X-Message-Number: 9244
Date: Thu, 05 Mar 98 16:24:57
From: Mike Perry <>
Subject: Re: CryoNet #9243
Thomas Donaldson raises some questions over my posting #9238, where in
particular I say that
>I think that "I" could, in principle, be emulated
>on or in a digital device. This conclusion seems fairly solid, based
>on quantum mechanics and the idea that, in effect, the whole of
>reality seems equivalent to a very large (hopefully infinite or
>unboundedly large) digital device.
Although we may think of a "digital device" as a finite construct,
e.g. a Turing machine with a finitely inscribed tape, for the most
general model I would allow an infinitely inscribed tape. I make the
conjecture that reality as a whole can be regarded as such a system,
which has some interesting consequences.
Thomas writes,
> Well, Mike! What is this digital business and why is it important?
Basically, the "digital business" amounts to a claim that all
significant events happen in discrete jumps, and events involving finite
constructs such as you and me have finite descriptions and form a
denumerable set, rather than being like the real numbers which occupy
a larger, nondenumerable set. (It leads to the conclusion that a
universal resurrection ought to be possible in principle, in a
universe that supports the immortality of some sentient beings.)
Moreover, equivalent systems must
produce equivalent effects. If I emulate, over some period of
time, in some digital device, a system of interacting atoms that
experiences emotion, say, a human being, a corresponding set of
emotions must recur in my digital device. (This does not mean
that the device "itself" has the emotions, but that it is supporting
a system that has emotions--I make a distinction between the two.)
This is more or less the claim of strong AI. It is useful and convenient,
for some of the
positions taken in my book, but perhaps not absolutely essential, at
least for the more important points I try to make. But I think the
"digital" conlcusion is warranted, at least if we invoke the
quantum-mechanical analogue of the Church-Turing thesis that is noted
in Deutsch's *The Fabric of Reality*. Everything is a quantum system,
ourselves, computers, etc. It's hard to see how we can escape from
that.
Thomas continues,
>I even gave you a reference to a paper in which a machine was described which
was
> PROVABLY not a Turing machine (a neural net with incommensurable lengths of
> message-paths between nodes). What did you think of it? You must have
> reasons to brush off something like that so easily.
>
And I thank you again for this reference ("Computation beyond the
Turing Limit", by Hava T. Siegelmann, *Science* v.268 p. 545-8, 28
Apr '95). When your post came in today
I knew I had to study this paper more closely than I had--and now
I have. The main computational model the author describes is
like a Turing machine, except that infinite rewriting of the 2-way
infinite tape is allowed to occur in finite time, subject to certain
rules. This is beyond the
power of Turing machines, since by an appropriate, infinite
inscribing, we can encode the solution of the unsolvable
halting problem and make it accessible. But on
the other hand, Siegelmann's model is only equivalent
in computing power to a certain
class of neural net, as is also noted, which makes this (finite)
neural net also more powerful than Turing machines. The neural net,
however, has to have neurons that individually are able to encode
infinite letter sequences "using a Cantor set representation"
(see "Sketch of Proof, Theorem 1" p. 547). Can a real neuron reliably
do this, and in particular, could one be inscribed with a
*non-computable* letter sequence, as would be required to exceed the
power of Turing machines? In any case, it is clear, if I haven't
crossed a wire somewhere, that the Siegelmann model is not more
powerful than a Turing machine *with an infinitely inscribed tape*
which (with equivalents) is the most general system I allow for the
digital paradigm.
> As you may remember me saying on other occasions, I have no problem with
> the idea that we may somehow and someday construct a "brain" capable of
> the same kind of thinking that we do and the same kind of perceiving, too.
> But I think we are on very shaky ground if we blithely assume that
> this "brain" will be a digital computer of any kind.
I would allow a pretty general kind of computer,
something based around the ideas
of Deutsch, which I think would apply to emulating any finite chunk of
spacetime and whatever is going on therein. There is really not a
sharp distinction beween "reality" and "reality emulated in some
type of computer"--the one shades into the other. But as a
philosophical point, the "digital" property, if it holds, has a
significance apart from other considerations, i.e. whether or not it
might be practical to carry out a particular emulation.
> I will make that
> a much stronger statement: a very good way to misunderstand completely
> how humans or other animals work is to assume that their brains act like
> computers.
Let's not misunderstand how computers can work, especially when we
are considering "in principle" arguments rather than details of
actual implementations.
Endless best to all,
Mike Perry
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