Modern Complexity Theory

The general systems theory originally concerned rather simple systems such as the solar system, and mechanical systems, such as clockwork. These are now called 'linear' systems, and they obey Newton's laws. Modern complexity theory concerns more complex systems, which are 'non-linear'. These somewhat technical definitions can best be explained by examples. The terms 'linear' and 'non-linear' have various meanings in mathematics and their exact meaning depends very largely on their context. In the context of complexity theory, 'linear' means that the parameters are fixed, while 'non-linear' means that the system parameters are likely to change. For example, 'linear' means that a man trying to escape from a maze has to contend with walls that are fixed in position. 'Non-linear', on the other hand, means that the walls move as the man approaches them.

The solar system is a linear system. It obeys Newton's laws of motion. Indeed, Newton formulated these laws to explain its behaviour. A feature of linear systems is that they are predictable.

We can predict the phases of the moon, and the tides, with great accuracy, for centuries ahead. Weather systems, on the other hand, are non-linear. They are just turbulence on a grand scale. They are also notoriously unpredictable. Weather forecasts of even a week ahead are famously unreliable. One of the main properties of nonlinear systems is that they are unpredictable.

A first class snooker player can play balls as he pleases. The balls obey Newton's laws of motion, the system is linear, and the result of each shot is predictable. But, if you put that snooker table on a ship at sea, it becomes a non-linear system, and the shots are entirely unpredictable.

In the context of complex adaptive systems, linear also means that the output is proportional to the input, and the whole is equal to the sum of the parts. Non-linear means that the output is greater than the input, and the whole is greater than the sum of the parts. This 'something extra' consists of emergent properties.

When the present book was being finalised, Stephen Wolfram (2002) published his remarkable work A New Kind of Science, in which, in effect, the mathematical equations of the linear systems and the hard sciences are replaced with the computer algorithms of the non-linear systems and the soft sciences. Simple algorithms can produce great complexity which is entirely unpredictable, as well as emergent properties that are equally unpredictable. This unpredictability is disliked by students of the hard sciences, and it is also the main reason for allowing non-linear systems to self-organise (see 2.4) as much as possible.

Table 2.1

SIMPLE SYSTEM

COMPLEX SYSTEM

linear

non-linear

output = input

output > input

whole = sum of parts

whole > sum of parts

non-adaptive

adaptive

non-living

mostly living

not self-organising

self-organising

predictable

unpredictable

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