Turing’s theory of computation

Abstract

In the paper On computable numbers, with an application to the Entscheidungsproblem (1936), Alan Turing described his computational machines as the idealized formal counterparts of the mechanisms at work in a real cognitive system, namely the one consisting of a human being performing calculations with paper and pencil. After a semi-formal description of Turing machines, I briefly present the mathematical meaning of Turing’s 1936 paper, showing that the soundness of Turing’s solution to the Entscheidungsproblem ultimately lies on some cognitive considerations, namely, the intuitive correctness of his analysis of the notion of effective procedure. Then, I discuss the historical and philosophical reasons that led to the widely accepted classic-computational interpretation of the Turing machine. Following Andrew Wells, I argue that this interpretation is wrong, because it treats the tape of a Turing machine as its internal memory, rather than as the external environment. Lastly, I introduce a different interpretation of the Turing machine’s architecture, namely Wells’ Ecological Functionalism, that recognizes the cognitive importance of Turing’s theory of computation.