Stephen Wolframs massive self-published tome, A new kind of science, has been criticized by various reviewers as overwrought, repetitive, egocentric, insufficiently documented, megalomaniacal, too Mathematica-focused, nothing new, self-indulgent, the raving of a crackpot, and false. Whether or not one wishes to believe Wolframs occasional extravagant claims, such as that continuity and motion in the physical world are illusions, or that the universe is a simple computer program, his manic but endlessly fascinating 6 lb behemoth of a book is a treasure trove of mathematical and computational ideas and techniques that is well worth mining for its possible relevance to problems in quantitative behavior analysis. Wolframs point of departure is that complex behavior can be produced by the repeated application of simple rules (nothing new); the rest of the book is a rococo elaboration of this theme. From cellular automata and Turing machines to iterated function systems and prime number sequences, there is enough raw material in this volume to keep a scientific miner digging and happy for a long time. In this tutorial I will discuss some of the raw material I have mined from Wolframs book that might be of interest to quantitative behavior analysts, with a special focus on cellular automata.
|Dr. Jack J. McDowell earned an A.B. in Psychology from Yale University in 1972 and a Ph.D. from the State University of New York at Stony Brook in 1979 under the mentorship of Dr. Howard Rachlin. He joined the faculty of Emory University in 1979 where he is currently Professor of Psychology. Dr. McDowell’s research has focused on mathematical and computational theories of behavior, including formal mathematical work, experimental work with rats, pigeons and humans, and computer experiments with virtual organisms. Much of Dr. McDowell’s experimental work has involved tests of matching theory, the results of which recently led him to argue that the traditional version of matching theory is false, and should be replaced by a revamped, modern, version. Most recently Dr. McDowell proposed a computational model of selection by consequences that instantiates the idea that behavior evolves in response to selection pressure from the environment in the form of reinforcement. Computer experiments show that this evolutionary dynamics produces steady-state behavior consistent with the modern version of matching theory. Dr. McDowell’s experience with and expertise in mathematical and computational techniques makes him uniquely qualified to evaluate Wolfram’s work.|