Though she's an excellent writer, I'm already a little disappointed in the book. For example, her first chapter is entitled What is Complexity?, and she then goes on to ignore the question and give lots of examples of complex systems. Chapter 7 is called Defining and Measuring Complexity, and would probably have been a better start to the book, since it actually attempts to lay out what the concept means and how it is difficult to find a consensus definition among people who study it.
But what made me even more disgruntled right off the bat is her assertion in the preface that reductionism is passe, or worse, dead:
But twentieth-century science was also marked by the demise of the reductionist dream. In spite of its great successes explaining the very large and very small, fundamental physics, and more generally, scientific reductionism, have been notably mute in explaining the complex phenomena closest to our human-scale concerns.
Now look...I'm a reductionist, and as far as I'm concerned, so is every other working scientist. That's why I get a bit peeved when I see reductionism mischaracterized as an outmoded approach that was good for studying classical problems, but a miserable failure for, you know, really complicated stuff.
Here's all reductionism is: Trying to understand a system by understanding its parts and how they work together. That's it. And guess what? That's a wholly sensible approach that works amazingly well.
Reductionism often gets propped up as a straw man and ridiculed for trying to understand a system at one scale in terms of parts at a much lower scale. For example, someone might say "It's ridiculous to try to understand an opera in terms of acoustical dynamics!" or "It's silly to try to explain the migratory patterns of birds in terms of subatomic particles!"
Hey, I agree! Such approaches are stupid. And that's not reductionism. And it doesn't work. The way reductionism bears fruit is by trying to understand a system in terms of its parts at the appropriate lower level of description. Richard Dawkins calls this hierarchical reductionism.
For example, if you want to explain how a car works, describing its function in terms of pistons and axles is going to yield far better results than describing its function at the level of atoms. If you skip too many levels of description between the parts and the whole, your explanation is simply going to suck.
Now, as a working scientist its often difficult to determine what the appropriate level of description of the parts needs to be. But what, exactly, is the alternative to such an approach? I've heard plenty of people knock their characterization of reductionism. But I have yet to hear a proposal for how you go about trying to understand a system without understanding how its elements interact. How do you "holistically" study or explain how a system works? Some of the early examples Mitchell gives of complex systems are ant colonies, human brains, and economic systems. She's correct that such systems composed of interacting elements can give rise to amazingly complex behavior. But I honestly don't see how we can go about trying to understand that behavior without examining the behavior of the constituent elements...which is reductionism.
I'm interested to read the rest of the book and see where it goes, but as far as I'm concerned she's already gotten off on the wrong foot.