X-Message-Number: 25584
References: <>
From: Peter Merel <>
Subject: Hypercomputation and the Singularity
Date: Wed, 19 Jan 2005 13:35:31 +1100

In researching the next round of replies on the "fantasy" thread I 
stumbled over Tien Kieu's 2002 paper that argues quantum computers can 
solve Turing-incomputable problems including the Halting Problem. See 
http://arxiv.org/abs/quant-ph/0110136 and more recently 
http://arxiv.org/pdf/quant-ph/0203034 .

Given a hypercomputer capable of Tien Kieu's Hamiltonian, we need only 
formally specify the parameters of MNT design and their constraints, 
and a globally optimal design will pop out without any delay. This 
presents a whole new ball game; no claim based on classical 
computability or complexity theory can stand.

The fundamentals of mathematics must be reframed to account for 
hypercomputation. The implications of such reframing for further 
physics and computer science aren't at all clear. Certainly the 
arguments I've made in the "fantasy" thread must be withdrawn and 
reconsidered. I encourage cryonet readers to consider Tien Kieu's 
papers and discuss their implications for AI and other fields.

Peter Merel.

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