Re: A modern view of the halting problem

randyhyde@xxxxxxxxxxxxx wrote:
Charles A. Crayne wrote:


To begin with, since the generalized proof applies to both humans and
computers,

This is where you are completely mistaken.
The generalized proof of undecideability (the generic problem posed by
the halting problem) does *not* apply to humans. It applies to *Turing
Machines* (an abstract model which models all real computers, as far as
we know). Human problem solving processes are *not* modelled by the
Turing machine. Yes, a human being *can* follow an algorithm
step-by-step, and by doing so be limited to the same results as any
proof about Turing machines, but humans can also transcend that.

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.


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?

Unless you can prove that the Human brain is Turing complete, you'll
have to accept the fact that humans *do* operate "outside the box".
Humans have things like "brainstorming", "flashes of brilliance",
"divergent thinking", etc., etc., that computers don't benefit from.


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


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.

[rest snipped]

--
Regards
Alex McDonald

.

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