Complexity: A Guided Tour by Melanie Mitchell
[Read in July of 2009 but was delayed in writing the review.]
I came across this book during a bookstore trip and decided to
purchase it as it included topics related to a couple of recent posts and
previously read book, Linked: The New Science of Networks. I'm glad I
did as it made me realize that many of the things that I am interested
in fall under the domain of Complex Systems.
The book is structured as five parts and nineteen chapters as
summarized below:
| PART | CHAPTER | THEME |
|---|
| 1 | | BACKGROUND AND HISTORY |
| 1 | What is Complexity? |
| 2 | Dynamics, Chaos, and Prediction |
| 3 | Information |
| 4 | Computation |
| 5 | Evolution |
| 6 | Genetics, Simplified |
| 7 | Defining and Measuring Complexity |
| 2 | | LIFE AND EVOLUTION IN COMPUTERS |
| 8 | Self-Reproducing Computer Programs |
| 9 | Genetic Algorithms |
| 3 | | COMPUTATION WRIT LARGE |
| 10 | Cellular Automata, Life, and the Universe |
| 11 | Computing with Particles |
| 12 | Information Processing in Living Systems |
| 13 | How to Make Analogies (if You Are a Computer) |
| 14 | Prospects of Computer Modeling |
| 4 | | NETWORK THINKING |
| 15 | The Science of Networks |
| 16 | Applying Network Science to Real-World Networks |
| 17 | The Mystery of Scaling |
| 18 | Evolution, Complexified |
| 5 | | CONCLUSION |
| 19 | The Past and Future of the Sciences of Complexity |
Part 1, nearly a third of the entire book, provides a thorough
introduction to Complex Systems which are defined by the author
as having the following properties:
-
Complex collective behavior (i.e. the whole is greater than the sum
of the parts)
-
Signaling and information processing
-
Adaptation to environmental changes
Example complex systems cited were insect colonies, the brain, the
immune system, economies, and the world wide web.
Chapter 2 was an enjoyable introduction to dynamical systems and chaos
theory which I had only a cursory awareness of. The simple "rabbit
population" example using logistic maps was a great aid in
understanding the concepts of fixed/periodic/strange attractors, and a
sensitive dependence on initial conditions (aka. the Butterfly
Effect). New to me were the concepts of the period doubling route to chaos and Feigenbaum's Constant (which is just plain odd).
Chapters 3 and 4 covered concepts related to information and
computation including: entropy, Maxwell's Demon, statistical
mechanics, Shannon's information theory, Hilbert's problems, Godel's
incompletness theorem, and Turing machines. Overall the treatment was
good and a sufficient introduction for readers unfamiliar with
these concepts.
Chapters 5 and 6 discussed the topics of evolution and genetics. I
found the discussion on evolution interesting as I don't recall
learning about the feud between the early Darwinians, who believed in
continuous small variations, and Mendelians, who believed in discrete
large variations. I also don't recall learning about the Modern Synthesis or the continued challenges in the form of punctuated equilibrium. Interesting stuff.
Chapter 7 discussed various ways of defining and measuring complexity
as:
-
size
-
entropy
-
algorithmic information content
-
logical depth
-
thermodynamic depth
-
computatoinal capacity
-
statistical complexity
-
fractal dimension
-
degree of hierarchy
While no single measure was identified as the measure, all were
interesting to consider.
Chapters 8 to 10 discussed cellular automata, genetic algorithms, and
artificial life. While the treatment was good, it felt light-weight after
having just read The Recursive Universe. That said, Chapter 10 did
provide a nice overview of Wolfram's work on cellular automata that
augmented the prior material I had read on this subject.
Chapter 11 discussed the use of cellular automata for majority
classification tasks. The specific task discussed was the
determination of the dominant color in a one-dimensional vector of
white and black pixels. The authors used genetic algorithms to evolve
a set of CA rules that reliably performed this task by creating
diagonal vectors that carried local majority-voting decisions which
eventually intersected to produce a majority-vote for the entire
original vector. The authors seemed unable to at first understand how
the evolved CA worked but I thought it obvious as clearly any solution
must involve the horizontal communication of local-majority votes in
order to reach a global decision. It seems obvious (to me) that such
horizontal communication would manifest as diagonal vectors when the
CA evolutions are graphed vertically. I thought the use of particle
equations to explain the phenomina was overkill but still interesting.
I enjoyed the author's account in Chapter 13 of her work on the
CopyCat program which was designed to process analogies. The problem
appears hard and the program was quite clever. I must admit I am
extermely jealous that she got to work so closely with Douglas Hofstadter.
Chapters 15 to 16 discussed real-world network theory which included
topics such as small-world phenomina, scale-free networks, clustering,
preferential association, and network resiliance. Overall the
treatment was good but mostly a review after having just read
(actually listened to) Barabasi's book Linked, which I highly
recommend reading.
Chapters 17 and 18 discussed network theory in the contexts of
metabolic scaling and evolution which was very interesting. Some of
this material was a review of Stuart Kauffman's work documented in his
book Origins of Order. I previously read another of Kauffman's books,
At Home in the Universe, which touched on some of the same topics but
perhaps I'll add Origins to the list of potential future readings.
Chapter 19 concluded the book with an overview of the state of
complexity science and the need for a unifying theory. While the
field has accomplished many great things, it appears that a lot
of difficult work remains which is perhaps why this is such an
appealing topic.
In summary, Complexity is a great book that covers a lot of
interesting topics. On a personal level, I am thankful to have
read this book because, as I mentioned, it helped me realize
that complexity science is the meta-topic that unifies many of
my long term interests and therefore serves a guide for future
research.
