"A certain theory of representation implies a certain theory of meaning - and meaning is what we live by." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)
"A formal system consists of a number of tokens or symbols,
like pieces in a game. These symbols can be combined into patterns by means of
a set of rules which defines what is or is not permissible (e.g. the rules of
chess). These rules are strictly formal, i.e. they conform to a precise logic. The
configuration of the symbols at any specific moment constitutes a ‘state’ of
the system. A specific state will activate the applicable rules which then
transform the system from one state to another. If the set of rules governing
the behaviour of the system are exact and complete, one could test whether
various possible states of the system are or are not permissible."
"A neural network consists of large numbers of simple neurons that are richly interconnected. The weights associated with the connections between neurons determine the characteristics of the network. During a training period, the network adjusts the values of the interconnecting weights. The value of any specific weight has no significance; it is the patterns of weight values in the whole system that bear information. Since these patterns are complex, and are generated by the network itself (by means of a general learning strategy applicable to the whole network), there is no abstract procedure available to describe the process used by the network to solve the problem. There are only complex patterns of relationships."
"Complex systems operate under conditions far from equilibrium. Complex systems need a constant flow of energy to change, evolve and survive as complex entities. Equilibrium, symmetry and complete stability mean death. Just as the flow, of energy is necessary to fight entropy and maintain the complex structure of the system, society can only survive as a process. It is defined not by its origins or its goals, but by what it is doing." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)
"Each element in the system is ignorant of the behavior of the system as a whole, it responds only to information that is available to it locally. This point is vitally important. If each element ‘knew’ what was happening to the system as a whole, all of the complexity would have to be present in that element." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)
"From a more general philosophical perspective we can say that we wish to model complex systems because we want to understand them better. The main requirement for our models accordingly shifts from having to be correct to being rich in information. This does not mean that the relationship between the model and the system itself becomes less important, but the shift from control and prediction to understanding does have an effect on our approach to complexity: the evaluation of our models in terms of performance can be deferred. Once we have a better understanding of the dynamics of complexity, we can start looking for the similarities and differences between different complex systems and thereby develop a clearer understanding of the strengths and limitations of different models."
"In order to constitute a complex system, the elements have to interact, and this interaction must be dynamic." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)
"In our analysis of complex systems (like the brain and language) we must avoid the trap of trying to find master keys. Because of the mechanisms by which complex systems structure themselves, single principles provide inadequate descriptions. We should rather be sensitive to complex and self-organizing interactions and appreciate the play of patterns that perpetually transforms the system itself as well as the environment in which it operates." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)
"It bears repetition that an argument against representation is not anti-scientific at all. It is merely an argument against a particular scientific strategy that assumes complexity can be reduced to specific features and then represented in a machine. Instead it is an argument for the appreciation of the nature of complexity, something that can perhaps be 'repeated' in a machine, should the machine itself be complex enough to cope with the distributed character of complexity." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)
"Modelling techniques on powerful computers allow us to simulate the behaviour of complex systems without having to understand them. We can do with technology what we cannot do with science. […] The rise of powerful technology is not an unconditional blessing. We have to deal with what we do not understand, and that demands new ways of thinking."
"Neural nets have no central control in the classical sense. Processing is distributed over the network and the roles of the various components (or groups of components) change dynamically. This does not preclude any part of the network from developing a regulating function, but that will be determined by the evolutionary needs of the system." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)
"Neural networks conserve the complexity of the systems they model because they have complex structures themselves. Neural networks encode information about their environment in a distributed form. […] Neural networks have the capacity to self-organise their internal structure." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)
"The concept ‘complexity’ is not univocal either. Firstly, it
is useful to distinguish between the notions ‘complex’ and ‘complicated’. If a
system- despite the fact that it may consist of a huge number of components - can
be given a complete description in terms of its individual constituents, such a
system is merely complicated. […] In a complex system, on the other hand, the
interaction among constituents of the system, and the interaction between the
system and its environment, are of such a nature that the system as a whole
cannot be fully understood simply by analysing its components. Moreover, these
relationships are not fixed, but shift and change, often as a result of
self-organisation. This can result in novel features, usually referred to in
terms of emergent properties."
"The ability of neural networks to operate successfully on
inputs that did not form part of the training set is one of their most
important characteristics. Networks are capable of finding common elements in
all the training examples belonging to the same class, and will then respond
appropriately when these elements are encountered again. Optimising this
capability is an important consideration when designing a network."
"The internal structure of a connectionist network develops through a process of self-organisation, whereas rule-based systems have to search through pre-programmed options that define the structure largely in an a priori fashion. In this sense, learning is an implicit characteristic of neural networks. In rule-based systems, learning can only take place through explicitly formulated procedures." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)
"There is no over-arching theory of complexity that allows us to ignore the contingent aspects of complex systems. If something really is complex, it cannot by adequately described by means of a simple theory. Engaging with complexity entails engaging with specific complex systems. Despite this we can, at a very basic level, make general remarks concerning the conditions for complex behaviour and the dynamics of complex systems. Furthermore, I suggest that complex systems can be modelled." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)
"To compound matters, complexity is not located at a
specific, identifiable site in a system. Because complexity results from the
interaction between the components of a system, complexity is manifested at the
level of the system itself. There is
neither something at a level below (a source), nor at a level above (a
meta-description), capable of capturing the essence of complexity."
"Whereas formal systems apply inference rules to logical variables, neural networks apply evolutive principles to numerical variables. Instead of calculating a solution, the network settles into a condition that satisfies the constraints imposed on it." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)
"The view from complexity claims that we cannot know complex things completely [...] modest positions are inescapable. [...] We can increase the knowledge we have of a certain [complex] system, but this knowledge is limited. [...] The fact that our knowledge is limited is not a disaster, it is a condition for knowledge. Limits enable knowledge." (Paul Cilliers, 2005)
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