When discussing the new science of complexity, there's often a tendency to address the issues that one more readily thinks of as "science," with equations; pictures of chaotic attractors and fractals; and discussions of the Feigenbaum number. Applications of complexity theory to something other than charting shorelines or tracking blood flow are often only alluded to. Paul Cilliers' Complexity & Postmodernism goes beyond the numbers and pictures to discuss how complexity provides paradigms for discussing learning, philosophy, and even ethics. In a relatively short, readable work Cilliers manages to fit not only an introduction to complexity theory in general but also an explanation of neural networks, approaches to linguistic representation theory, and branches of philosophy — and it all fits together very nicely.
Cilliers first makes clear that his discussion centers around complexity itself, which is in his mind quite separate from the older science of chaos. "My claim is rather that chaos theory, and especially the notions of determinisitic chaos and universality, does not really help us to understand the dynamics of complex systems," he says, and thus embarks on a road of holism, of coherence, and of sums-greater-than-parts.
The fundamental model of a complex system presented here is, appropriately enough, is the neural network; Cilliers provides an excellent explanation which even the non-computer-literate can easily comprehend. From this groundwork he immediately addresses differences in models of language structure and understanding. Most of the thoughts here are based upon the work of Saussure, later embellished by Derrida. Here, as in other areas of the book, Cilliers excellently illustrates how complexity theory re-frames, supports, and furthers independent lines of thought across several disciplines.
Saussure claims that words in themselves carry no meanings, but that meaning is communicated by how words (as signs) differ from others in the language (or system) (39). Derrida furthers this by saying that meaning is only held in this différance between signs, and that meaning is only found in a work through traces. As soon as a word is used in the system in a particular context, that use slightly modifies any meaning found in the system, both for the word being used and for other signs in the system. "As soon as a certain meaning is generated for a sign, it reverberates through the system" (44).
These thoughts by Saussure and Derrida are very much part of a specific area of thought pertaining to the philosophy of meaning and representation in language. After Cilliers is finished with his explanation, it seems quite obvious how complex systems apply: words in a language (as signs in a system) are no more than nodes in a neural network. There is a very real analogy to how connectionist systems (i.e. neural networks) encode meaning not in any particular node, but by a holistic arrangement of all the nodes. Signs then do not take on any particular meaning (82), but rather represent meanings through their use in the system, at the same time changing whatever meaning is being generated by the very usage of these signs.
The signs in a system therefore encode no actual meaning — there is no true global representation. Similarly, history is important but elusive in complex systems. "No complex system, whether biological or social, can be understood without considering its history. Two similar systems placed in identical conditions may respond in vastly different ways if they have different histories. To be more precise, the history of a system is not merely important in the understanding of the system, it co-determines the structure of the system" (107-108). However, "Global behaviour of the system is the result of 'patterns of traces'... The same arguments hold for memory in the context of the brain. Memories are not stored in the brain as discrete units that can be recalled as if from a filing cabinet" (108). This entire discussion brings up the fascinating aspect that "there are no 'memories'" (108). While there may be actual events that happened in the past, they can never be accurately reconstructed from the contents of the network, because what are left are only traces. The formation of the system interacts with the actual history reflexively, each altering the other.
Throughout these discussions, Cilliers advances deep into philosophical territory, yet explains all the concepts as if one were completely unfamiliar with the subject. Derrida's deconstruction, for example, is explained as the pointing out of contradictions that occur when one uses traditional ideas of meaning and representation and in doing so claims a "privileged position" for a particular view or expression (81).
If complexity invades thought, memories, history, and meaning, it is not a large stretch to assume that it might affect ideas of morality as well. Cilliers, following logically from his analysis of neural networks and philosophy of representation, makes some startling conclusions about ethics, following ideas of Cornell:
Cornell's suggestion (following Derrida, and reformulated in my terminology) is to take present ethical (and legal) principles seriously — to resist change — but to be keenly aware of when they should not be applied, or have to be discarded. We therefore do follow principles as if they were universal rules (Cornell and Derrida use the term "quasi-transcendental"), but we have to remotivate the legitimacy of the rule each time we use it. To behave ethically means not to follow rules blindly — to merely calculate — but to follow them responsibly, which may imply that the rules must be broken (139).
Of course, complexity and postmodernism having similarities in the areas stated above, they have similar problems of explanation: by denying overall algorithms (or, as Lyotard says, "meta-narratives), an effort to encapsulate such a system would therefore in itself seem to be invalid. Cilliers is aware of this, and does not attempt to meet every criticism that might be offered to his approach; instead, he tries to share "the spirit in which this book is offered: one of openness, provisionality and adventure" (142).
There are many introductory works on complexity theory, but few that strike a balance between algorithmic explanations and postmodern philosophy as does Complexity and Postmodernism. Cilliers does a fine job of bringing together two areas of thought, mathematics and philosophy, into one coherent holistic (to use a term important to complexity theory itself) pictures. It would be a loss for someone from either field to miss this well-discussed work.
Note: This work was read over a period of many months as part of research on my MA dissertation. General notes on the book are included below.
- Cilliers finds it necessary to separate chaos theory from complexity theory, and in fact almost ignore chaos in the discussion of the complex: not ignoring it altogether, but "My claim is rather that chaos theory, and especially the notions of determinisitic chaos and universality, does not really help us to understand the dynamics of complex systems" (ix).
- Cilliers mentions the position of the viewer in forming a description of the system. A complex system doesn't really have borders (in contrast to what Waltz tries to do in his hierarchical analysis) but instead must be "framed" for analysis (4).
- "From a more general philosophical perspective we can say that we wish to model complex systems because we want to understand them better... Once we have a better understanding of the dynamics of complexity, we can start looking for the similarities and differences between complex systems and thereby develop a clearer understanding of the strengths and limitations of different models" (13).
- "Put in the language of systems theory, Saussure still understands language as a closed system, whereas Derrida wants to argue for language as an open system. In denying the metaphysics of presence, the distinction between 'inside' and 'outside' is also problematised. There is no place outside of language from where meaning can be generated. Where there is meaning, there is already language. We cannot separate language from the world it describes" (43).
- "Models of complex systems will have to be as complex as the systems themselves" (58).
- "A theory of representation is essentially a theory of meaning. It is an attempt to explain how the words of our language or the structures in our brain become meaningful, by trying to define relationships between these words or structures and the world." "Unfortunately, the ease with which symbols can be made to represent something vanishes when we deal with complex problems, problems for which clear definitions and well defined borders are less easily found" (58).
- "...the states of a complex system are determined not only by external circumstances, but also by the history of the system" (66).
- In explaining the reasoning behind Derrida's deconstruction, Cilliers says that, "The danger [in explanations] lies in falling under the spell of a specific picture and claiming a privileged position for it. Since it would not only deny the limitations of the specific angle, but also prevent further explorations, this spell must be broken by relentlessly showing the contradictions that result from fixing the boundaries from one perspective. Pointing out the contradictions that follow from such a closure is an activity that Derrida calls 'deconstruction'" (81).
- "In this complex pattern of interaction [in a neural network] it is impossible to say that a certain sign (or node) represents anything specific" (82).
- "Self-organisation is an emergent property of a system as a whole (or of large enough sub-systems). The system's individual components only operate on local information and general principles. The macroscopic behaviour emerges from microscopic interactions that by themselves have very meagre information content (only traces)" (92).
- "Self-organising systems increase in complexity. Since they have to 'learn' from experience, they have to 'remember' previously encountered situations and compare them with new ones" (92).
- "Claiming that self-organisation is an important property of complex systems is to argue against foundationalism. The dynamic nature of self-organisation... cannot be explained by resorting to a single origin or to an immutable principle. In point of fact, self-organisation provides the mechanism whereby complex structure can evolve without first having to postulate first beginnings or transcendental interventions. It is exactly in this sense that postmodern theory contributes to our understanding of complex, self-organising systems" (106).
- "No complex system, whether biological or social, can be understood without considering its history. Two similar systems placed in identical conditions may respond in vastly different ways if they have different histories. To be more precise, the history of a system is not merely important in the understanding of the system, it co-determines the structure of the system" (107-108).
- "Global behaviour of the system is the result of 'patterns of traces'... The same arguments hold for memory in the context of the brain. Memories are not stored in the brain as discrete units that can be recalled as if from a filing cabinet" (108). This entire discussion brings up the fascinating aspect that "there are no 'memories'" (108). While there may be actual events that happened in the past, they can never be accurately reconstructed from the contents of the network, because what are left are only traces. The formation of the system interacts with the actual history reflexively, each altering the other.
- Lyotard describes consensus as being "a horizon that is never reached" (117), and this might shed some light on free-market economics. While Marx analyzed the economical system as if it were a perfect capitalist system, the fact that such a pure system cannot ever be reached may change the perspective of the benefits of such a system.
- When referring to a book by Rouse, Cilliers switches from his objective explanation, to a very clear subjective opinion: "For me, reading this book was about as pleasant as it would be to eat it" (133).
Copyright © 2000 Garret Wilson