# November 2006: Complexity and complex systems

## Complexity

The increase in computer power over recent decades has allowed extensive modelling of systems to be carried out. This has revealed an unexpected level of complexity, which presents the modelling community with a number of dilemmas. The basic problem lies in our comprehension of what complexity is.

This is not a simple question to answer and the results of investigations carried out so far are inconclusive. Paradoxically, the deeper we look into complexity the more we see. As a result, we now appreciate that high fidelity prediction of complex systems is (probably) impossible and this has been demonstrated with the uncertainty associated with long term climate modelling.

These problems also apply to complex engineering systems, which is of interest to the work we do at the EDC.

## Complex systems

One of the many issues associated with complex systems is; when does complexity begin? Although a good question, an answer is not obvious or forthcoming - a good reason why researchers are interested! Think for a moment; when is something simple and when is it complex? If we can define these then there must be a point, somewhere in between, where a line is crossed between simplicity and complexity. Even if we cannot confidently define boundaries between complexity and simplicity, we can identify systems which demonstrate some degree of complexity. These make a useful starting point for an investigation.

... if you divide a complex system into two, you end up with two complex systems

Interestingly one method of trying to understand such systems is to reduce them to a simple system. This is a contentious approach, since complexity is a purely relative term. For example, if you divide a complex system into two, you end up with two complex systems. Are we saying that if we continue this process, eventually we will end up with a number of systems we can describe as simple? This is doubtful as complexity can be demonstrated at the sub-molecular level. The boundaries are in fact far from clear.

## Implications

There are serious implications to our lack of a full understanding of complex systems. Consider if someone is designing a system, which we assume will at some stage demonstrate complex behaviour. How can they predict the full implications of that system throughout its lifecycle? Indeed how can useful safety analyses and costing be carried out if a systems behaviour is inherently unpredictable.

Climate modellers also suffer a high level of uncertainty associated with their work. Inevitably this leads to disputes over the accuracy and reliability of their modelling predictions. The gravity of this is highlighted when one considers governments are now making important economic decisions based on such low levels of confidence.

## Potential solutions

Over recent years theoreticians have attempted to provide
*measurements* for complexity. Many have tried to define it
based on the characteristics of complexity in the context of
their own research fields. For example, theoretical work has been
done to analyse complex systems, which demonstrate chaotic
behaviour (i.e. climate modelling). As yet no single definition
seems to suit all situations where complexity exists. As we said
earlier, in practical representations of engineering systems, it is
still considered difficult to define exactly when complexity
begins and this remains a problem.

The objective of the work at the EDC is to reconcile existing theoretical methods with practical modelling simulations of complex systems to develop a reliable means of defining and measuring the relative complexity of systems.

For example, approaches we have considered include:

- Entropy:
- The concept that is sometimes used as a measure of complexity is entropy. The entropic measure is a way of quantifying the disorder that arises in a system due to variety and uncertainty. Also rooted in information theory, entropy is defined as the expected amount of information necessary to describe a system. A measure for complexity then? This may be so since this is a reflection of the various possible states of a system.
- Chaos theory:
- Another (much prettier - see Figure 2) approach is to use phase portraits to graphically show a systems states at discrete time intervals. These are useful because they can easily highlight stable points in systems called attractors. They can also clearly show when a system is oscillating. The attributes associated with these systems can indicate both the sensitivity of a system to initial conditions and their intrinsic unpredictability.

## Benefits of understanding complexity

The systems we design and use are getting more and more complex. Therefore, this is not just an academic exercise; there are consequences if we don't solve these problems. Our work in this area aims to provide a number of benefits to our industrial partners, these include:

- A greater understanding of complexity, which is increasingly becoming a costly element in the design and production of large engineer-to-order systems.
- Implementation of more efficient and effective use of modelling capability to better represent complex systems.
- Reduction in the uncertainty associated with emergent properties, and a corresponding improvement in the dependability of modelling results.
- Ability to apply comparison and optimisation techniques to the emergent properties of complex systems by developing metrics for them.
- Provision of a means of anticipating and appreciating the relative complexity of systems early in the design stage, thus saving costs later in the lifecycle.

Recent thoughts in this area propose that the route to tackling complexity is to reduce it. While this is laudable, the EDC believes the route to reducing complexity cannot be properly achieved until we fully understand complexity and have resolved the issues highlighted here.

### Author: John Dalton

Contact: John.Dalton@ncl.ac.uk