THEORY OF CYBERNETIC AND INTELLIGENT MACHINE BASED ON LIE COMMUTATORS

Abstract

Abstract Many attempts1, 7, 8, 35 have been made to overcome the limit imposed by the Turing Machine34 to realise general mathematical functions and models of (physical) phenomena. They center around the notion of computability. In this paper we propose a new definition of computability which lays the foundations for a theory of cybernetic and intelligent machines in which the classical limits imposed by discrete algorithmic procedures are offset by the use of continuous operators on unlimited data. This data is supplied to the machine in a totally parallel mode, as a field or wave. This theory of machines draws its concepts from category theory, Lie algebras, and general systems theory. It permits the incorporation of intelligent control into the design of the machine as a virtual element. The incorporated control can be realized in many (machine) configurations of which we give three: a) a quantum mechanical realization appropriate to a possible understanding of the quantum computer and other models of the physical microworld, b) a stochastic realization based on Kolmogorov-Gabor theory leading to a possible understanding of generalised models of the physical or thermodynamic macroworld, and lastly c) a classical mechanical realization appropriate lo the study of a new class of robots. Particular applications at a fundamental level are cited in geometry, mathematics, biology, acoustics, aeronautics, quantum mechanics, general relativity and. Markov chains. The proposed theory therefore opens a new way towards understanding the processes that underlie intelligence. INDEX TERMS: Intelligent machineLie algebrasgeneral system theorycomputabilityholographyquantum computerstochastic realizationrobotcategory theorytensorial calculus Additional informationNotes on contributorsP. J. MARCER Current address, Aikido Enterprises, 53 Old Vicarage Green, Keynsham BS18 2DH, UK.