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C00002 00002	%penros.3[s90,jmc]	Another try at review of Penrose for Reason
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%penros.3[s90,jmc]	Another try at review of Penrose for Reason
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\noindent {\it The Emperor's New Mind}, by Roger Penrose.
Oxford University Press, Oxford, New York, Melbourne,
1989, xiii + 466 pp., \$24.95. ISBN 0-19-851973-7


	The first programmable computer was in 1948, and the first
person to work full time on making intelligent computer programs
began in 1954.  Artificial intelligence (abbreviated AI) requires
programming intellectual mechanisms and putting knowledge in
the memory of the computer.  Some intellectual mechanisms were
identified in the first years of AI research, and some of the
needed knowledge was easy to express in a usable way.  By 1980
enough was known to make possible a minor industry---expert systems
that help people with some not-too-difficult intellectual problems
that arise in business and industry.

	Other intellectual mechanisms are harder to program and even
hard to identify precisely.  Much of the commonsense knowledge that
everyone possesses has proved difficult to express in a way that
arbitrary computer programs can use.  As a result present AI programs
to use knowledge in a specialized form.

	A major theme in AI has been the expression of knowledge
in the form of sentences of mathematical logic.  Sometimes this
knowledge is used via logical deduction, but sometimes it is used
by ad hoc computer programs.  A major discovery around 1980 is
{\it formalized non-monotonic reasoning}.  It
allows jumping to conclusions that are sometimes denied when more
information is obtained.  It expresses the advice of the 12th
century philosopher William of Ockham ``not to multiply entities
beyond necessity'' in a form that computers can use.  This greatly
expands the power of mathematical logical methods in application
to common sense.

	Major conceptual problems remain before we can make
computer programs that can compete with people across the
intellectual spectrum.  Someone may get the required ideas in the
next five years, but it is not impossible that it will take five
hundred years.

	Some people think that we will never get computer programs
as smart as humans, and that brings us to the present book.

	Roger Penrose is a mathematician at Oxford University,
famous for his work on black holes and for his invention of the
Penrose tiles.  Like square or hexagonal floor tiles they can
cover any flat surface provided you trim the edges.  Unlike
squares or hexagons, Penrose tiles, which are modified pentagons,
only cover the surface in an irregular way.  (``Non-periodic'' is
the technical term).  That there should be anything like the
Penrose tiles was quite unexpected, and shortly after Penrose
announced them, non-periodic crystals were discovered when x-ray
diffraction gave pictures with a pentagonal symmetry that the
crystallographers thought were impossible.

	Penrose undertakes to refute ``strong AI'', a notion
invented by the University of California philosopher John Searle
in order to be refuted.  According to Penrose and Searle, {\it strong
AI} is the doctrine that intelligence is only a matter of
having the right algorithm.  Searle argued that no matter
what a computer program was able to do it wouldn't be intelligent
but doesn't declare any specific limit on what a program might
do.  Penrose presents Searle's argument on this point but goes
on to doubt that a program on a computer based on present day
physics could equal human performance.

	For the first point he uses Searle's ``Chinese room''.
This room contains a man who doesn't know Chinese
and a book of rules.  Chinese sentences are passed under the door,
and the man uses the book of rules to decide what to do with them.
Obeying the rules, he does various computations with the
input sentences, and copies some Chinese characters onto paper
and passes back out under the door.  Searle postulates that this
results in a good conversation with a (very very patient) Chinese
outside the door.  It is pointed out that the man needn't understand
Chinese in order to carry out the rules, and it is therefore argued
that a computer carrying out the rules wouldn't understand Chinese
either.  Therefore, computers don't understand.

	Indeed, computer hardware doesn't understand the programs
it executes or what these programs themselves ``understand''.
This is particularly clear when a time-shared computer is executing
several different programs simultaneously.  The programs may have
quite different capabilities.  However, the relation of the computer
program to certain facts may be quite similar to the relation of
a human who understands the facts to them.  The similarity resides
in the fact that the human and the computer can use the facts to
accomplish very similar tasks.  Searle and Penrose confuse the
capabilities of a computer with the capabilities of its program.
If multiple personalities were really encountered in daily life,
ordinary language would use different words for a person's body
and the various personalities inhabiting it.

	Unfortunately, there still aren't computer programs that
can engage in plausible general purpose conversation, and one
of the major obstacles to achieving it is that we still don't
understand well enough what is involved in {\it understanding} a
language.

	The Chinese room argument doesn't purport to restrict
what computer programs can do, only whether it counts as
intelligence.  Penrose goes on to appeal to Kurt G\"odel's 1931
theorem about the incompleteness of arithmetic to argue that
there are tasks a person can do that a computer can't.  G\"odel
showed that if you have a formal system of arithmetic that is
non-contradictory, you can construct a sentence in the language
of arithmetic that is clearly true but which has no proof in the
system.  In fact the sentence can be taken as one whose intuitive
meaning is that the system is non-contradictory.  I apologize for
the complexity of the last sentence, but I don't see how to
avoid it.

	The simplest reply to Penrose is that forming a G\"odel
sentence from a proof rule is just a one line program in the LISP
programing language.  Imagine a dialog between Penrose and a
mathematics computer program.

\noindent Penrose: Tell me the logical system you use, and
I'll tell you a true sentence you can't prove.

\noindent Program: Your proposal is like a contest to see who can
name the largest number with me going first. You tell me what
system you use, and I'll tell you a true sentence you can't
prove.

\noindent Penrose: I don't use a fixed logical system.

\noindent Program: I can use any system you like, although mostly
I use a {\it variant of set theory called ZF.}
Would you like me to print you a manual?

I'm programmed to use any {\it extension of arithmetic by the
addition of self-confidence principles of the Turing-Feferman
type iterated to constructive transfinite ordinals.}

\noindent Penrose: But the {\it constructive ordinals aren't
recursively enumerable}.

\noindent Program: So what?  You supply the {\it extension} and
whatever confidence I have in the {\it ordinal notation}, I'll grant
to the theory.  If you supply the confidence, I'll use the
theory, and you can apply your confidence to the results.

	All the italicized stuff in the above dialogue
is mathematical logical jargon.  I included it to illustrate at
what point a rigorous argument gets technical.  The non-technical idea
is that is that you can strengthen a logical system by adding an
assertion that it is consistent or has some other nice
mathematical property, but then you get a new system that also
can't prove itself consistent.  You can repeat this proces
infinitely often but so can a computer program.

	Penrose has an interesting positive proposal arising
from his research in Einstein's general theory of relativity.
This theory, which originally had little connection with experiment,
is getting more support and applications all the time, especially
in astronomy.  However, it is inconsistent with quantum mechanics
in its present form, and quantum mechanics has even more experimental
support.  Something has to give, and most physicists would like
to figure out how to modify general relativity to make it fit
quantum mechanics.  Penrose wants to go the other way, to modify
quantum mechanics to fit general relativity.

	His idea is that quantum mechanics works only on a small
scale in which the {\it curvature of space-time} consequent to
general relativity is too small to have much effect.  On a larger
scale, he thinks quantum mechanics doesn't give the right
answers.  Penrose hopes that in some way he can't now specify,
this would permit machines with an intelligence not achievable by
computer programs running on present machines.  In fact, he
conjectures that human intelligence is based on a breakdown of
ordinary quantum mechanics.  This is because he thinks G\"odel's
theorem shows humans can intuit facts computers can't infer.

	Although Penrose's idea is vague, it
might be possible to test whether quantum mechanics is valid
on a larger scale than that at which it has been tested.  This is
because some quantum mechanical interactions can take place, not
at a definite point, but over a region.  Quantum mechanics tells
us what experimental results to expect, but maybe Penrose would
expect something different.  I'd bet on quantum mechanics, partly
because I think presently known physics is entirely adequate to
allow computer programs of human-level intelligence.  All it requires
is a few more geniuses to figure out how to do it.

	There's lots more in the book than the argument about AI,
although that's the main thread.  Penrose gives very nice expositions
of his famous tiles, of Turing machine computers and of some
problems in the philosophy of mathematics.  I think that to understand
all of it requires more mathematics than Penrose purports to
assume, but if you get stuck just skip a section.  You'll soon come
to something interesting that's not so mathematical.
\smallskip\centerline{Copyright \copyright\ 1990\ by John McCarthy}
\smallskip\noindent{\fiverm This draft of PENROS.3[S90,JMC]\ TEXed on \jmcdate\ at \theTime}
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