Linear Systems

The Scientific Era

The Age of Enlightenment in Europe, reaching maturity in the 18th century, impacted on the way life is perceived at all levels from the mundane to the profound. Its indelible effects colour human beliefs and actions to this day. In the wake of numerous remarkable discoveries, science liberated minds from centuries of control by religious dictates and ancient philosophies. However, the new age of reason substituted its own conventions, more enlightened than before but just as limiting in some respects.

Descartes (1596-1650) and Newton (1642-1727) set the scene. The former advocated rationalism while the latter unearthed a wondrous collection of fundamental laws. A flood of other scientific discoveries soon followed injecting a heightened sense of confidence in the power of reason to tackle any situation.


Positivism, an expression coined by Comte (1798-1857), describes the structure of beliefs associated with the scientific era. It rejects value judgments in all issue areas, including the social sciences, and advocates unwavering focus on observable facts and relationships. In principle, and contrary to arguments put forward by certain postmodernists, there is nothing wrong in using objective facts and relationships as a basis for decision-making. In practice, however, selecting the pertinent facts and determining relevant relationships in some instances is somewhat difficult.

Essentially, in nonlinear situations, where the internal dynamics of a system determine its global pattern and its future evolution, it is far from easy to discern the ‘facts’ and to model causal relationships. In theory, it is always possible to determine facts and relationships for all situations. However, in a nonlinear process one would require a vast amount of computing power to do so. Think of the difficulties involved in computerised simulation of a ‘simple’ chess game involving a small number of interacting elements and rules and this point will become instantly obvious. The difference between linear and nonlinear processes often lies in this computing feasibility. In the first case, mental arithmetic or pencil and paper might suffice to solve a problem. In the latter case, the most powerful computer might find the task beyond its capability.

The Linear Paradigm

The traditional scientific method survived well into the twentieth century, and the linear paradigm it reflects is founded on four golden rules:

  • Order: given causes lead to known effects at all times and places.
  • Reductionism: the behaviour of a system could be understood, clockwork fashion, by observing the behaviour of its parts. There are no surprises; the whole is the sum of the parts, no more and no less.
  • Predictability: once global behaviour is defined, the future course of events could be predicted by application of the appropriate inputs to the model.
  • Determinism: processes flow along orderly and predictable paths that have clear beginnings and rational ends.


The conventional method worked remarkably well for certain systems, yielding guaranteed results each and every time up to and including space travel. The systems concerned are described as being linear; a projectile moving under the influence of gravity being a typical example. Such systems behave in a gradual manner devoid of sudden and unexpected upheavals. In general, their behaviour could be depicted on a line diagram, hence the reference to linearity.

Reductionist styles of management based on command-and-control methods are most effective in the case of linear systems. A system or process is divided into smaller units and these are then managed separately to achieve desirable ends for the total entity. The assembly lines, used in car manufacture for instance, provide a perfect illustration of that approach. Detailed planning and rigid control from the top through a well-defined hierarchy are necessary components for ultimate success.

And Failures

Success in the fields associated with linear systems in the natural sciences had a profound effect on attitudes in all sectors of human activity, including politics and economics. Theorists and practitioners alike entered into the prevailing spirit of certainty and predictability by slicing the issue areas under study into smaller segments more amenable to modelling, and then putting them together again to make pronouncements on how the larger units would behave under specified conditions.

When that form of management was applied to certain situations, such as a large company, the macro-economy or a whole nation, the outcomes were indifferent and sometimes disastrous. Persistent failure in that respect is clearly exemplified by the meager results achieved from efforts spanning over half a century in the field of development.

A Fundamental Shift

Efforts were made to address the problems associated with the linear paradigm by a variety of ad-hoc measures that dealt with isolated difficulties on a firefighting basis without tackling the root issues. It is only in the last few decades that fundamental questions were asked about the intrinsic nature of the systems under consideration. And that re-thinking only came about after those working in the natural sciences had concluded, following lengthy debate, that the science envelope should embrace both linear and nonlinear phenomena. Having received the scientific seal of approval, nonlinear analytical methods are now being increasingly deployed by scholars in the social sciences.

In sum, application of linear methods to nonlinear systems, in which the internal dynamics play a significant part in determining global patterns and modes of behaviour, proved ineffective and occasionally harmful and a radical change in viewpoint became unavoidable. The search is now on for a new consensus, and this website is published to assist in that endeavour.