I'm trying to understand the Church-Turing thesis, and it's philosophical implications, and I can't seem to figure out something from reading Wikipedia. Perhaps some of the knowledgeable people here can help?
I think that I'm referring to the Physical Church-Turing Thesis (PCTT), which I understand to mean "anything that can be physically calculated can be calculated by a Turing Machine".
Suppose you have a machine that spits out random bits, perhaps generated by a quantum-mechanical process. The output can be interpreted as the binary representation expansion of a number between 0 and 1. In the limit, this will (almost surely) approach a non-computable number. But writing out arbitrarily many digits of a non-computable number is something that no Turing machine can do. Is the explanation that:
1) this a violation of PCTT,
2) the present ignorant poster has misunderstood PCTT
3) the quantum-mechanical process isn't as random as I think?
Or something else?
Thanks for any clarification.
I think that I'm referring to the Physical Church-Turing Thesis (PCTT), which I understand to mean "anything that can be physically calculated can be calculated by a Turing Machine".
Suppose you have a machine that spits out random bits, perhaps generated by a quantum-mechanical process. The output can be interpreted as the binary representation expansion of a number between 0 and 1. In the limit, this will (almost surely) approach a non-computable number. But writing out arbitrarily many digits of a non-computable number is something that no Turing machine can do. Is the explanation that:
1) this a violation of PCTT,
2) the present ignorant poster has misunderstood PCTT
3) the quantum-mechanical process isn't as random as I think?
Or something else?
Thanks for any clarification.
via JREF Forum http://ift.tt/1f6czlS
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