From: H C (firstname.lastname@example.org)
Date: Mon Mar 06 2006 - 20:29:26 MST
>Sounds promising! What is a superrecursive algorithm as the author defines
The gist of the idea is effective non-terminating algorithms in general.
Some examples he gives are called "inductive Turing machines" (of which
Turing machines, including the universal Turing machine, are special cases),
which are said to solve the halting problem, as well as basically annihilate
the "absolute" interpretation of the Church-Turing thesis.
Also he describes something called limit Turing machines. His math looks
really solid (most of it is beyond me). He takes a formal and very thorough
approach, and there are probably more references to other works than there
are sentences in the book (really).
In a strange twist of fate, I am reading The Emperor's New Mind at the same
time, and (although the math is beyond me, like I said), from an abstract
perspective, it appears as though Superrecursive Algorithms completely
dominates the ideas of Penrose.
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