Complexity: a very short introduction.
OUP. 2014
When I saw that John Holland had written “A Very Short Introduction” to complexity, I was excited, and snapped up a copy. Given Holland’s stature in the field, I was looking for a good distillation of concepts, and, maybe, a suitable introduction for my students.
Unfortunately, I cannot recommend this book. This is for two main reasons. Firstly, it is riddled with errors. Secondly, the part on Complex Adaptive Systems, or CAS (as opposed to the somewhat simpler Complex Physical Systems, or CPS), appears to be a summary of Holland’s own work in the area, not the more general introduction I was looking for.
The first issue is more of a problem. Here are a few examples. On p.7, Holland discusses von Neumman’s cellular automaton (CA) replicator, a complex pattern that can replicate itself, then references figure 1, which shows a glider from Conway’s Game of Life CA. On p.11, he says that CPS tend to be modelled using partial differential equations (despite most of his examples being discrete space and time CAs), then states that the theory of partial differential equations (PDEs) is additive, that is, linear (and says this again on p.25); by p.13 he is talking about PDEs being used to describe chaotic (necessarily non-linear) systems. On p.15 he states that the Koch snowflake fractal curve is “everywhere discontinuous”, rather, it is everywhere continuous, but nowhere differentiable. And so on.
Okay, so maybe the part on CAS is better than the part on CPS, because that’s his area of expertise? But no. Take figure 6, which has two parts, one a set of rules, and the other supposedly a network representation of the behaviour of those rules. Except that the two parts don’t fully correspond, and the hash notation in the rules (a wildcard) is nowhere explained; the figure as it stands is unintelligible. Furthermore, this specific formulation of rules is Holland’s own model of CAS, which would be absolutely fine in a book about his model, but not so much in a general introduction.
I gave up reading soon after this point. Even if there are some interesting insights (and I’m sure they must be) how can they be picked out from the mass of erroneous statements, and the potentially over-specific model presented? Unfortunately, this book will have to go back on my shelf; I will not be recommending it to my students, or to anyone else.
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