Comments on `two undecidable problems of analysis'

Minds and Machines 13 (1):79-85 (2003)
Abstract
We first discuss some technical questions which arise in connection with the construction of undecidable propositions in analysis, in particular in connection with the notion of the normal form of a function representing a predicate. Then it is stressed that while a function f(x) may be computable in the sense of recursive function theory, it may nevertheless have undecidable properties in the realm of Fourier analysis. This has an implication for a conjecture of Penrose's which states that classical physics is computable.
Keywords analogue computer  hypercomputation  neural computation  Turing machines  undecidability
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