Book Review: A NEW KIND OF SCIENCE BY STEPHEN WOLFRAM

Abstract

This is a very unusual book. In 846 pages of text and 349 pages of notes, author Stephen Wolfram claims no less than that we have all been doing science with an outmoded set of analytical tools and that he has invented a new approach that can lead to rapid progress in fields ranging from mathematics to biology. This new way of doing science is, in short, to run computer simulations of complex systems. Wolfram’s claim is based on two major subclaims: First, that essentially all phenomena of interest to scientists can be described and studied as computations; and second, in what Wolfram calls the Principle of Computational Equivalence, that above a certain level of simplicity, essentially all computational systems embody a similar level of complexity. In an idea that seems close in spirit to Turing’s treatment of the halting problem, he further suggests that the only way to predict the behavior of such systems is to run them on a computer and see what happens. Embedded in this innocent-sounding proposal is a very deep criticism of the way theoretical science, particularly physics and mathematics, has developed up to the present day, namely, that scientists have always selected which theories to pursue based on a kind of aesthetic principle which favors those theories that most easily yield predictions via standard mathematical analysis. The reason for this idea of beauty in theories is that before the advent of modern computers it was not practical to develop predictions from theories by working out the consequences of simple rules at very large numbers of points in space and time; rather, short cuts, for example, the analytical solution of equations that might be more complex, had to be used to reduce the amount of work involved in projecting the outcome of a theory to distant times and places. Wolfram’s main thesis, and, indeed, I think the main contribution of this book, is to point out that we now have the computational means to look at theories based on simpler rules that may not admit of shortcut routes to their predictions.