Minds and Machines

, Volume 13, Issue 1, pp 79-85

First online:

Comments on `Two Undecidable Problems of Analysis'

  • Bruno ScarpelliniAffiliated withMathematics Institute, University of Basel

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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.

analogue computer hypercomputation neural computation Turing machines undecidability