From: axs@cs.bham.ac.uk (Aaron Sloman)
Newsgroups: comp.ai,comp.ai.philosophy
Subject: Re: discussion with Penrose
Date: 23 Dec 92 22:46:02 GMT
Organization: School of Computer Science, University of Birmingham, UK

hughes@mercury.cis.udel.edu (John Hughes) writes:

> Date: 22 Dec 92 22:16:13 GMT
> Organization: University of Delaware, Newark
> In article <1992Dec22.021109.4401@oracorp.com> daryl@oracorp.com
> (Daryl McCullough) writes:
> ....
> > ..... There are only finitely many sequences of questions
> >that could possibly be asked within the time limit, so all it would
> >take in principle to pass it would be a finite lookup table that gave
> >an appropriate answer for each question. If you want to include such
> >questions as "What time is it?", or "Was it raining yesterday?", then
> >you would have to have inputs corresponding to the current time, the
> >weather report, etc. As long as the total information needed to answer
> >each question is finite, then a lookup table could in principle answer
> >it.
>
> This is not so. Though in a finite amount of time there are indeed only a
> finite number of questions I can ask, those questions can be chosen from
> an infinite set.
> ..... etc

No: Daryl is right.

It is a simple mathematical fact that if you have a discrete and
finite alphabet of characters c1, c2, c3, c4, ...... ck (e.g.
printed characters, phonemes, or whatever) and a minimum time dt
required to print or utter one of them, then in any finite time T
there will be an upper bound N (= T/dt) to the length of the
character string that can be produced in time T.

The total number of strings of length N of characters from an
alphabet of size k, is itself finite, i.e. k to the power N (and
most of these strings will be nonsensical). If you take all possible
strings of length less than or equal to N, the set is larger but
still finite. (Adding N finite numbers gives you a finite number).

So the questions cannot be "chosen from an infinite set", and the
lookup table will not need to have more than some finite number of
entries.

Of course, for even quite small N and k (e.g. N = 500, k = 2) the
table could be too large to fit into our universe (assuming that
there are no more than about 10 to the power 73 electrons in the
universe) but that doesn't undermine the argument about what is
theoretically possible.

Some people wish to include the CONTEXT in the conditions
determining the answer to the question. It can't be the *actual*
context that matters, but the *perceived* context, or perhaps the
history of perceived contexts since the "agent" was "born". If the
agent uses quantized sensory devices, such as an array of photon
detectors, (or a digital memory of finite size) then exactly the
same sort of argument can be used to show that for any finite period
there is only a finite (though admittedly huge) number of possible
sequences of perceived histories.

Thus the set of possible combined histories followed by a question
(or if you wish to include perceived questions as part of the
history, then just the set of possible histories) that can occur in
any bounded time period (e.g. 1000 years) will also be finite, and
therefore appropriate responses can, in principle, be associated
with them, in a *finite* lookup table.

It would be possible to reduce the size of the table and the lookup
time by transforming the table into a discrimination tree by merging
histories with common initial strings, though it would still, for
any reasonable time period, be too large to fit in our universe
(which doesn't matter for the argument).

It is because, on the assumption of a quantised universe, a finite
table-driven machine can in principle pass *any* behavioural test
you like (not just the Turing test) that I argued in my review of
Penrose (in the Journal Artificial Intelligence, August 1992) that
all such behavioural tests are inappropriate as definitions of
intelligence, or definitions of any particular mental state.

It's not *what* behaviour is produced but *how* it is produced that
makes it reasonable to ascribe mental predicates to an agent.

(Of course, what it does may be compelling evidence concerning how
it does it, if you make enough assumptions, and that's why we don't
poke inside people's brains before regarding them as intelligent,
but that's irrelevant to the conceptual argument.)

-------------------------------------------------------------------

I believe that this simple fact is all the truth that lies behind
Searle's claim that the causal powers of brains, i.e. *how* they do
things, at some appropriate level of description, would need to be
replicated in order to replicate human intelligence.

Corresponding to different levels of description of how brains do
what they do there are different "Strong AI" theses about what can
be replicated on a Turing machine.

E.g. If all the strong AI thesis requires is replicating
input-output behaviour via fixed-size digital interfaces, then the
finite lookup table argument trivially suffices to prove the truth
of strong AI.

If there are things in the brain at the relevant level of
description that involve asynchronous concurrent processes with
continuously varying speeds, then it may or may not be possible for
a single Turing machine to replicate them, depending on the precise
kind of asynchrony. (I think).

If there are non-digital, e.g. continuously varying, processes that
play an essential role in the relevant level of description of how
the brain does things, and Strong AI requires these processes to be
replicated, then it is trivially true that a Turing machine cannot
replicate them. (This seems to be what some people claim about
neural systems.)

Additional cases are discussed in my review of Penrose.

Thus some versions of the Strong AI thesis are trivially true,
others trivially false, and some interestingly open, i.e. whether
there is some interesting description of how brains do things that
cannot be applied to any Turing machine.

However most people who discuss the Strong AI thesis fail to
distinguish the different versions, and consequently their
disagreements are likely to be at cross purposes, making argument
futile.

Aaron
---
-- 
Aaron Sloman, School of Computer Science,
The University of Birmingham, B15 2TT, England
EMAIL   A.Sloman@cs.bham.ac.uk  OR A.Sloman@bham.ac.uk
Phone: +44-(0)21-414-3711       Fax:   +44-(0)21-414-4281