The observers' paradox: apparent computational complexity in physical systems

Abstract Many researchers in AI and cognitive science believe that the complexity of a behavioural description reflects the underlying information processing complexity of the mechanism producing the behaviour. This paper explores the foundations of this complexity assumption. We first distinguish two types of complexity judgements that can be applied to these descriptions and then argue that neither type can be an intrinsic property of the underlying physical system. In short, we demonstrate how changes in the method of observation can radically alter both the number of apparent states and the apparent generative class of a system's behavioural description. From these examples we conclude that the act of observation can suggest frivolous computational explanations of physical phenomena, up to and including cognition.

[1]  David J. Weir,et al.  The convergence of mildly context-sensitive grammar formalisms , 1990 .

[2]  I. Introduction , 1961 .

[3]  Noam Chomsky,et al.  वाक्यविन्यास का सैद्धान्तिक पक्ष = Aspects of the theory of syntax , 1965 .

[4]  S. Sajami,et al.  Representation and reality , 1993 .

[5]  Chris A. Fields,et al.  Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems , 1990, J. Exp. Theor. Artif. Intell..

[6]  W. Ashby,et al.  An Introduction to Cybernetics , 1957 .

[7]  E. Feigenbaum,et al.  Computers and Thought , 1963 .

[8]  Christopher G. Langton,et al.  Computation at the edge of chaos: Phase transitions and emergent computation , 1990 .

[9]  Jordan B. Pollack,et al.  Recursive Distributed Representations , 1990, Artif. Intell..

[10]  Daniel C. Dennett,et al.  The Rediscovery of the Mind , 1992, Artif. Intell..

[11]  J. Fodor,et al.  Connectionism and cognitive architecture: A critical analysis , 1988, Cognition.

[12]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[13]  John R. Searle,et al.  The Rediscovery of the Mind , 1995, Artif. Intell..

[14]  P. Bak,et al.  A forest-fire model and some thoughts on turbulence , 1990 .

[15]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[16]  合田 周平,et al.  The science and praxis of complexity : contributions to the symposium held at Montpellier, France, 9-11 May, 1984 , 1985 .

[17]  Zenon W. Pylyshyn,et al.  Connectionism and cognitive architecture , 1993 .

[18]  Robert C. Berwick,et al.  Computational complexity and natural language , 1987 .

[19]  L. T. Fan,et al.  Fractals in Chaos , 1991 .

[20]  Allen Newell,et al.  GPS, a program that simulates human thought , 1995 .

[21]  Allen Newell,et al.  Computer science as empirical inquiry: symbols and search , 1976, CACM.

[22]  Stephen Grossberg,et al.  Competitive Learning: From Interactive Activation to Adaptive Resonance , 1987, Cogn. Sci..

[23]  James P. Crutchfield,et al.  Computation at the Onset of Chaos , 1991 .

[24]  Stephen Wolfram,et al.  Universality and complexity in cellular automata , 1983 .