Complexity_ A Guided Tour - Melanie Mitchell [147]
Can we similarly invent the calculus of complexity—a mathematical language that captures the origins and dynamics of self-organization, emergent behavior, and adaptation in complex systems? There are some people who have embarked on this monumental task. For example, as I described in chapter 10, Stephen Wolfram is using the building blocks of dynamics and computation in cellular automata to create what he thinks is a new, fundamental theory of nature. As I noted above, Ilya Prigogine and his followers have attempted to identify the building blocks and build a theory of complexity in terms of a small list of physical concepts. The physicist Per Bak introduced the notion of self-organized criticality, based on concepts from dynamical systems theory and phase transitions, which he presented as a general theory of self-organization and emergence. The physicist Jim Crutchfield has proposed a theory of computational mechanics, which integrates ideas from dynamical systems, computation theory, and the theory of statistical inference to explain the emergence and structure of complex and adaptive behavior.
While each of these approaches, along with several others I don’t describe here, is still far from being a comprehensive explanatory theory for complex systems, each contains important new ideas and are still areas of active research. Of course it’s still unclear if there even exists such a theory; it may be that complexity arises and operates by very different processes in different systems. In this book I’ve presented some of the likely pieces of a complex systems theory, if one exists, in the domains of information, computation, dynamics, and evolution. What’s needed is the ability to see their deep relationships and how they fit into a coherent whole—what might be referred to as “the simplicity on the other side of complexity.”
While much of the science I’ve described in this book is still in its early stages, to me, the prospect of fulfilling such ambitious goals is part of what makes complex systems a truly exciting area to work in. One thing is clear: pursuing these goals will require, as great science always does, an adventurous intellectual spirit and a willingness to risk failure and reproach by going beyond mainstream science into ill-defined and uncharted territory. In the words of the writer and adventurer André Gide, “One doesn’t discover new lands without consenting to lose sight of the shore.” Readers, I look forward to the day when we can together tour those new territories of complexity.
NOTES
Preface
“REDUCTIONISM is”: Hofstadter, D. R., Gödel, Escher, Bach: an Eternal Golden Braid. New York: Basic Books, 1979, p. 312.
“to divide all the difficulties under examination”: Descartes, R., A Discourse on the Method. Translated by Ian Maclean. Oxford: Oxford University Press, 1637/2006, p. 17.
“it seems probable that most of the grand underlying principles”: Quoted in Horgan, J., The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age. Reading, MA: Addison-Wesley, 1996, p. 19.
“emerging syntheses in science”: The proceedings of this meeting were published as a book: Pines, D., Emerging Syntheses in Science. Reading, MA: Addison-Wesley, 1988.
“pursue research on a large number of highly complex and interactive systems”; “promote a unity of knowledge”: G. Cowan, Plans for the future. In Pines, D., Emerging Syntheses in Science. Reading, MA: Addison-Wesley, 1988, pp. 235, 237.
“a conference … on the subject of ‘emergent computation’ ”: The proceedings of this meeting were published as a book: Forrest, S., Emergent Computation. Cambridge, MA: MIT Press, 1991.
Part I
“Science has explored