Simply Complexity: A Clear Guide to Complexity Theory [Paperback]

If you are unfamiliar with Complexity Theory ("The Science of Sciences") then this is a great book to start with. Neil Johnson has done an impeccable job of keeping the intricacies of Complexity within a very manageable framework that any layman can understand. Take this quote for example: "Complexity can be summed up by the phrase "Two's company, three is a crowd." In other words, Complexity Science can be seen as the study of the phenomena which emerge from a collection of interacting objects - and a crowd is a perfect example of such an emergent phenomenon, since it is a phenomenon which emerges from a collection of interacting people." The real strength of this book lies in Johnson's unsophisticated and plain approach towards Complexity Science which he couples with many real world examples. But neither does Johnson leave anything out; Self-Similarity, Fractals, Power-Laws, Networks, etc. - it's all here.

My only complaint about this book comes on page 100. Here, Johnson explains how the "six degrees of separation" network was conceived by Stanly Milgram in 1967. I am sure that Johnson knows that this was debunked by later research, but Johnson fails to mention this in the book (one only has to look to Wikipedia, Complexity: A Guided Tour by Melanie Mitchell or The Numbers Game: The Commonsense Guide to Understanding Numbers in the News, in Politics, and inLife for confirmation. I do not fault Johnson here because given the 'basic' level at which this book was written, he probably didn't feel like complicating the issue - the point he was trying to make was satisfied - and he therefore surely didn't feeling like going into the whole mess by upending the urban legend. So, with that aside, I do recommend this book as a great introduction to Complexity and recommend Complexity: A Guided Tour by Melanie Mitchell for the interested reader as a great book to continue learning about Complexity Science.

Complexity science is a broad field with vague boundaries, so no single book can cover the whole field in depth. In this book, Neil Johnson focuses on a definition of complexity associated with a particular class of computational models, and he describes these models and their resulting behaviors at a level suitable for the general reader (somewhat detailed descriptions, but essentially no formal math). He has a PhD in physics and has himself done considerable research on these types of models (see the references at the end of the book), so his knowledge in this area is fairly authoritative.

For Johnson, a complex system has the following characteristics:

(1) A population of multiple (at least three) interacting objects or "agents" which typically form a network. These objects may be very simple, but they don't have to be.

(2) Competition among the objects for limited resources. As part of this overall competition, there can also be local cooperation within the system.

(3) Feedback processes, which give the system memory and history.

(4) Ability of the objects to adapt their strategies in response to their history.

(5) Ability of the system to interact with its environment.

(6) Self-organization of system behavior, without the need for a central controller.

(7) Emergence of non-trivial patterns of behavior, including a complicated mixture of ordered and disordered behavior. This can include chaotic behavior, as well as extreme ordered behavior (eg, traffic jams, market crashes, human diseases and epidemics, wars, etc.).

Johnson gives many examples of complex systems, and a jazz band is among the most interesting of these examples (the jazz performance is the behavior of the system).

Here are some of the key results from the models he describes:

(1) Even if the objects comprising the population of the system are complicated and heterogeneous (eg, people), this variability tends to "average out" in a way that allows the objects to be modeled as being fairly simple and homogeneous (at least as a first approximation).

(2) Due to competition, the population of objects will often become polarized into two opposing groups (eg, bears and bulls in financial markets, opposing political parties, etc.). This competition tends to reduce fluctuations in the behavior of the system.

(3) It's sometimes possible to steer the behavior of a system by manipulating a subset of the system's objects.

(4) Network structure tends to make complex systems more robust.

(5) The overall behavior of a system, and the ability of individual objects in the system obtain resources, depends on both the amount of available resources and the level of connectivity (network structure) between objects. When resources are only moderate, adding a small amount of connectivity widens the disparity between successful and unsuccessful objects, whereas adding a high level of connectivity reduces this disparity. By contrast, when resources are plentiful, adding a small amount of connectivity is sufficient to increase the average success rate and enable most objects to be successful. These patterns are consistent with what I've observed in the competition among engineering firms over the years (including during the current recession, a time of reduced resources).

(6) The behavioral outcomes of complex systems often follow a power law distribution, with smaller events being most common, but with extreme events also occurring more often than one might expect.

One of my main motivations to read this book was to get insight into how malignant tumors might be modeled as complex systems, with the hope that such models might provide clues regarding more effective ways to treat cancer. I was pleased to see that Johnson does discuss cancer at several points in the book, but I was disappointed to find that his discussion of cancer modeling is relatively superficial. Nevertheless, I'm firmly convinced that cancer is best modeled as a complex system, so I believe that much more research along these lines is (urgently) needed.

Overall, I do recommend this book. Johnson is qualified to write it, and it works well as an easily understood introduction at a level of detail suitable for general readers. However, again, keep in mind that the scope of the book is fairly narrow, so many important topics aren't mentioned at all. As a result, the book provides a good understanding of some of the trees in the forest of complexity science, but not much sense of the overall forest. For a broader introduction to complexity science, I recommend Complexity: A Guided Tour by Melanie Mitchell.

The book is composed of two parts: the first titled "what exactly is complexity theory?", and the second "what can complexity science do for me?". While I pretty much liked the first part, I got some mixed feeling with respect to the second which I'll try to explain below.

Part one describes the ideas behind the complexity field of research, its properties and provides some toy examples (such as mob behavior). The text is very clear, easy to follow and explained in a way that *anyone* can follow. On a personal note, while most was already known to me, I really enjoyed the Jazz music analogy in chapter 3. Generally, this part was very interesting; I was missing some discussions about the differences between the complexity theory and other related (or equivalent) ideas that can be found under different umbrellas such as "agent based models", "multi agent systems".

The problem starts with Part two of the book. In this part the goal of each chapter (six of them) is to show the application of the complexity ideas to various domains: from financial markets, through warfare and terrorism, to quantum physics. My criticism is that while the author spends lots of space to describe each model, he makes very little effort to discuss the results/theorems/conclusions that can be derived from the model and their impact on reality. That is, we learn to appreciate the nice model for couple of pages but than, as the model is an extremely simplified description of reality, I kept baffling at what valuable information can be actually derived from it. The author, with only few vague sentences about the actual impact of the model, does not make a good point with that regard.

For example, chapter 10 ends with a model on sheep-wolf-dog game where one needs to decide whether to send the dogs to attack the wolf or keep them to defend the sheep. One of the conclusions is that for small numbers, attack is the best defense. That is a nice slogan but obviously not something that we can really conclude from the model. Moreover, the author claims that this result is analogous to a navy boats problem from WW2, who were hunted by German U-boat submarines. The navy ships put on a device to change course randomly to avoid contact. I think that a more accurate description for the success of the random strategy might actually come from a game theory analysis which includes mixed strategies (as oppose to the suggested game). The whole part of critical evaluation with discussion on the limitation of the models and the presentation of alternative ideas is severely lacking in this book.

That problem was pretty much consistent with all the chapters, and left me questioning whether the complexity ideas are as strong as was advocated in part one of the book. Another issue that I had while reading is the poor writing style: there are numerous repetitions of the phrases "in other words" and "in particular", often several times in the same paragraph. Going back to my mixed feeling here, I grade the book with three stars.

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