  ‘Calculable by finite means’ was Turing's characterisation of computability, which he justified with the argument that ‘the human memory is necessarily limited.’ (Turing 1936, p. 231). The whole point of his definition lies in encoding infinite potential effects, (e.g. the printing of an infinite decimal) into finite ‘tables of behaviour’. There would be no point in allowing machines with infinite ‘tables of behaviour’. It is obvious, for instance, that any real number could be printed by such a ‘machine’, by letting the Nth configuration be ‘programmed’ to print the Nth digit, for example. Such a ‘machine’ could likewise store any countable number of statements about all possible mathematical expressions, and so make the Entscheidungsproblem trivial.