Complexity Facts


clip_image001 The amount of fitness of a system is proportional to its complexity – higher complexity implies higher fitness

clip_image001[1] The amount of functionality of a system is proportional to complexity – more complex systems can perform more functions

clip_image001[2] Each system can only reach a specific maximum value of complexity

clip_image001[3] Close to the upper limit the system is fragile – it is unwise to operate close to this limit

clip_image001[4] High complexity = difficulty in management – highly complex systems are able to perform more functions but at a price: they are not easy to manage

clip_image001[5] When a system is very complex and becomes difficult to manage, it is necessary to restructure it, add new structure or to remove excess entropy

clip_image001[6] More components don’t necessarily imply more complexity – systems with few components can be more complex than systems with many components

clip_image001[7] When presented with two equivalent options, for example in terms of performance, risk or profit, select the one with the lower complexity – it will be easier to manage

clip_image001[8] Spasms or dramatic changes in dynamical systems are always accompanied by sudden changes in complexity

clip_image001[9] In nature, systems tend toward states of higher complexity, but only until they reach the corresponding maximum. This poses limits to growth and evolution

clip_image001[10] Systems with high complexity can behave in a multitude of ways (modes)

clip_image001[11] Systems with high complexity are more difficult to manage and control because of the need to compromise

clip_image001[12] A system with a given complexity will be more difficult to manage if it is made to operate in a more uncertain environment

clip_image001[13] “High complexity is incompatible with high precision” – this is known as L. Zadeh’s Principle of Incompatibility. In essence, you can’t make precise statements about a highly complex system

clip_image001[13] A fundamental characteristic of highly complex systems: they are robust yet fragile!