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Whatever happened to Stephen Wolfram? A new kind of science revisited.

Article Excerpt
THE PUBLICATION OF STEPHEN WOLFRAM'S A New Kind of Science (NKS) in 2002, (1) stimulated much research and debate on complexity theory and computability theory, with much of the debate centered around the possibility of the applications of these disciplines to the natural and social sciences. Wolfram's supporters heralded his work as the beginning of a modern-day scientific revolution, akin to the emergence of Newtonian physics and predictive science. Wolfram's critics denounced NKS as only marginally significant at best and pseudoscientific at worst, the vehemence of their convictions often morphing into ad hominem attacks. For a thorough overview of NKS and its critics, I refer the reader to David Naiditch's analysis in SKEPTIC (Vol. 10 No. 2) (2) to which this article is a follow-up.

The questions that arise for the critical reader of NKS: are Wolfram's ideas "new" and are they "scientific"? I posit that one may frame these questions in the context of two notions, what I call Weak NKS and Strong NKS, as described below. These are essentially two interpretations of Wolfram's Principle of Computational Equivalence.

Weak NKS: Any computational system whose behavior is not obviously simple is equivalent in computational sophistication to all other such computational systems. As complexity is a prerequisite for universal computation, it is also the case that any computational system whose behavior is not obviously simple is a universal computer. Strong NKS: Any system whose behavior is not obviously simple is equivalent in computational sophistication to all other such systems. As complexity is a prerequisite for universal computation, it is also the case that any system whose behavior is not obviously simple is a universal computer.

The slight, yet consequential distinction between these two notions is in the modification of "system" with "computational" in Weak NKS. The term "computational system" refers to abstract machines like cellular automata and Turing machines, which have been the object of Wolfram's rigorous study for the past twenty years. Strong NKS eschews this modification and purports that the argument of Weak NKS holds for all systems, both abstract and natural. I argue that Weak NKS is an important guiding principle and a fully scientific statement, with several pieces of supporting evidence. I contend, however, that Strong NKS is untestable and unfalsifiable, disqualifying it as science.

Computability and Complexity, pre-NKS

Theoretical computer science is the formal study of computability and complexity. Researchers focusing on the former seek to define the limits of computation, classifying problems that are solvable and unsolvable, while those focusing on the latter study computable problems that are classified as hard or easy. Such inquiries into computability and complexity were inspired by Kurt Godel's Incompleteness Theorems and David Hilbert's Entscheidungsproblem. Alan Turing introduced the notion of an abstract machine capable of computation of arbitrary sophistication if given unlimited memory. (3) Turing's mechanistic model of computation, along with Alonzo Church's lambda calculus,...

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