What Is a Complex System?
James Ladyman and Karoline Wiesner
New Haven, CT: Yale University Press, 2020, £25.00
In 1984, a group of renowned scientists from a variety of disciplines, many associated with the Los Alamos National Laboratory, convened a series of meetings in Santa Fe, USA. They were interested in systems that have many interacting parts and display novel or emergent behaviours when studied at various levels of description. Although inaugurating a new field of research was not the stated intention of those meetings, and the word ‘complexity’ or ‘complex system’ does not appear in the initial notes of those meetings, nearly four decades later they are viewed as the founding moments of the study of complex systems. Today, there are institutes explicitly devoted to complex systems research on every continent except Antarctica.
Nevertheless, the meaning of the term ‘complex system’ remains unclear. On its own, defining a branch of science using terms with some referential ambiguity is not unusual. For example, although biologists and philosophers of biology have yet to produce a wholly uncontroversial definition of ‘life’, biology can nevertheless operate with a working definition of itself as the study of life, and the scientific community only rarely disagrees about whether a given area of research counts as biology or not. In practice, it is only upon deep reflection on the nature of life that someone with a background in the subject can get seriously confused about what biology is. This surely owes something to the fact that life is a concept almost as old as human intellectual inquiry; this relatively long history informs common-sense judgements whether or not a scientist is studying living systems. By contrast, ‘complex system’ is a neologism that lacks a clear ordinary language definition; it is easy to get confused about what counts as a complex system.
In light of all this, the titular question of the book What Is A Complex System?, by philosopher of science James Ladyman and physicist Karoline Wiesner, should be of interest to anyone trying to understand this new scientific paradigm.
In what follows, I’ll give an opinionated summary of the book’s five chapters, before making some concluding comments. Since I will be critical at several points in my summary, I should say up front that I wholly recommend this book. Most people who find themselves working in the complex systems paradigm are formally trained in a more traditional discipline. For these researchers (myself included), it can be intimidating trying to get one’s head around the fundamental nature of complex systems while simultaneously participating in complex systems research. This compact, well-written, and well-researched book will be of great value to anyone who finds themselves in this position, and more generally should be read by anyone interested in complex systems research.
In Chapter 1, the book sets up the context of its inquiry. Nine truisms of complexity science (p. 9), and ten features associated with complex systems (p. 10) are identified. In this review, I will focus on the features of complex systems that the book identifies. They are: numerousity, disorder and diversity, feedback, non-equilibrium behaviour, spontaneous order and self-organization, non-linearity, robustness, nested structure and modularity, history and memory, and adaptive behaviour. It is clear at this point that these features do not define the term ‘complex system’, but rather provide a conceptual starting point from which one might attempt to define the term. The chapter concludes with a brief history of complexity science, identifying four research programmes as precursors to complexity science: cybernetics, systems theory, dynamical systems theory, and cellular automata.
Chapter 2 discusses seven putative examples of complex systems: matter and radiation, the Universe, Earth’s climate, groups of eusocial insects, markets and economies, the world wide web, and the human brain. In all of these examples, the system in question is said to display emergent patterns in the behaviour of the components of the system that allow for tractable description and accurate prediction of the behaviour of the system as a whole. For example, in the section on matter and radiation, it is noted that a box of gas can be described by a model with three degrees of freedom, even though the collection of gas particles really has 1023 degrees of freedom (p. 22). Each of these systems also operates according to dynamical laws in which the dynamics of the system at different spatial and temporal scales can in some cases be regarded as independent (for example, the structure of the universe at various spatial scales, or the carbon cycle of the Earth’s climate at different temporal scales without human interference), and which in other cases exhibit patterns of dependence (for example, micro- and macro-economics, the carbon cycle of the Earth’s climate with human interference).
While the examples in this section are both well presented and fascinating, it is at this point in the book that one might begin to have some doubts as to the feasibility of answering its central question. If matter and the Universe both count as complex systems in at least some respects, then it stands to reason that anything is either a complex system or a component thereof. I found myself wishing more had been said in this chapter to address this sort of concern. Having said that, the concern is, I believe, answerable: even if everything is part of a complex system (the universe), components of the universe might themselves be a complex system (a beehive) or not (putatively, a cutlery drawer), such that there is still work for a definition of complex systems to do even if the entire universe is itself a complex system.
Chapter 3 adumbrates the features of complex systems listed in Chapter 1. It does this by identifying four foundational features of complex systems: numerousity, disorder and diversity, feedback, and non-equilibrium behaviour. It is then stated that these foundational features give rise to the six secondary features, or ‘products’, of complex systems: spontaneous order and self-organization, non-linearity, robustness, nested structure and modularity, history and memory, and adaptive behaviour.
Throughout this chapter, various statements are made about the role of these features in a potential definition of a complex system. Numerousity, spontaneous order or self-organization, feedback, and robustness are each identified as necessary for a system to be complex, whereas disorder and diversity, non-linearity, and adaptive behaviour are all deemed, explicitly or implicitly, to be neither necessary nor sufficient for complexity. As far as I can tell, the chapter makes no precise claim about whether non-equilibrium behaviour, nested structure and modularity, and history and memory are either necessary or sufficient for complexity. All of this amounts to a somewhat jumbled understanding of the importance of each of these features to a putative definition of a complex system. As a reader from a philosophy of science background, I found myself wanting somewhat more precise book-keeping in this chapter with respect to the role that each of these features play in the promised definition of complex system. Nevertheless, this chapter does paint an evocative picture of what each of these features of complex systems are, with reference to many fascinating scientific examples that are very perspicuously described.
At several points in Chapter 3, the book claims that various features of complex systems must be understood in relation to the particular system under study or the particular perspective of a scientist. Regarding numerousity, it is stated that ‘in general, how much numerosity is needed [for complexity] depends on the system’ (p. 67). Regarding order and disorder, it is argued that ‘ideas of order and disorder are always applied to specific features, and care must be taken to define clearly what the relevant notions of order and disorder are’ (p. 69). It is also stated that ‘robustness is only ever within a particular regime’ (p. 79), and that ‘persistence of memory is only ever over some relevant time scale’ (pp. 81–82). Despite all of this context-sensitivity, a completely subjective definition of a complex system is described as ‘tantamount to giving up’ on the book’s goal of defining a complex system (p. 64). Here I found myself wanting more of an argument and asking the question: why not accept an entirely pragmatic or subjective definition of complexity? This question arises again in my comments on Chapter 5.
Chapter 3 also contains an interlude on the concept of ‘emergence’ in complex systems. This interlude notes (correctly, I would argue) that many complex systems practitioners are guilty of loose talk with respect to emergence and reductionism. The authors endorse a version of emergence wherein complex systems exhibit ‘emergent’ structure, dynamics, order, and behaviour at higher levels of description that cannot be predicted by individually examining the smaller, constituent elements of the system, because the emergent properties are due, at least in part, to the interactions between the constituent properties of the system. This thesis is perhaps summed up best by a quote from Chapter 4: ‘the whole is never more than the sum of its parts when interactions are taken into account’ (p. 99). This understanding of emergence seems at first glance to be in tension with the book’s claim, in Chapter 5, that ‘the emergence from the physical systems in the universe to the immensely intricate and structured system of life on Earth, including the human brain and the complexity of human culture and social life, is ontological emergence’, although I believe that this tension can be resolved by an understanding of ontology in keeping with Dennett’s classic paper, ‘Real Patterns’.1Dennett, D. : ‘Real Patterns’, Journal of Philosophy, 88, pp. 27–51. That is, we can understand the emergent structure, dynamics, order, and behaviour of complex systems as real patterns that exist in more fine-grained descriptions of those systems. This holds even though said patterns cannot necessarily be predicted solely by examining the constituent elements of the system.
Chapter 4 was my favourite part of the book. It provides quantitative measures of the various features of complex systems described more qualitatively in Chapter 3 (although there is no quantitative discussion of adaptive behaviour). In my opinion, the chapter does students of complexity science a great service by putting all of this material in one place, and giving aspiring complex systems researchers a clear sense of the baseline mathematics needed for said research. Some background in probability theory and calculus is very helpful in order to understand this chapter, although the book contains appendices to help with this, though one subsection on ‘critical slowing down and tipping points’ seems to be written for someone with more training in thermal physics than the typical reader of this book.
In several cases, what is presented in this chapter is not so much a measure of the degree to which a feature of a complex system is present, but rather a description of how that feature is mathematically operationalized, or a diagnostic procedure for determining whether that feature is present or absent in a system. For example, in the case of feedback, what we get is a description of how coefficients in a system of coupled equations act as parameters for setting the amount of feedback in a system (p. 95). For non-linearity, we are told what it means for a system to obey a power law distribution, and given a mathematical criterion for determining whether or not this is the case (p. 100). The mathematical treatments of non-equilibrium behaviour and robustness are similar in this respect, and stand in contrast to other features of complex systems such as modularity, for which a measure of the degree to which a system possesses that feature is indeed given (p. 108). As a reader, I would have appreciated more of a distinction between the various ways that features of complex systems are rendered mathematically tractable.
In Chapter 5, we get an answer to the book’s titular question. The chapter begins by dividing possible answers into categories. Nihilist answers hold ‘that “complex system” is a vague and ambiguous term that covers a variety of things and that complexity science is just a collection of techniques and methods that does not have a domain of its own’, such that ‘it seems advisable to stop using the terms “complexity” and “complex system” as if they were well-defined scientific concepts’ (pp. 117–18). The authors reject nihilism on the grounds that the same kinds of invariance and universal behaviour are observed in systems studied by various different sciences, and so the study of complex systems cannot be fully absorbed into other, more well-defined disciplines. On a pragmatist approach, ‘the term “complex system” refers to a collection of systems in various disciplines that are all amenable to related mathematical and computational techniques, such as network theory or agent-based modelling, but which otherwise have nothing fundamental in common’ (p. 119). Nothing is said to reject the pragmatist view, although this is ultimately not the view that the book endorses.
Instead, the book defends a version of realism about complex systems, that is, the view that ‘complex systems form what philosophers call a natural kind’ (p. 120). That is, the authors hold that nature is divided, in an observer-independent way, into complex and non-complex systems. Complex systems, the book argues, are systems that have emergent features, as defined in Chapter 3. This definition of emergence is very broad, and indeed the authors note that ‘there are different kinds of complex systems and […] different features of complexity are displayed by them’ (p. 130). The book then demonstrates how this understanding of complex systems is in keeping with the analysis and examples given at the previous chapters. Here I found myself wanting a more concrete statement of the distinction between the book’s view and the pragmatist account, and a defence of the former over the latter. The book ends fairly abruptly at this point, without a sustained defence of the authors’ positive answer to the book’s motivating question. This left me with the impression that the book should be read more as an opinionated introduction to complex systems than a sustained defence of a particular definition thereof.
I conclude by suggesting two alternative takes on the nature of complex systems. First, in possible contrast with Ladyman and Wiesner’s realism, I would argue that complexity in science is closer to what Neurath called a Ballung, or a ‘cluster concept’.2Neurath, O. : ‘Encyclopedia as Model’, in R. S. Cohen and M. Neurath (eds), Philosophical Papers 1913-1946, Dordrecht: Reidel, pp. 145–58. Cluster concepts are inherently vague concepts that may have some uncontroversial exemplars (for instance, an ant colony or beehive might be considered an archetypical complex system), while still not admitting of necessary and sufficient conditions for determining when the concept does or does not apply in a given case. Neurath held that the unavoidability of cluster concepts stood in the way of the logical axiomatization of all science. It strikes me as highly plausible that complexity is such a concept. This view might fall somewhere between nihilism and pragmatism in Ladyman and Wiesner’s taxonomy. However, one could also read the proposal that complexity is a cluster concept as more in keeping with Ladyman and Wiesner’s realism about complexity, especially if one takes on board the idea of natural kinds as ‘homeostatic property cluster kinds’, in keeping with arguments by Boyd.3Boyd, R. : ‘Realism, Anti-foundationalism, and the Enthusiasm for Natural Kinds’, Philosophical Studies, 61, pp. 127–48. That is, one could hold that even though there may not be an uncontroversial set of necessary and sufficient conditions for a system to be complex, it is nevertheless the case that a system’s being complex is due to the causal structure of that system, and not due to social or scientific convention.
Second, I want to raise the possibility that there is an ineliminable aesthetic component to the demarcation of complex systems, which is not discussed in Ladyman and Wiesner’s book. One could argue that, in practice, a complex system is anything that the community of complexity scientists finds interesting and therefore deems worthy of investigation under the auspices of complex systems research. Institutes and departments dedicated to complexity science regularly make decisions about who to hire, who to teach, and who to invite for talks and workshops. These decisions, one could argue, are what determine the fluid and vague boundaries of what counts as a complex system. Thus, it is tempting to hold that ultimately the question of what counts as a complex system can only be fully answered by getting a better handle on the aesthetic and intellectual factors that influence complexity scientists’ judgements about what counts as an interesting object of scientific inquiry. 4I am grateful here to my colleague Anthony Eagan, who has frequently impressed upon me the importance of the aesthetics of interestingness in understanding the social structure of complex systems research. I believe this to be a potentially fruitful topic for future research in the aesthetics, sociology, and philosophy of science.
I am grateful to James Ladyman and Karoline Wiesner for their comments on an earlier draft of this review.
Santa Fe Institute
Boyd, R. : ‘Realism, Anti-foundationalism, and the Enthusiasm for Natural Kinds’, Philosophical Studies, 61, pp. 127–48.
Dennett, D. : ‘Real Patterns’, Journal of Philosophy, 88, pp. 27–51.
Neurath, O. : ‘Encyclopedia as Model’, in R. S. Cohen and M. Neurath (eds), Philosophical Papers 1913-1946, Dordrecht: Reidel, pp. 145–58.