Comments on `Two Undecidable Problems of Analysis'

Author: Scarpellini B.

Source: Minds and Machines, Volume 13, Number 1, February 2003 , pp. 79-85(7)

Publisher: Springer

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

Language: English

Document Type: Research article

Affiliations: 1: Mathematics Institute, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland

Publication date: 2003-02-01

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