Laplace, Turing and the "Imitation Game" Impossible Geometry [chapter]

Giuseppe Longo
2009 Parsing the Turing Test  
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
more » ... re this tentative imitation with Turing's 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. Turing's hinted distinction between imitation and modelling is developed, jointly to a discussion on the repeatability of computational processes in relation to physical systems. The main references are of a physico-mathematical nature, but the analysis is purely conceptual.
doi:10.1007/978-1-4020-6710-5_23 fatcat:tbybvft3tzfjzhwb3t3xilti4q