differentiation and integration, where higher differentiation and integration is related with higher complexity.

So we define the *degree *of complexity of a system as the degree of integration *and *differentiation of the system. High complexity is related to high degrees of integration and differentiation, while low complexity with the opposite.

Differences in the levels of complexity are also related with differences in the properties of systems and the way they behave.

**Physical properties of complex systems**

Complex systems are *non-linear*; that is, their effects are not proportional to their causes. Given an initial condition, the effects are different than the linear sum of the causes.

One characteristic of non-linear systems is that they are *irreducible*; that is, the behaviour of whole cannot be reduced to the sum of the individual behaviour of the constituting parts.

And another characteristic of complex non-linear systems is that they are *unpredictable* and *uncontrollable*. One of the reasons for their unpredictability is their *indeterminism*. Simple non-linear systems (e.g. a pendulum) can be predicted on deterministic causal relations. But in complex systems determinism ceases to be applicable and systems becomes unpredictable. And another reason for the unpredictability of complex systems is that they involve an element of *randomness *in their change. Random noise can influence the feedback relations of the system with unpredictable effects.

The non-linearity of systems is relative to its level of complexity. The lower the complexity, the easier it is to approximate it in terms of linear causal relations. But the higher the complexity, this simplification is lost, and the more irreducible and unpredictable it becomes.

As a corollary to the above, we have that the behaviour of complex systems cannot be reduced to the behaviour of fundamental elements. Even if science succeeds in unifying Quantum Mechanics with General Relativity (the two most fundamental theories in physics) in a Theory of Everything, our current scientific understanding of the world wouldn’t get us much closer to an understanding of the world around us without an understanding of complexity. Complexity is everywhere around us, and the behaviour of complex systems cannot be reduced to the behaviour of fundamental elements like particles or strings.

**Dynamic properties of complex systems**

Complex systems differ from all other systems on the way they behave. The behaviour of complex systems is shaped by two fundamental properties they possess: autonomy and flexibility

*Autonomy*is the relative independence of the dynamics of the system to external perturbations.*Flexibility*is the capacity of the system to change its internal structure and dynamics.

Autonomy and flexibility gives complex systems higher resilience

*Resilience*is the capacity of systems to maintain their dynamic stability against internal or external perturbations.

The autonomy and flexibility of systems are relative to their level of complexity, where higher complexity is related with higher autonomy and flexibility.

With higher complexity, systems manifest new properties related with higher dynamic stability.

At a first level of complexity systems can become self-regulating systems (like ecosystems, the climate and the earth’s natural system).

*Self-regulation*is the capacity of systems to correct themselves through feedback of information into more stable states.

One characteristic of self-regulation is its spontaneity; that is, its lack of internal or external control. So another characteristic of complex systems is having a collective behaviour with

*Non-centralised control*

At a higher level of complexity (and with higher autonomy and flexibility) systems can become self-organising systems (like genes or living organisms).

*Self-organisation*is the capacity of systems to organise themselves and gain resilience and stability against internal and external perturbations.

Higher flexibility on self-organising systems can develop into adaptability.

*Adaptability*is the capacity of systems to organise their dynamics adjusting to variations on internal or external conditions.

Self-organising systems can also manifest synergetic and emerging properties.

*Synergy*is the capacity of constituting elements to collaborate or co-operate to produce an outcome positive to all, which otherwise wouldn’t be achievable on their own.*Emergence*is the production of a collective behaviour or function, irreducible to the behaviour or function of the constituting parts.

**Monism and complexity**

Complexity is a very peculiar phenomenon. It is an occurrence that brings order out of chaos. But why does it occur at all? Why does complexity exist in nature?

From a monist point of view, complexity is a consequence of the behaviour of Space. In a monist universe, everything has a dynamic existence tending towards states of higher dynamic stability. Complex systems exist in nature because they are systems that find in complexity states of higher stability.

When among the chaos, elements interact and join their dynamics they can become more stable. And when this happens, system arises. And when systems increase their diversity and interconnectivity complex system comes to be.

Complexity then, is a natural occurrence in a monist world.

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