Plain text is unavailable for this page.

Complexity and postmodernism Complexity and Postmodernism explores the notion of complexity in the light of contemporary perspectives from philosophy and science. Paul Cilliers contributes to our general understanding of complex systems, and explores the implications of complexity theory for our understanding of biological and social systems. Postmodern theory is reinterpreted in order to argue that a postmodern perspective does not necessarily imply relativism, but that it could also be viewed as a manifestation of an inherent sensitivity to complexity. As Cilliers explains, the characterisation of complexity revolves around analyses of the process of self-organisation and a rejection of traditional notions of representation. The model of language developed by Saussure—and expanded by Derrida—is used to develop the notion of distributed representation, which in turn is linked with distributed modelling techniques. Connectionism (implemented in neural networks) serves as an example of these techniques. Cilliers points out that this approach to complexity leads to models of complex systems that avoid the oversimplification that results from rule- based models. Complexity and Postmodernism integrates insights from complexity and computational theory with the philosophical position of thinkers like Derrida and Lyotard. Cilliers takes a critical stance towards the use of the analytical method as a tool to cope with complexity, and he rejects Searle’s superficial contribution to the debate. Complexity and Postmodernism is an exciting and an original book that should be read by anyone interested in gaining a fresh understanding of complexity, postmodernism and connectionism. Paul Cilliers lectures in philosophy at the University of Stellenbosch, South Africa. He worked as a research engineer for over a decade, specialising in computer modelling.

Plain text is unavailable for this page.

Complexity and postmodernism Understanding complex systems Paul Cilliers London and New York

First published 1998 by Routledge 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 Routledge is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2002. © 1998 Paul Cilliers All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalogue record for this book has been requested ISBN 0-203-01225-9 Master e-book ISBN ISBN 0-203-17457-7 (Adobe eReader Format) ISBN 0-415-15286-0 (hbk) ISBN 0-415-15287-9 (pbk)

For Ilana and Cornel

Plain text is unavailable for this page.

Contents Preface viii 1 Approaching complexity 1 2 Introducing connectionism 25 3 Post-structuralism, connectionism and complexity 37 4 John Searle befuddles 48 5 Problems with representation 58 6 Self-organisation in complex systems 89 7 Complexity and postmodernism 112 8 Afterword: Understanding complexity 141 Notes 143 Bibliography 149 Index 155

Preface ‘Complexity’ and ‘postmodernism’ are both controversial notions. Contemporary society is readily described as being postmodern, but reactions to this description diverge sharply. For some (like Zygmunt Bauman) postmodernism creates the possibility to escape from the strictures of modernism and to re-enchant the world. For others (like Ernest Gellner) it exemplifies relativism—a theoretical framework in which anything goes—and leaves them with a feeling of vertigo. Postmodernism can also be seen as being parasitic on modernism, or as modernism’s underbelly. In such a case it could be argued that we should drop the concept altogether if we want to move beyond the oversimplified ideals of the Enlightenment. The different responses to postmodernism are based on different understandings of the word’s meaning. Even if it were possible to clarify this debate, it is not my intention to do so in this book nor shall I attempt to provide an apology for postmodernism. My main concern is with the notions of complexity and complex systems. As far as postmodernism is concerned, the argument is simply that a number of theoretical approaches, loosely (or even incorrectly) bundled together under the term ‘postmodern’ (e.g. those of Derrida and Lyotard), have an implicit sensitivity for the complexity of the phenomena they deal with. Instead of trying to analyse complex phenomena in terms of single or essential principles, these approaches acknowledge that it is not possible to tell a single and exclusive story about something that is really complex. The acknowledgement of complexity, however, certainly does not lead to the conclusion that anything goes. 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. Things like jumbo jets or computers are 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

Preface ix 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 brain, natural language and social systems are complex. The problem of understanding this kind of complexity is a central issue throughout the book. Secondly, it is necessary to say something about the relationship between complexity and chaos theory. The hype created by chaos theory has abated somewhat, but the perception that it has an important role to play in the study of complex systems is still widespread. Although I would not deny that chaos theory could contribute to the study of complexity, I do feel that its contribution would be extremely limited. When analysing complex systems, a sensitivity to initial conditions, for example, is not such an important issue. As a matter of fact, it is exactly the robust nature of complex systems, i.e. their capability to perform in the same way under different conditions, that ensures their survival. Although the metaphor of the butterfly’s flapping wings causing a tornado on the other side of the globe is a good one for describing a sensitivity to initial conditions, it has caused so much confusion that I feel it should not be used at all. Chaotic behaviour—in the technical sense of ‘deterministic chaos’—results from the non-linear interaction of a relatively small number of equations. In complex systems, however, there are always a huge number of interacting components. Despite the claims made about aspects of the functioning of the olfactory system, or of the heart in fibrillation, I am unsure whether any behaviour found in nature could be described as truly chaotic in the technical sense. Where sharp transitions between different states of a system are required, I find the notion of self-organised criticality (see Chapter 6) more appropriate than metaphors drawn from chaos. This might sound too dismissive, and I certainly do not want to claim that aspects of chaos theory (or fractal mathematics) cannot be used effectively in the process of modelling nature. My claim is rather that chaos theory, and especially the notions of deterministic chaos and universality, does not really help us to understand the dynamics of complex systems. That showpiece of fractal mathematics, the Mandelbrot set— sometimes referred to as the most complex mathematical object we know—is in the final analysis complicated, not complex. Within the framework of the present study, chaos theory is still part of the modern paradigm, and will not receive detailed attention. The objective of the book is to illuminate the notion of complexity from a postmodern, or perhaps more accurately, post-structural perspective. The most obvious conclusion drawn from this perspective is that there is no overarching theory of complexity that allows us to ignore the contingent aspects of complex systems. If something is really complex, it cannot be 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. The models could be computationally implemented, and may lead to machines that can perform more complex tasks. The models themselves,

x Preface however, will have to be at least as complex as the systems they model, and may therefore not result in any simplification of our understanding of the system itself. As an example of such models, I make extensive use of neural networks—an approach also known as connectionism. As a matter of fact, the significance of postmodern theory for the study of complexity is underscored by arguing that there are structural similarities between the operation of neural networks and Derrida’s descriptions of the working of language. Apart from introductory chapters on connectionism (Chapter 2) and post- structuralism (Chapter 3), and a dismissal of Searle’s contributions to the debate (Chapter 4), the central issues discussed are representation (Chapter 5) and self-organisation (Chapter 6). A discussion, or perhaps a deconstruction, of the notion of representation exemplifies the contribution that a primarily philosophical analysis can make to modelling techniques. Conversely, the discussion of self-organisation—a notion usually (but certainly not exclusively) encountered in a scientific context—helps us to make the (philosophical) point that the behaviour of a system without a predetermined or fixed structure is not necessarily random or chaotic, in other words, that anything does not go. The book does not engage with moral theory in a systematic way, but it is impossible, of course, to operate in a value-free space. Ethical issues therefore do surface now and then, especially in Chapter 7. The characterisation of complexity and complex systems developed in the present book certainly has implications for social and moral theory that demand to be developed further. This, I hope, will be a more central aspect of future projects. I would like to thank the following people for the contributions they have made towards the development of the ideas presented here: Johan Degenaar, Mary Hesse, Jannie Hofmeyr, and the members of the two interdisciplinary discussion groups at the University of Stellenbosch, one based in the arts faculty, the other in the sciences. The help of Esmarié Smit in the completion of the manuscript was invaluable. Previous versions of some of the material used in Chapters 2, 3 and 7 have appeared in the South African Journal of Philosophy. Permission to rework that material is gratefully acknowledged.

1 Approaching complexity The worlds of science and philosophy have never existed in isolation, but one could perhaps argue that the relationship between them is entering a new phase. The ubiquitous pressure to do applied research certainly has something to do with it, but there is also another, overtly less political, reason: the immense increase in the importance of technology. At first glance one would suspect that this may decrease the importance of the philosophical perspective, that the importance of philosophy is somehow linked to the importance of theory only, but my suggestion is that the contrary is true. Not that theory is unimportant, or that theoretical aspects of science are not philosophical. Few scientific endeavours have been as ‘philosophical’ as contemporary theoretical physics. The argument is rather that the technologisation of science (as well as the rest of our life-world) is changing the relationship between science and philosophy in a radical way. Since we are in the midst of this process of change, a clear description of what is happening is not easy, but the heart of the matter is that our technologies have become more powerful than our theories. We are capable of doing things that we do not understand. We can perform gene-splicing without fully understanding how genes interact. We can make pharmaceutics without being able to explain effects and predict side-effects. We can create new sub-atomic particles without knowing precisely whether they actually exist outside of the laboratory. We can store, and retrieve, endless bits of information without knowing what they mean. Central to all these developments are the phenomenal capacities of the electronic computer. It forms part of most of our tools (like washing machines and motor cars) it infiltrates our social world (think of financial matters and entertainment) and it is rapidly becoming the most important medium for communication. Although we know that nothing ‘strange’ happens inside a computer, nobody can grasp all aspects of what happens when a computer is performing a sophisticated task—at least not down to the level of switching between zeros and ones. It is simply too complex. The power of technology has opened new possibilities for science. One of the most important scientific tools has always been the analytical method. If something is too complex to be grasped as a whole, it is divided into

2 Approaching complexity manageable units which can be analysed separately and then put together again. However, the study of complex dynamic systems has uncovered a fundamental flaw in the analytical method. A complex system is not constituted merely by the sum of its components, but also by the intricate relationships between these components. In ‘cutting up’ a system, the analytical method destroys what it seeks to understand. Fortunately this does not mean that the investigation of complexity is hopeless. 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 increased interest in the theory of complexity over the past decade is therefore not surprising. 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. It is in this sense that I argue that philosophy has an important role to play, not by providing a meta-description of that which happens in science and technology, but by being an integral part of scientific and technological practice. Specific philosophical perspectives can influence the way we approach complex systems, and I want to argue that some of these perspectives—often broadly labelled as postmodern—are of special value to the study of complexity. In order to apply some aspects of postmodern theory to the study of complex systems, a general understanding of what a complex system is should first be developed. A SKETCH OF COMPLEX SYSTEMS At this stage it could be expected of one to provide at least a working definition of what ‘complexity’ might mean. Unfortunately the concept remains elusive at both the qualitative and quantitative levels. One useful description, by Luhmann (1985:25), states that complexity entails that, in a system, there are more possibilities than can be actualised. This can hardly serve as definition, but perhaps one should not be surprised if complexity cannot be given a simple definition. Instead, an analysis of characteristics of complex systems can be attempted in order to develop a general description that is not constrained by a specific, a priori definition. That is what will be attempted in this section. I will turn to the problem of quantifying complexity in the next section. Before turning to some characteristics of complex systems, we have to look at two important distinctions. The distinction between ‘simple’ and ‘complex’ is not as sharp as we may intuitively think (Nicolis and Prigogine 1989:5). Many systems appear simple, but reveal remarkable complexity when examined closely (e.g. a leaf). Others appear complex, but can be described simply, e.g. some machines, such as the internal combustion engine. 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

Approaching complexity 3 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. The distinction between complex and simple often becomes a function of our ‘distance’ from the system (Serra and Zanarini 1990:4, 5), i.e. of the kind of description of the system we are using. A little aquarium can be quite simple as a decoration (seen from afar), but as a system it can be quite complex (seen from close by). This does not imply that complexity is merely a linguistic phenomenon, or simply a function of our description of the system. Complex systems do have characteristics that are not merely determined by the point of view of the observer. It does, however, imply that care has to be taken when talking about complexity. The simple and the complex often mask each other. A second important distinction, and one that is equally difficult to maintain consistently, is the one between complex and complicated. Some systems have a very large number of components and perform sophisticated tasks, but in a way that can be analysed (in the full sense of the word) accurately. Such a system is complicated. Other systems are constituted by such intricate sets of non-linear relationships and feedback loops that only certain aspects of them can be analysed at a time. Moreover, these analyses would always cause distortions. Systems of this kind are complex. I have heard it said (by someone from France, of course) that a jumbo jet is complicated, but that a mayonnaise is complex. Other examples of complicated systems, systems that can, in principle, be given an exact description, would be a CD-player, a snowflake, the Mandelbrot set. Complex systems are usually associated with living things: a bacterium, the brain, social systems, language. This distinction remains an analytical one that is undermined specifically by powerful new technologies (e.g. is a fast computer with a very large memory complex or complicated?), but it is useful in developing a description of the characteristics of complex systems. I offer the following list:1 (i) Complex systems consist of a large number of elements. When the number is relatively small, the behaviour of the elements can often be given a formal description in conventional terms. However, when the number becomes sufficiently large, conventional means (e.g. a system of differential equations) not only become impractical, they also cease to assist in any understanding of the system. (ii) A large number of elements are necessary, but not sufficient. The grains of sand on a beach do not interest us as a complex system. In order to constitute a complex system, the elements have to interact, and this interaction must be dynamic. A complex system changes with time. The interactions do not have to be physical they can also be thought of as the transference of information. (iii) The interaction is fairly rich, i.e. any element in the system influences, and is influenced by, quite a few other ones. The behaviour of the

4 Approaching complexity system, however, is not determined by the exact amount of interactions associated with specific elements. If there are enough elements in the system (of which some are redundant), a number of sparsely connected elements can perform the same function as that of one richly connected element. (iv) The interactions themselves have a number of important characteristics. Firstly, the interactions are non-linear. A large system of linear elements can usually be collapsed into an equivalent system that is very much smaller. Non-linearity also guarantees that small causes can have large results, and vice versa. It is a precondition for complexity. (v) The interactions usually have a fairly short range, i.e. information is received primarily from immediate neighbours. Long-range interaction is not impossible, but practical constraints usually force this consideration. This does not preclude wide-ranging influence—since the interaction is rich, the route from one element to any other can usually be covered in a few steps. As a result, the influence gets modulated along the way. It can be enhanced, suppressed or altered in a number of ways. (vi) There are loops in the interactions. The effect of any activity can feed back onto itself, sometimes directly, sometimes after a number of intervening stages. This feedback can be positive (enhancing, stimulating) or negative (detracting, inhibiting). Both kinds are necessary. The technical term for this aspect of a complex system is recurrency. (vii) Complex systems are usually open systems, i.e. they interact with their environment. As a matter of fact, it is often difficult to define the border of a complex system. Instead of being a characteristic of the system itself, the scope of the system is usually determined by the purpose of the description of the system, and is thus often influenced by the position of the observer. This process is called framing. Closed systems are usually merely complicated. (viii) Complex systems operate under conditions far from equilibrium. There has to be a constant flow of energy to maintain the organisation of the system and to ensure its survival. Equilibrium is another word for death. (ix) Complex systems have a history. Not only do they evolve through time, but their past is co-responsible for their present behaviour. Any analysis of a complex system that ignores the dimension of time is incomplete, or at most a synchronic snapshot of a diachronic process. (x) Each element in the system is ignorant of the behaviour 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