José Félix Costa fgc at math.ist.utl.pt
Mon Jan 12 11:12:23 EST 2004


A different but more exciting view is then: the physical CT versus the
mathematical CT, the first corresponding to Robin's points 1 and 3, the
second corresponding to Robin's 2 and 4. Physical CT corresponds to a
discussion being held by Penrose and others since his first book.

Yes, we have large bibliography on the subject, e.g.,

The Universal Turing Machine
A Half Century Survey
Edited by Rolf Herken

Machines and Thought
The Legacy of Alan Turing
Edited by Peter Millican and Andy Clark
Oxford University Press

Also recommend is the excellent monograph

Computing more than the Turing machine
by Toby Ord

Remarks: (1) many books INDEED (!) make use of the Church-Turing thesis to
prove Robin's 1 and 3; (2) recent studies in physics and computability make
the point about the effectivity of the Halting -- take as example

Non-Turing computations via Malament-Hogarth space-times
by Gábor Etesi
Yukawa Institute for Theoretical Physics



J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc at math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm

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