A number of such idealized universal computers have been studied (ranging from Turing machines through John Conway's Game of Life to more recent examples), but Wolfram's rule 110 is especially simple. He concludes from it and a myriad of other considerations too numerous and detailed to even adumbrate here that scientists should direct their energies toward simple programs rather than equations since programs are better at capturing the complicated interactions that characterize scientific phenomena.
A New Kind of Science also puts forward a "Principle of Computational Equivalence," which asserts, among other things, that almost all processes, artificial (such as his rule 110) or natural (such as those occurring in biology or physics) that are not obviously simple can give rise to universal computers. This is reminiscent of an old result known as the Church-Turing thesis which maintains that any rule-governed process or computation that can be performed at all can be performed by a Turing machine or equivalent universal computer. Wolfram, however, extends the principle, gives it a novel twist, and applies it everywhere.
In fact, his polymathic approach is part of what is exciting about the book. Simple programs, he avers, can be used to explain space and time, mathematics, free will, and perception as well as help clarify biology, physics, and other sciences. They also explain how a universe as complex-appearing and various as ours might have come about: the underlying physical theories provide a set of simple rules for "updating" the state of the universe and such rules are, as Wolfram demonstrates repeatedly, capable of generating the complexity around (and in) us, if allowed to unfold over long enough periods of time.
Some of the book's claims are hubristic and hyperbolic. Many others have been around for a while, but no one has put them all together in such a compelling way to articulate if not a new kind of science, at least a new way of looking at the established kind.
Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Reads the Newspaper. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.