Beyond continuous mathematics and traditional scientific analysis: understanding and mining Wolfram's A New Kind of Science

Abstract

In A New Kind of Science, Stephen Wolfram recommends abandoning traditional scientific analysis and the continuous mathematical description that it affords in favor of the study of simple rules. He focuses on a machine known as a cellular automaton as the prototype generator of complex phenomena such as those we see in nature. The simplest cellular automaton consists of a row of cells, each existing in one of two states. The states of the cells are updated from moment to moment by simple rules. Wolfram shows that these machines and their many variations can generate a host of outcomes ranging from very simple to extremely complex. He argues that among these outcomes representations of all the phenomena in the universe will be found, including presumably the behavior of organisms. The output of cellular automata can be mapped to behavior by considering, for example, one of the states of a cell to represent the emission of a behavior. For some cellular automaton rules, these mappings generate cumulative records and inter-response time distributions that are similar to those produced by live organisms. In addition, at least one cellular automaton generates the Herrnstein hyperbola as an emergent outcome. These results suggest that Wolfram's program and its mainstream version, which is known as complexity theory, is worth pursuing as a possible means of understanding and accounting for the behavior of organisms.