2008/12/26 Günther Greindl <guenther.grei...@gmail.com> wrote:

>> And this assumption is quite close to comp in the sense that nobody
>> knows about
>> any "natural" machine not being turing emulable. Even quantum machine,
>> accepting QM without collapse.
> That is true, but we have to be careful in our reasoning.
> Look at Thesis M:
> http://plato.stanford.edu/entries/church-turing/#Bloopers
> That is quite different from CT. And while the two may be identical in
> the real world (empirical question), they are logically distinct.
> (and, as you can read in the article, hypercomp would refute comp,
> showing that logical distinction remains even if we can let them
> coincide in this universe).
>> All known physical causal system are Turing emulable.
> Yes - "known". There could be others (I don't believe it, but there could)

From the SEP article:

"Turing did not show that his machines can solve any problem that can
be solved "by instructions, explicitly stated rules, or procedures",
nor did he prove that the universal Turing machine "can compute any
function that any computer, with any architecture, can compute". He
proved that his universal machine can compute any function that any
Turing machine can compute; and he put forward, and advanced
philosophical arguments in support of, the thesis here called Turing's
thesis. But a thesis concerning the extent of effective methods --
which is to say, concerning the extent of procedures of a certain sort
that a human being unaided by machinery is capable of carrying out --
carries no implication concerning the extent of the procedures that
machines are capable of carrying out, even machines acting in
accordance with 'explicitly stated rules'. For among a machine's
repertoire of atomic operations there may be those that no human being
unaided by machinery can perform."

Is this just being pedantic in trying to stick to what the great man
actually said? What is an example of a possible operation a machine
could perform that a human, digital computer or Turing machine would
be unable to perform?

Stathis Papaioannou

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