Randomness, Determinism and Programs in Turing’s Test

Abstract

From the physico-mathematical view point, the imitation game between man and machine, proposed by Turing in his 1950 paper for the journal “Mind”, is a game between a discrete and a continuous system. Turing stresses several times the laplacian nature of his discrete-state machine, yet he tries to show the undetectability of a functional imitation, by his machine, of a system (the brain) that, in his words, is not a discrete-state machine, as it is sensitive to limit conditions. We shortly compare this tentative imitation with Turings mathematical modelling of morphogenesis (his 1952 paper, focusing on continuous systems, as he calls non-linear dynamics, which are sensitive to initial conditions). On the grounds of recent knowledge about dynamical systems, we show the detectability of a Turing Machine from many dynamical processes. Turings hinted distinction between imitation and modelling is developed, jointly to a discussion on the repeatability of computational processes in relation to physical systems.