Hypercomputation: Philosophical issues
type: Item
instance of: scholarly article
title: Hypercomputation: Philosophical issues
zbMATH Open document ID: 1055.03007
author: B. Jack Copeland
published in: Theoretical Computer Science
publication date: 2004-08-04T00:00:00Z
review text: The term hypercomputation refers to the computation of functions or numbers which are uncomputable by a universal Turing machine. In this paper the author surveys several models of hypercomputation resulting from acceleration, asynchronous coupling and environmental interaction of standard Turing machines. He also considers hypercomputation based on ``random'' input and the measurement of observables. Well-known epistemic and physical objections to the possibility of hypercomputation are discussed. They concern the identification and verification of the presence of a non-recursive source and the very realizability of such a source under various finiteness conditions. The author attempts to rebut these ``a priori'' qualms. Accordingly, he asserts that the possibility of hypercomputation is a downright empirical question. The author then defends the relevance of Turing's conception of an oracle machine for the hypercomputation debate. Finally the paper contains a brief but informed exegesis of Turing's writings on the notion of machine, the scope of computability, and their relation to mind and learning.
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 68Q05
Mathematics Subject Classification ID: 03D99
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 68-03
zbMATH DE Number: 2081207
zbMATH Keywords: Turing
zbMATH Keywords: Church
zbMATH Keywords: Super-Turing
zbMATH Keywords: oracle
zbMATH Keywords: mind
zbMATH Keywords: epistemic and physical objections to the possibility of hypercomputation
MaRDI profile type: Publication
full work available at URL: j.tcs.2003.12.014
OpenAlex ID: W2133694272
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DOI: 10.1016/J.TCS.2003.12.014
description: scientific article; zbMATH DE number 2081207