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From: jsmith@king.mcs.drexel.edu (Justin Smith)
Newsgroups: comp.ai
Subject: Artificial vs. ''real'' intelligence
Message-ID: <1990Jul2.182411.4441@king.mcs.drexel.edu>
Date: 2 Jul 90 18:24:11 GMT
Organization: Drexel University, Dept. of Math. and Comp. Sci.
Lines: 104


\hsize=6in
\hoffset=.4in
\centerline {\it The Possible Limitations of Artificial
Intelligence.}
\medskip
\centerline{by}
\medskip
\centerline{Justin R. Smith}

Roger Penrose has suggested that the human brain
has properties that may enable it to carry out actions
that are not reproducible by any computer.  This
argument is used to imply that attempts to simulate the
reasoning cabability of the human mind mechanically are
essentially {\it futile}. His argument makes use of human
consciousness.  I contend that one can come to the same
conclusion without appealing to human consciousness.

The basic idea is:
\item {1.} that the human brain is a {\it physical
object}.
\item {2.} Physical objects have the potential for
performing activities that are not reproducible by a
computer.

We will couch this in the terms of Computability Theory. 
Consider two classes of functions defined (for the sake of
simplicity) with domain and range in the integers: 
{\it recursive} functions; and {\it physical}
functions.

{\it Recursive functions} are  essentially functions that
can be computed by executing a {\it computer program} of
some kind.

{\it Physical functions} are functions whose evaluation is
the result of observing some {\it physical process}. 
An example of this is the number of ticks on a geiger
counter per minute as a function of time.

\proclaim{Claim}.  The set of physical functions includes
the set of recursive functions.

This follows from the existence of physical
devices that are excellent {\it simulators} of Turing
machines --- I am using one to type this news item.  

On the other hand, it is quite likely that the set of
physical functions is {\it strictly larger} than the set
of recursive functions.  In fact,
quantum-mechanical phenomena suggest {\it precisely
this}.  Quantum mechanics contains many manifestations
of ``random'' phenomena  --- basically contending that
certain physical phenomena can only be analyzed {\it
statistically}.  One can interpret ``random'' as meaning
``not computable'' rather than ``entirely devoid of
meaning''.

The human brain, being physical, has a {\it natural
tendancy} to make use of {\it physical functions} rather
than recursive functions in its computations. 
Over the course of evolution (and we have to include the
evolution of the reptilian and mammalian as well as the
human brain) any physical functions that gave rise to
useful information {\it were utilized}.  A rat fleeing
from a predator didn't ask whether the decision to flee
was the result of a recursive function evaluation.

The human brain wasn't designed by engineers who have an
interest in {\it filtering out} physical phenomena that
cause it to {\it depart} from strict turing-machine
computations (i.e., the effects of random thermal noise). 
This is the only reasonable policy to follow in designing
computers
 --- no engineer (nor anyone else, for that matter) 
knows enough physics to ``program'' physical phenomena
{\it fully}.  By this I mean:  if ``random'' atomic
transitions turn out to really {\it mean something} we
don't know {\it what} they mean, or how to {\it exploit}
this ``information'' to solve problems.

The brain, on the other hand, has tens of millions of
years of ``experience'' at attempting to survive by any
means at its disposal, and it appears {\it likely} that
it makes use of physical computations that are {\it not}
Turing-computable. 

I feel, that if we must regard the brain as a ``computer
program'', we have to concede that it uses {\it many 
oracles} (in the sense of computability
theory)
\footnote*{Computability theory is concerned  (among
other things) with: a. the question of what {\it is}
Turing-computable and, b. if one is {\it magically given}
information that might {\it not} be Turing-computable
(such a source of information is called an {\it oracle})
what {\it other} conclusions can one {\it derive} from
this source via Turing-machine-type computations. (I.e.,
given two recursively unsolvable problems, can a solution
to {\it one} be {\it recursively transformed} into a
solution of the other).}. Even the overall high-level {\it
control mechanism} of the brain may be a physical program
that isn't Turing computable. \end