Re: A modern view of the halting problem


Alex McDonald wrote:

Cites? I would be interested to see any references that are
categorically as definite as your statement "does *not* apply to
humans". You appear to be suggesting that the human mind is a
hypercomputer or some form of quantum device. None of the articles or
literature I have read is so dogmatic as to claim this.

I am simply suggesting that the human mind is not bound by Church's
hypothesis.

But if you want a citation, try here: (the first thing that came up in
Google when I ask for "incompleteness theorem"):

http://www.miskatonic.org/godel.html

In particular:

"Gödel's Theorem has been used to argue that a computer can never be
as smart as a human being because the extent of its knowledge is
limited by a fixed set of axioms, whereas people can discover
unexpected truths ... It plays a part in modern linguistic theories,
which emphasize the power of language to come up with new ways to
express ideas. And it has been taken to imply that you'll never
entirely understand yourself, since your mind, like any other closed
system, can only be sure of what it knows about itself by relying on
what it knows about itself."





any proof which is derived from his proof also applies to both
humans and computers. There is no "wiggle room" for a human to "step
outside the box" and decide what a computer can not decide.

Yes, there is. Try reading Godel's incompleteness theorem some time.

How does this apply?

A program that runs and decides something about another problem is
bound by the limitations of the system on which it runs. People can
think "outside the box" (the box being the computer in this case, the
"unexpected truths" from the paragraph above).


What proof do you have that these are "outside the box" or
uncomputable?

There is no proof that a human being can compute any undecideable
problem, but the fact that no one has provided a proof demonstrating
that humans cannot solve such problems (or, at least, recognize them)
offers us a little hope. Computer programs have no such hope.

That's why, for example, designing an *interactive* disassembler is
always a good idea. We know that a computer program cannot
automatically disassemble any computer program, but thus far, human
beings have been pretty good at solving this problem, correctly
disassembling lots of programs that automated software has failed on.




So long as the
argument derives from Turing's proof, then anything which is undecidable
by a computer, is also undecidable by a human.

Wrong.

Cites.

See above.
Cheers,
Randy Hyde

.

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