Comments on `two undecidable problems of analysis'

Minds and Machines 13 (1):79-85 (2003)
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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DOI 10.1023/A:1021364916624
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