This book starts off well enough, with a fascinating chapter on the limits of mathematics, focusing on Godel's refutation of formalism (the idea that the whole of mathematics can be derived from a set of logical statements), followed by a brief history of computers and the computation. But once the authors begin their explanation of complexity, they come off as smug and overzealous about their field. They seem to take every opportunity to belittle other fields of science, and try to convince us that complexity will provide the ultimate explanaion of every facet of the universe, from biology to physics to chemistry to social sciences.
This may sound like an exaggeration, but it really isn't: at the beginning of their chapter on complexity in chemical reactions, they dismiss the idea that chemistry (and by extension, biochemistry) can be explanied by quantum physics because the calculations it requires are too complicated. I understand that it is difficult to use quantum physics, and that its effects are only significant on the atomic level, but that does not mean that quantum effects do not exist! The chapter on chemistry marks the end of any reasonable explanation of complexity, and by end of the book complexity is almost completely forgotten, as the writing gushes on about neural networks and aritficial life.
It is these later chapters on life and aritificial life that are the most poorly written. The authors commonly say things like "It is becoming clear that obstacles to creating aritfical consciousness may not be as formidable as we had thought", yet provide little proof of this. They basically claim that neural networks are only a few innovations away from becoming fully funcitoning human brains, but they provide a one-sided explanation of their usefulness and fail to mention their failings, especially in cognitive science (which is the study of the brain, of all things). They strongly hint that current ALife programs are creating new life, when they are pretty must just clever programs that manipulate computer memory according to a set of rules. They just don't seem to realize that simulating certain aspects of life with computers and life itself are very different things! We are not even certain that neurons are the basic building block of the brain, yet they are claiming that we now know enough about the brain to create a computerized one in no time. Their argument is very smug and one-sided: the only time they ever mention a criticism to current ALife and AI practices is when they present Roger Penrose's very reasonable hypothesis about how computers cannot simulate intelligence in large part due to their reliance on mathematical logic, which, as Godel proved, can sometimes break down. Yet they quickly dismiss this view, seeming to think that Godel's theorems are nothing more than irrelevant parlor tricks. Their claim that a neural network can be taught to do anything, and therfore can overcome Godel's theorems, is especially poor: we could never teach a human brain to fly, for example, because it (and the body it is in) are not equipped to do this. So why do they think that our arcane artificial neural networks are equipped to create consciousness?
Despite this heavy criticism, however, this book is still quite interesting if you are new to complexity, chaos, and artificial life. The author's overexcitement about their field seems to be common when new branches of science emerge, like when AI was first getting off the ground. If you read this book, just realize that its bold claims may be grounded in false hope.