THEORY BUILDING IN THE ENTREPRENEURSHIP PARADIGM

Ever since Newton's Principia set mathematical models at the pinnacle of a scientific paradigm, scientists in all disciplines-not just the physical sciences-have striven to express their theories mathematically. In the social sciences, mathematical models are more often than not a little more than a Laplacian fantasy. Nevertheless, mathematics is being used more and more extensively by social scientists-none more so than economists and business researchers. This paper focuses on one area of social science, entrepreneurship, and examines the difficulties of trying to use mathematics to model entrepreneurship processes. The entrepreneurial process is a dynamic, discontinuous change of state. It involves numerous antecedent variables. It is extremely sensitive to initial conditions. To build an algorithm for a physical system with those characteristics would be daunting to the most gifted applied mathematician. But when you add the requirement that the entrepreneurial process is initiated by the volition of a unique human being, mathematical modeling may be impossible, because there is ''an essential non-algorithmic aspect to conscious human action.'' This article argues that today's most prominent mathematical representation of entrepreneurship, population ecology, falls far short of Penrose's specification for a ''useful theory.'' Some observers believe that the answer to entrepreneurship theory may be found in the chaos theory-a relatively new science that was popularized by Gleick in his book Chaos: Making a New Science. This article explores the chaotic zones of several algorithms that provide alluringly simple representations for the entrepreneurial process. One of them is the fundamental equation for population ecology theory. It shows how under some conditions that equation exhibits some wild, chaotic behavior that gives an observer the feel of entrepreneurship. But it is no more than a mathematical metaphor because the accuracy of the measurements that are needed to observe true scientific chaos in the entrepreneurial process are unattainable in practice.