Characteristics of linear systems

At their simplest, linear systems are those that display the common cause-and-effect relationships that we see around us, for example: girl kicks football, football hits wall. Other characteristics of linear systems are that input is proportionate to output: how hard the ball is kicked has a clear relationship to how quickly it accelerates from rest, and that in the absence of external force the system will settle back to rest: the ball will come to a standstill. Our understanding often uses mechanistic metaphors. For example, the workings of a child’s wind-up clockwork toy can be understood by looking at the parts; the relationships are deterministic and, therefore, predictable and controllable. There are no surprises either, in that no new properties emerge: a mechanical/linear system is equal to the sum of its parts, and each of its parts is in distinct external connection to other parts.

A linear materials economy is a throughput economy and, therefore, it has limited feedback, in this case replenishment – although money flows within it are full of feedback and some resource categories are renewable. It, too, has become identified with a mechanism.

'' “Businessmen, intellectuals, and revolutionaries of the Industrial period were mesmerized by machinery-fascinated by steam engines, clocks, looms, pumps, pistons and they constructed endless analogies based on simple mechanistic technologies of their time. No accident Ben Franklin and Thomas Jefferson were scientists and inventors as well as political revolutionaries. They grew up in the wake of Newton’s great discoveries – i.e. he had concluded that the entire universe was a giant clockwork operating with exact mechanical regularity. La Mettrie the Fr. physician and philosopher, in 1748 declared man himself to be a machine. Adam Smith later extended the analogy of the machine to economics, arguing that the economy is a system and that systems ‘in many respects resemble machines.’” ''

- Alvin Toffler

The importance of linear systems clearly goes beyond machines and economies and many writers have described the effect that assuming society and the world at large also works in a mechanical, linear way has had on our thinking. This is especially true since the Enlightenment raised reason and the scientific method to prominence.

Stephen Sterling described it as ‘boxed thinking’ as opposed to more connective or systems thinking. Here are ten assumptions of boxed-thinking:
 * 1) ‘To every problem, there’s a solution’ belief in the power of problem-solving approaches
 * 2) ‘We can understand something by breaking it down into its component parts’ understanding a complex whole by looking at the detail
 * 3) ‘The whole (of something) is no more than the sum of its parts’ there are no emergent properties
 * 4) ‘Most processes are linear’ events and phenomena have a definable beginning and finishing point
 * 5) ‘Most issues and events are fundamentally separate or may be regarded as such, and may be dealt with adequately in a segregated way’ issues are essentially unrelated
 * 6) ‘It is acceptable to draw your circle of attention or concern quite tightly, as in ‘that’s not my concern’ we do not need to look beyond our immediate concerns as an individual, a householder, a consumer, a businessman, etc
 * 7) ‘We can define or value something by distinguishing it from what it is not, or from its opposite’ a belief that economics is separate from ecology, people are separate from nature, facts are separate from values, etc
 * 8) ‘Objectivity is both possible and necessary to understand issues’ it is important to exclude our feelings and values in our analysis and judgement
 * 9) ‘We can understand things best through a rational response. Any other approach is irrational’ we need to downplay our intuition and non-rational knowing
 * 10) ‘If we know what the state of something is now, we can usually predict future outcomes’ a belief in certainty, prediction, and the possibility of control

Of course, it is not as simple as this, but these ten assumptions are a start to understanding the way we tend to think.

But this is not the universe which we now apprehend, when we stand back and look or get up really close and look.



Classical physics has been bookended by the work of Einstein with relativity and the very large scale an d the incredibly small with quantum theory, and in both arenas the Newtonian view was found wanting. The linear mech

anisti c assumptions were always an approximation, not least because the mathematics of modelling systems with feedback was very laborious and difficult before the advent of computing. Since we now can run the maths it seems that real world systems, all the interesting systems in the world are actually non-linear. The linear has become the special case and the non-linear the generality. It seems we inhabit a world full of connection, full of surprise caused by feedback, a world where we do not step outside and observe but must participate and where separateness is often more illusory than real and the lines which so conveniently allowed us to say what is important and what is not have been blurred.

The key to understanding the non-linear, where input need not be proportional to output and the whole can have different characteristics – in short be more than the sum of the parts – is feedback (see 1B). The shock to the linear economy from resource and energy limits is not the only shock. The thinking is becoming redundant too, or rather its limitations are ever more obvious. A part of this broader shift, of which the circular economy is only one aspect, is the rise of systems thinking – thinking related to non-linear relationships. Since the circular economy requires systems thinking and since it is in turn a reflection of changes in science then it might be seen as part of an ‘enlightenment’ fit for the 21st century. In this way it could be seen as reinventing progress, as discussed by the Royal Society of Arts.