Complexity: The Emerging Science at the Edge of Order and Chaos

by M. Mitchell Waldrop

Kurt Gödel showed that even some very simple mathematical systems—arithmetic, for example—are inherently incomplete. They always contain statements that cannot be proved true or false within the system, even in principle. At about the same time (and by using essentially the same argument), the logician Alan Turing showed that even very simple computer programs can be undecidable: you can’t tell in advance whether the computer will reach an answer or not. In the 1960s and 1970s, physicists got much the same message from chaos theory: even very simple equations can produce results that are surprising and essentially unpredictable. Indeed, says Arthur, that message has been repeated in field after field. “People realized that logic and philosophy are messy, that language is messy, that chemical kinetics is messy, that physics is messy, and finally that the economy is naturally messy. And it’s not that this is a mess created by the dirt that’s on the microscope glass. It’s that this mess is inherent in the systems themselves. You can’t capture any of them and confine them to a neat box of logic.”