A gentle introduction to complexity theory


Complexity: A Guided Tour
by Melanie Mitchell (2009, Oxford)

Melanie Mitchell has written a wonderful book on a subject that defies simple explanation. Complex systems science, as she aptly refers to the interdisciplinary field commonly called complexity, is admirably presented to a general audience without diminishing the intellectual content of the discussion. The breadth and depth of her exposition are more than adequate to convey a clear notion at an introductory level of what complex systems are all about.

After first illustrating what complexity means through a variety of real-world examples, Dr Mitchell provides a historical background of the principal theoretical bases underpinning complex systems science, namely, dynamical systems and chaos, information and entropy, Turing computation, evolution, and genetics. Following is a thorough discussion of the difficulties of coming up with a universal definition of complexity. Then a number of problem areas are investigated, such as self-reproducing systems (computer programs, DNA, von Neumann’s automaton), genetic algorithms, cellular automata, dynamical information processing structures, actual living systems (the immune system, ant colonies, biological metabolism), analogy making by computers, and computer modeling and simulation as a third way of doing science, the traditional two being theory and experiment. Four subsequent chapters delve into the intricacies of networks, including the alluring mysteries of the ubiquitous power law and the complexification of genetics and evolution. The book ends with a candid appraisal of the past and future of the sciences of complexity.

That Mitchell is able to intelligently expound on such a wide range of technical topics while resorting to but a single mathematical equation (for the logistic map) is a testament to her command of the subject as well as her fluid writing skills. Her editor must have been pleased. (Well, a couple of English sentences logically amounting to mathematical equations were deployed to show a power-law distribution and the formula for the volume of a sphere but, hey, the equal signs were duly avoided!) The end notes, however, do explain the math behind various verbal assertions in the main text.

Complex systems science is the third major attempt to launch an autonomous and self-sustaining field of academic inquiry devoted to this intriguing domain. The first two, cybernetics and general systems theory (both discussed in the book), did not fare all that well. An uneasy feeling that history may recur yet again permeates the atmosphere of the final chapter. It may indeed be the case that complex cybernetic systems is much too rarefied a conceptual domain to ever congeal into a conventional discipline. Yet perhaps that is how things ought to be. For the true value of systems thinking lies in the deep transcendent insights it affords about phenomena, perspectives which traditional disciplines often can scarcely come to fathom.



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