Hal,
I understand this. But the usual expectations of quantum orthodoxy are not
what I'm speaking about.
In this mysticism thing, I'm referring to the ideas of people who see modern
QM as a degenerate form of a wider case. Who see room for the empirical
validation of mysticism & spiritism in physics already hinted at by the
developments in quantum & computational science of the first half of the
20th century.
If quantum computations arise out of a much bigger set than the continuum...
(eg., in a many worlds situation - if the manifold was
(uncharacteristically) also propagated for each one of the superpositions
as, I think, the physics maverick Roger Gouin pointed out...), then it may
be possible to do wierd things.
Check my wording that you quote below... I'm not asserting things about
classical quantum machines, cool as they admittedly are; I'm suggesting
things about quantum weirdness that might arise if we continue the trail in
the 21st century - following the spirit of the formulations done in the
20th century... and what we might find when we go and actually build mature
quantum computers.
If quantum computations arise, not in this physical manifold but, beyond...
in some set much larger than that amenable to our current mathematical
analysis, then this might show up in the things that I mentioned.
Certainly the trail is suggestive - the QWF is deterministic to a flaw; yet
the stupid Born criterion isn't... I smell a rat there!
The nice thing about all this is that it's empirically testable - and we can
actually start doing real experiments shortly ( 3 - 10 years); as the
quantum computer technology becomes available.
Actually... hmmm... one is available - it's quite degenerate. A tunnel
diode. You can look at it as a quantum computer that outputs a random stream
of numbers. If it doesn't - you'd better ask why.
***************************
As for the very last part of your letter, remember the poor Turing machine
runs on some serious limitations, it's crummy tape is denumerable and not
even dense. Ugh!
So it's quite possible that quantum systems of the types we're positing are
not computationally isomorphic with an infinite Tiring (...er, Turing...)
machine. From that you might beable to swing a deterministic yet
'noncomputable' universe.
cymm
-----Original Message-----
From: hal@finney.org <hal@finney.org>
To: extropians@extropy.org <extropians@extropy.org>
Date: Thursday, August 31, 2000 3:05 PM
Subject: Re: Mysticism (WAS) E.S.P. in the Turing Test
>Cymm writes:
>> But once we develop quantum computers we'll probably find out: not only
will
>> they handle exponential problems in polynomial time - but they'll
probably
>> (in these weird scenarios) solve Turing Incomputable problems in
polynomial
>> time - or even flat time.
>
>Actually, no, quantum computers are not expected to solve exponential
>problems in polynomial time. More precisely, there are no problems
>known to be exponential on classical computers which are polynomial on
>quantum computers.
>
>Quantum computers can cut the exponent down on search problems, which
>are known to be exponential on both kinds of computers. The speedup
>is potentially even greater on some special math problems (factoring
>for example) but the true complexity of those problems on convential
>computers is not known.
>
>Quantum computers are not at all expected to solve Turing uncomputable
>problems like the halting problem. From what I understand, they are
>subject to the same proofs of uncomputability.
>
>Hal
This archive was generated by hypermail 2b29 : Mon Oct 02 2000 - 17:36:52 MDT