Murky water and a business card
Han van der Maas has written an open textbook on complexity science for psychologists: rich in models and simulations, with applications for the consulting room that are still only lightly developed.
Han L. J. van der Maas (2024). Complex Systems Research in Psychology. Santa Fe: SFI Press. 310 pages. Open access: santafeinstitute.github.io/ComplexPsych
Take a business card, stand it upright on the table and press down on it from above. If you then push sideways, the card suddenly flips to the left or to the right, and it stays there, even when you let go. Without that pressure from above, the card simply springs back to the middle. With this kitchen-table experiment, Han van der Maas explains one of the central ideas of his book: some systems change gradually, others jump, and whether a system jumps depends on a second variable that is not directly visible. Anyone working in mental health care who has seen a client tip over in a single week after months of standstill, or remain stuck despite every effort, is likely to recognise the idea.
What is the book about?
Van der Maas, professor of psychological methods in Amsterdam and external faculty member of the Santa Fe Institute, wrote this book on the basis of a master's course. It has three aims: to give an overview of complexity research with an emphasis on psychology and the social sciences, to teach skills, and to encourage critical thinking about applications. Mathematically it asks for no more than secondary school level, although some basic knowledge of R is needed.
The structure follows a clear division into two. Chapters 2 to 4 deal with systems with few variables: chaos (the logistic map, the butterfly effect, the Lyapunov exponent), transitions and catastrophe theory, and building dynamic models with differential equations. Chapters 5 to 7 deal with systems with many variables: self-organisation and agent-based modelling in NetLogo, psychological network models, and finally "sociophysics", models of opinion formation and polarisation. An epilogue looks back. Each chapter ends with exercises, marked with one or two stars for difficulty.
What makes the book strong
For us, the heart of the book is chapter 3, on jumps and catastrophe theory. Van der Maas wrote his PhD on the question of whether Piaget's stages really are separated by transitions, and that background is clearly noticeable. He explains the cusp catastrophe step by step: a behavioural variable, a "normal" control variable that pushes the system to the left or right, and a "splitting" variable that determines whether there is one equilibrium or two. With two equilibria, hysteresis arises: the way back does not pass through the same point as the way there.
At least as valuable as the mathematics is the empirical methodology he provides with it. A jump in a time series says little in itself, because a rapid but continuous acceleration looks almost the same. He therefore works with Gilmore's catastrophe flags: bimodality, inaccessible intermediate states, divergence, hysteresis, and early warning signals such as critical slowing down and increasing variance. Only in combination do these features make a transition plausible. He also shows how to fit a cusp model to cross-sectional data using Cobb's method (the R package cusp). There is a clinical example too: weekly SCL-90 depression scores of a single patient who tapered off his antidepressant under blind conditions, with a statistically established jump around week 18 (pp. 49 to 50).
A second strength is the way he distinguishes phenomenological models (you assume a cusp) from mechanistic models (the cusp follows from simpler assumptions). A fine example is in chapter 6: the Ising model of attitudes, in which attitudes are networks of beliefs, feelings and behaviours and attention plays the role of (inverse) temperature, turns out in the mean-field approximation to yield exactly the cusp. What was first an assumed form thus becomes a derived result.
A third strength is his case for analogical modelling. He borrows a model of addiction from outbreaks of the spruce budworm in Canadian forests, complete with a self-control term that only kicks in after a certain number of drinks (pp. 91 to 92). The panic model (Robinaugh and colleagues) links arousal and perceived threat in a vicious circle and likewise turns out to be a cusp, with a panic attack as a metastable state (pp. 85 to 88). Models like these, he shows, help to formulate verbal theories more precisely.
What does it offer the mental health clinician?
More than the limited space given to psychopathology would suggest. The image that has stayed with us most comes as early as chapter 1 (and we wrote about it earlier in The shallow-lakes analogy): shallow lakes that suddenly turn murky when there is too much phosphate, and do not become clear again when the phosphate is brought back down. What did work was removing all the fish. Van der Maas compares the murky lake with depression and formulates the lesson as follows: "The dogma of intervention, that the cause of the problem is the key to the solution, does not necessarily apply to complex systems" (p. 13). For those who treat, it is a thought that both opens up room and gives pause.
In chapter 6 this is developed through the network perspective on psychopathology: disorders as alternative stable states of strongly connected symptom networks, as an alternative to a hidden common cause such as the p factor. His distinction between perturbations and interventions (pp. 143 to 144) is clinically very usable. If someone is in a metastable unhealthy state, almost any perturbation will work, even a waiting list; if someone is in a deeply stable state, no brief intervention will stick. In this model, a lasting effect is mainly to be expected from an intervention that changes the landscape itself. This offers an illuminating reading of varying treatment effects, and an argument for monitoring resilience when timing interventions.
For diagnostics and process monitoring, the book mainly contains warnings that we find useful. Centrality analyses on cross-sectional group data say little about causality; his own simulation shows that the most "central" node may be precisely the one influenced by all the others. Statements about direction require time series from a single person. And on early warning signals he is strikingly sober: "the problem with early warning signals is that both type 1 and type 2 errors should be low for predicting transitions" (p. 54). A reliable prediction of relapse would be of great clinical value, but in his view that is not yet achievable with noisy psychological data.
Critical notes
The book promises an overview of complexity research "in psychology", but clinical psychology receives relatively little space. The section on mental disorders in the chapter on self-organisation barely fills a page and mainly refers elsewhere. The therapeutic process itself, with idiographic process monitoring, daily self-ratings and the work of Schiepek, and of Tschacher and Haken, among others, is cited but not developed. How to follow tipping points in a client in practice is hardly addressed in this book.
It is also noticeable that the author writes from within his own research group. He says so himself ("I'm naturally somewhat biased toward our own work", p. 19), and the chosen examples (mutualism, Ising attitudes, HIOM) are strong as a result, but also somewhat one-sided. The chapter on sociophysics is intellectually rich, but probably the least relevant for the clinician.
Finally, the book asks for a considerable investment. It contains a lot of R code, NetLogo is introduced from scratch, and the exercises (from programming a bifurcation diagram to building a Zeeman catastrophe machine) presuppose time and a laptop. For students that is a strength, for the busy clinician rather a threshold. It is to Van der Maas's credit that he is honest about limits: he calls the application of chaos theory to psychological data limited, acknowledges that network models increase our understanding but have so far yielded hardly any interventions, and in the epilogue names the measurement crisis as the biggest problem in the field.
Who is this book for?
First and foremost for master's students, PhD candidates and researchers who want to learn complexity thinking formally, with simulations as the route to learning. For teachers it is particularly useful: open access, with code, datasets and exercises of increasing difficulty. For health care psychologists, clinical psychologists and psychotherapists, the chapters that seem to us most worthwhile are chapter 1, chapter 3 (up to and including the critique of catastrophe theory), the clinical models in chapter 4 and the sections on symptom networks and resilience in chapter 6. Readers short of time can skip the code and still take away a great deal, although they will then miss the part in which the author locates the actual learning.
In closing
Van der Maas does not offer an all-encompassing theory of the human mind, nor does he claim to. What he does offer is a toolkit and a way of seeing: towards equilibria, towards jumps, and towards networks in which cause and solution need not coincide. The book makes the translation to the consulting room only in part, but it does provide the concepts with which we can make that translation together. Because it has been published open access, it is moreover available to everyone.