From: Patrick van den Berg (cirandar@yahoo.com)
Date: Wed Sep 17 2003 - 11:31:29 BST
Hi Pete,
> It featured Gregory Chaitin and Roger Penrose and there were some
> interesting suggestions, that ‘quantum computers’ solve problems in
> fewer steps than is logically possible,
That's not really true. Quantum computers are logical. Only they solve
problems faster then ordinary computers by using qubits, a '0' and a '1'
at the same time. That means that with 1 qubit, you can perform 2 steps
at once. With 2 qubits, you have a superposition of 4 steps (<01>,<00>,
<10>, <11>), and with 3, 8 steps. In general a quantum computer with N
bits can compute 2^N (N=power) at the same time.
There exist now quantum computers with maybe 3 qubits: more than that is
technologically not possible thus far. But there must be practical
limits to this theoretical computing capability.
Also there are problems with getting the solution out of a quantum
computed result, because when you perform a classical measurement, you
only can see one of the results of the many simultaneous computations.
Someone told me that there were ways to get around this problem,
however. Anyhow, this quantum computing has interested me for some time,
and I know too little of it than I would like to :-)
> that you can’t start at one
> point in mathematics and use logic to understand mathematics as a
> whole,
> rather mathematics has islands of logic and the only way between them
> was inspiration and insight,
Islands of logic! Nice.
> and arguing that Artificial Intelligence
> solely based on logic and computability is doomed to failure.
Hm... I agree, it's on Penrose's interpretation of Goedel's theorem.
Quite interesting, we have had a discussion about .5 or 1 year ago here
on the MoQ on it. I didn't quite pull it off with me defending Penrose,
'cause I had forgot the details of his mathematical reasoning.
so I won't try and explain it here once again...
Anyhow, The Emperor's New Mind of Penrose (lying incidentally on my desk
right now) explains it thouroughly and understandable. It is a dense
book about physical theories all together: excellent if you don't want
another popular book on physics but something somewhere inbetween
popular and academic.
I hope someone else will try to formulate similarities between Penrose
and Pirsig. (Platt?) Never read anything from Gregory Chatin.
GReeting, Patrick.
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