Innovation in Complex Adaptive Systems: Some Mathematical Sketches

During the twentieth century, innovations have produced revolutionary effects on the locus of capital, labor and productivity--we need only look at the changes produced by the airplane or the computer to convince ourselves of this. Despite innovation’s impact, and a widely held consensus that innovation will have an even greater role in the economy of the twenty-first century, our theoretical understanding of its mechanisms and consequences remains at best fragmentary. Part of the problem is that innovation produces a perpetual novelty that is the very antithesis of equilibrium; when innovation is a major factor, tendencies to equilibrium are repeatedly frustrated. For this reason, some of our most powerful mathematical tools, such as fixed point theorems and other techniques that focus on equilibria, are of little help in studying innovation. It would seem that studies of innovation must concentrate on the ontogeny of the process. What follows is an abbreviated description of one possibility, an approach that uses computer-based gedanken experiments guided by fragments of mathematical analysis.