Re: Penrose vs the Robot


Stephen Harris wrote:

> >
>
> Penrose put forth the view that a human mathematician could surpass
> a computable process. Recall that Turing said that a computable
> program could produce anything that a human could that was done
> by rote or a mechanical procedure; pencil, paper, eraser and requring
> no ingenuity. The Penrose view may be correct, but his argument was
> quite a bit less than convincing. That does nothing to establish the
> opposite view that a computable program can discover all mathematical
> truth that a human can recognize (perhaps more). Just like the current
> failure of programs to recognize faces that an infant can recognize, does
> not establish that facial recognition is a non-computable process beyond
> the ken of robotic simulation. Absence of evidence is not evidence of
> absence. Chemical reactions, digestion, are considered analog. There is
> evidence that firing of neurons employs both digital and analog processes.
>
> I think Daryl's argument is that all brain processes, whether analog or not
> can be simulated by a computable process that there is a corresponding
> digital function to produce the same output, even if the inner process
> differs. Recall that a continuous process can be simulated by discrete
> pulses of very high frequency.

Strictly speaking you are correct. We can grid the four-dimensional
Universe (or at least the Universe to some large finite limit) in a
very fine way, so finely that for all pratical purposes, our
perceptions are unable to distinguish the difference between the grid
and continuous reality. Because points on the lattice would be finite,
then the behaviour of what goes on is necessarily computable (assuming
the usual axioms).

But this begs the question, in the sense that ultimately the question
is not whether a theoretical computer can imitate human behaviour, but
whether an actual computer, with finite resources, can. Certainly it
is of little interest if you are endowing the computer with more
resources than posited in the Universe. I think in such cases it also
becomes reasonable to throw out the Successor Axiom, in which case the
assertion that there is a computable function mimicking a lattice does
not follow automatially.

Now maybe a computer will be able to imitate a muscle's behaviour. I
don't know of any valid argument against, but I don't see any valid
argument for, other than actually constructing the thing. Basically I
think arguments *for* in this domain (either Penrose's or Daryl's) are
almost always invalid. Peoples' fancies catch hold and they almost
always try to establish too much.



We do not know, we will probably not know for some time, and we may
never know.

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