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 Certainly the arguments I've made in the "fantasy" thread must be withdrawn and reconsidered.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. Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=25584