From: scerir (scerir@libero.it)
Date: Wed Apr 17 2002 - 00:41:02 MDT
A truly magical prospect. I wonder what would be
the physical manifestation of a solution to an unsolvable
problem - would it open the way to actions which
at present seem to be forbidden by the known laws
of physics? (this is just a totally uninformed deliberation
on my part).
Rafal
There are more interesting papers ...
Incompleteness, Complexity, Randomness and Beyond
Authors: Cristian S. Calude
Comments: 16 pages
http://arxiv.org/abs/quant-ph/0111118
Goedel's Incompleteness Theorems have the same scientific
status as Einstein's principle of relativity, Heisenberg's
uncertainty principle, and Watson and Crick's double helix
model of DNA. Our aim is to discuss some new faces of the
incompleteness phenomenon unveiled by an information-theoretic
approach to randomness and recent developments in quantum
computing.
Strong Determinism vs. Computability
Authors: C. Calude, D. I. Campbell, K. Svozil, D. Stefanecu
Comments: 13 pages
http://arxiv.org/abs/quant-ph/9412004
Are minds subject to laws of physics? Are the laws
of physics computable? Are conscious thought processes
computable? Currently there is little agreement as to
what are the right answers to these questions. Penrose
goes one step further and asserts that: {\it a radical
new theory is indeed needed, and I am suggesting, moreover,
that this theory, when it is found, will be of an essentially
non-computational character.} The aim of this paper is
three fold: 1) to examine the incompatibility between
the hypothesis of strong determinism and computability,
2) to give new examples of uncomputable physical laws,
and 3) to discuss the relevance of G\"odel's Incompleteness
Theorem in refuting the claim that an algorithmic theory
---like strong AI---can provide an adequate theory of mind.
Finally, we question the adequacy of the theory of
computation to discuss physical laws and thought processes.
Cristian S. Calude site :
http://www.cs.auckland.ac.nz/~cristian/
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