Bezerk's original comment makes two assumptions. 1) continuum phenomena are real and space is not merely quantized at a level which is undetectable by experiment (just because physics models it as a continuum doesn't mean it is so) 2) all of this precision actually makes a difference For instance, at the level of brain chemistry, who cares about quantum precision when thermal noises will swamp it anyway? (the Penrose argument even goes as far as assuming quantum gravity, a force pitifully weak, as a signficant factor) One of the reasons digital manipulation became popular was because analog data was too prone to error. Why will a quantum computer, which seems even more sensitive to external perturbation, be any different? And regardless of whether quantum computers work or not, they are still algorithmic if they can be simulated (however slowly) by a turing machine. It's a rigorous mathematical definition. Claiming otherwise uses algorithm in a manner different than was intended. It's like the way Ludwig Plutonium solves all those famous problems in sci.math by assuming different definitions of primality, etc. Quantum computers might be faster than classical computers, but non-algorithmic, I don't think so.
1) continuum phenomena are real and space is not merely quantized at a level which is undetectable by experiment (just because physics models it as a continuum doesn't mean it is so)
2) all of this precision actually makes a difference
On Tue, 26 Jul 1994, Ray Cromwell wrote: true. true.
For instance, at the level of brain chemistry, who cares about quantum precision when thermal noises will swamp it anyway? (the Penrose argument even goes as far as assuming quantum gravity, a force pitifully weak, as a signficant factor) What does that have to do with the above?
One of the reasons digital manipulation became popular was because analog data was too prone to error. Why will a quantum computer, which seems even more sensitive to external perturbation, be any different? Are you trying to say that things have to be digital to have noise imunity? If so, you are totally wrong. Examples abound from analog elctronics specifically transmission.
And regardless of whether quantum computers work or not, they are still algorithmic if they can be simulated (however slowly) by a turing machine. It's a rigorous mathematical definition. Claiming Sure, I never said otherwise, just that it is conceivable that some continum phenomina can't be described algorithmicly AT ALL. otherwise uses algorithm in a manner different than was intended. It's like the way Ludwig Plutonium solves all those famous problems in sci.math by assuming different definitions of primality, etc. Quantum computers might be faster than classical computers, but non-algorithmic, I don't think so. Hmmm, argument by plutonium? Try again.
Berzerk.
Berzerk:
2) all of this precision actually makes a difference true.
For instance, at the level of brain chemistry, who cares about quantum precision when thermal noises will swamp it anyway? (the Penrose argument even goes as far as assuming quantum gravity, a force pitifully weak, as a signficant factor) What does that have to do with the above?
The principle the arbitrary precision that comes from continuum is swamped by just about everything else so building a machine based on it is practically impossible?
And regardless of whether quantum computers work or not, they are still algorithmic if they can be simulated (however slowly) by a turing machine. It's a rigorous mathematical definition. Claiming Sure, I never said otherwise, just that it is conceivable that some continum phenomina can't be described algorithmicly AT ALL.
I wasn't talking specifically to you, I was talking to James Donald. It's conceivable that little green men also exist, do you have a particular example in mind of your non-algorithmic phenomena?
otherwise uses algorithm in a manner different than was intended. It's like the way Ludwig Plutonium solves all those famous problems in sci.math by assuming different definitions of primality, etc. Quantum computers might be faster than classical computers, but non-algorithmic, I don't think so. Hmmm, argument by plutonium? Try again.
Your turn. I already layed out the definition. I can quote it from as many automata theory texts as you like. One can not simply change the definition of algorithm just because one doesn't like it. If you do, you're no better than dear old Ludwig.
Ray Cromwell writes
And regardless of whether quantum computers work or not, they are still algorithmic if they can be simulated (however slowly) by a turing machine. It's a rigorous mathematical definition.
This is flagrantly false. A frog can be simulated, give infinite time and infinite tape size, but a frog is not an algorithm.
Ray Cromwell writes
And regardless of whether quantum computers work or not, they are still algorithmic if they can be simulated (however slowly) by a turing machine. It's a rigorous mathematical definition.
I think this is a misquote of the definition. If a turing machine can *perform* it, then it is an algorithm. Since a turing machine certainly cannot perform quantum "algorithms", then by definition they are not algorithms. -- --------------------------------------------------------------------- We have the right to defend ourselves and our property, because of the kind of animals that we James A. Donald are. True law derives from this right, not from the arbitrary power of the omnipotent state. jamesd@netcom.com
James A. Donald says:
If a turing machine can *perform* it, then it is an algorithm.
Since a turing machine certainly cannot perform quantum "algorithms", then by definition they are not algorithms.
If a turing machine can *perform* it, then it is an algorithm. Since a turing machine certainly cannot perform Sun Workstation "algorithms", then by definition they are not algorithms. Perry
Berzerk says:
On Wed, 27 Jul 1994, Perry E. Metzger wrote:
Since a turing machine certainly cannot perform Sun Workstation "algorithms", then by definition they are not algorithms. Sorry, a turing machine can.
I suppose the sarcasm impaired are everywhere. Perry
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Berzerk -
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Perry E. Metzger -
Ray Cromwell