Learning the Ashby Box: an experiment in second order cybernetic modeling

Abstract

Purpose W. Ross Ashby’s elementary non-trivial machine, known in the cybernetic literature as the “Ashby Box,” has been described as the prototypical example of a black box system. As far as it can be ascertained from Ashby’s journal, the intended purpose of this device may have been to exemplify the environment where an “artificial brain” may operate. This paper describes the construction of an elementary observer/controller for the class of systems exemplified by the Ashby Box – variable structure black box systems with parallel input. Design/methodology/approach Starting from a formalization of the second-order assumptions implicit in the design of the Ashby Box, the observer/controller system is synthesized from the ground up, in a strictly system-theoretic setting, without recourse to disciplinary metaphors or current theories of learning and cognition, based mainly on guidance from Heinz von Foerster’s theory of self-organizing systems and W. Ross Ashby’s own insights into adaptive systems. Findings Achieving and maintaining control of the Ashby Box requires a non-trivial observer system able to use the results of its interactions with the non-trivial machine to autonomously construct, deconstruct and reconstruct its own function. The algorithm and the dynamical model of the Ashby Box observer developed in this paper define the basic specifications of a general purpose, unsupervised learning architecture able to accomplish this task. Originality/value The problem exemplified by the Ashby Box is fundamental and goes to the roots of cybernetic theory; second-order cybernetics offers an adequate foundation for the mathematical modeling of this problem.