; School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K.; in mathematics ar...
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Abstract. Computability concerns information with a causal – typically algorithmic – structure. As such, it provides a schematic analysis of many naturally occurring situations. We look at ways in which computabilitytheoretic structure emerges in natural contexts. We will look at how algorithmic structure does not just emerge mathematically from information, but how that emergent structure can model the emergence of very basic aspects of the real world. The adequacy of the classical Turing model of computation — as first presented in  — is in question in many contexts. There is widespread doubt concerning the reducibility to this model of a broad spectrum of real-world processes and natural phenomena, from basic quantum mechanics to aspects of evolutionary development, or human mental activity. In 1939 Turing  described an extended model providing mathematical form to the algorithmic content of structures which are presented in terms of real numbers. Most scientific laws with a computational content can be framed