Re: noncomputability

From: John Stick (
Date: Thu Jul 26 2001 - 02:02:17 MDT

Mitchell J. Porter wrote:

> John Stick said
> > Once you
> > find a "new physics" phenomenon that is uncomputable, if you ever do,
> > I will bet the uncomputability will be able to be manifested in a
> > substrate employing only the old physics as well. Uncomputability is
> > ultimately a mathematical phenomenon, not a phvsical one, and it will
> > be independent of the details of brain chemstry or physics.
> This doesn't make any sense.

Perhaps. It was certainly less than clear, so let me try again. My
argument is that one must be careful to distinguish between the properties
of the substrate of the computation and the properties of the computation
itself (and that the argument from Penrose seems troubling only if one runs
them together). We don't think that the difference between a digital and
analog computer arises from constructing one of digital matter and one of
analog matter. We don't think that a computer doing Euclidian calculations
must be situated in Euclidian space, while one doing nonEuclidian
calculations must be situated in nonEuclidian space. We don't think that
the transition to quantum computing will by that mere fact alone make our
computers better at calculating the position of an electron. Yet the
argument from Penrose is assuming a direct connection from a noncomputable
physical event to a noncomputable thought process, (I agree with your gloss
on what a noncomputational physical event would be)and a very strong
connection at that: not merely causal, but some form of necessary and
sufficient relationship, so that the thought process cannot be instantiated
on a different type of physical substrate. This struck me as being remotely
possible, but extremely unlikely. That is, the relationship is very
unlikely even if both forms of uncomputability are true of humans. I could
think of no other mathematical property that one might even be tempted to
think could be exclusively passed on from substrate to thought in such a
way. And so I argued unclearly above that if we have a difficulty in
reproducing human quality thought, it will most likely be for reasons that
are independent of the physical substrate.

Your example of an oracular function would work in tying thought to a
quantum process (which could in theory "look forward in time"), if it
seemed to have anything to do with how we humans think. But if foretelling
the future is the best example we can come up with of an uncomputable brain
event/ mind process pair, I think that shows the weakness of the argument
from Penrose.

One could argue that uncomputability is so rare that if you find it in two
related areas, brain physics and thought processes, they must be intimately
related. I think that really boils down to a belief that the only way a
mental process could be uncomputable is if it arises from an uncomputable
physical process. (Maybe so, and if so then the paragraph I wrote that you
quoted above, if not nonsense, is yet incorrect.) But even so, this seems
to me much more reassuring than disturbing. If the only fundamental block
on the road to AI were the small possibility that a noncomputable quantum
process, present in our brains and not reproducable in our devices, is
essential to human quality mentation, I would be elated. I am much more
worried that the "frame" problem will slow the progress to AI down by 40-50

My overall point, which I think survives all this, is that the appeal to
Penrose's hypothetical about qualia, which is meant to strengthen a general
concern that AI cannot be constructed by giving the concern some
particularity, instead weakens it.

John Stick

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