Countless popular math/science books have been written over the last 30 years that weave together most if not all of the following topics.
Sensitive dependence on initial conditions
One of the first and most successful books in this genre was Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. Melanie Mitchell’s Complexity: A Guided Tour follows in the tradition of Gödel, Escher, Bach. Not only are the books related, so are their authors: Hofstadter was Mitchell’s PhD advisor. She decided she wanted to study artificial intelligence with Hofstadter after reading Gödel, Escher, Bach.
Those who are familiar with contemporary popular science literature will find much of the material in Complexity familiar, especially Part I: Background and History. What distinguishes Mitchell’s book from the myriad other books concerned with the same topics? I would say two things: the author’s personal perspective and the inclusion of recent developments.
As mentioned above, Mitchell studied with Hofstadter. Her book includes anecdotes from her acquaintance with him and in particular her graduate research under his direction. She has also worked at the Santa Fe Institute, the Mecca of much research into complexity since it was founded in 1984. Her first-person accounts add a warm personal element to the book.
Mitchell writes with candor, admitting when she finds something hard to understand. For example, in discussing Stephen Wolfram’s 1,200-page book A New Kind of Science she says
I read the whole book, but I still don’t completely understand what Wolfram is getting at here.
(Many people share her assessment of Wolfram’s book, though not as many have invested the effort to read every page.)
Complexity stands out from other popular science books by mentioning recent discoveries and theories from genetics. For example, the penultimate chapter, “Evolution, Complexified,” discusses evolutionary developmental biology (“evo-devo”) and Stuart Kauffman’s theory of random Boolean networks.
Many readers will find the material in Complexity: A Guided Tour familiar. However, these same readers may enjoy Mitchell’s personal perspective and her inclusion of recent research. Readers who have not been introduced to the ideas explored in Complexity will find the content fascinating.
John D. Cook is a research statistician at M. D. Anderson Cancer Center and blogs daily at The Endeavour.