CS80--Senior Seminar
Discussion Questions--Hodges
Jim Rogers
jrogers@cs.earlham.edu
Fall 2000
These are a few questions for thought and discussion.
- 1.
- In what ways are computing machines different in type than more
traditional sorts of machines? In what ways are they similar?
- 2.
- In distinguishing earlier computing machinery from ``computers'' in the
modern sense, people often cite capabilities like programmability, the ability
to modify program flow depending on the results of prior operations
(``conditional branching''), and the ability to operate on programs (of the
same type they execute) as ordinary data (``stored programs''). We can
classify computing machinery on the basis of whether or not they have these
capabilities.
Is the halting problem solvable for any of these classes of
machines? Which? Thinking, for a moment, of the human brain as a physical
device, does it necessarily fall into any of these classes?
- 3.
- The existence of uncomputable problems is necessarily dependent on how
we choose to model computation--we can only say that there are problems that
are not computable by any machine of some particular type. The diagonalization
argument sketched on pages 100-102, however, is quite general. It, in
essence, says that there are functions that cannot be computed by any machine
that can be described with finitely many symbols (``finitely presentable'').
But it doesn't really tell us anything intuitively meaningful about what
those functions might be. Turing, on the other hand, went on to argue that
there was a particular problem that is undecidable, at least for TMs--the
halting problem. This is actually also quite general, the argument works for
any notion of computation for which there is a universal program
(Universality).
How does the argument depend on Universality?
- 4.
- Note that this is stronger than simply being able to operate on programs
as data--any machine that is programmable can be presented with a program (of
its own sort) as
input which it will, inevitably, operate on. Universality comes closer to a
kind of introspection: not only does the universal program operate on the input
program as data, but it must have the meaning of the program built into it in
the sense that it can emulate the operation of the machine on that
program.1
Is introspection necessary for intelligence? If it is, does this imply that
there are problems that are unsolvable by human intelligence.
- 5.
- In Turing's initial proposal for ACE he notes (Pg. 332-333) that, while
it might be capable of playing chess it would play badly since ``chess requires
intelligence'', but then goes on to say that ``it is possible to make the
machine display intelligence at the risk of its making occasional serious
mistakes'' and that under these circumstances it might be possible to program
ACE to play chess well.
This is, apparently, a reference to his ideas about machine
learning (see Pg. 358ff).
Why did Turing's focus turn from programs (``rules-of-thumb'') for
playing chess to programs for learning to play chess? Is learning necessary
for intelligence? Fallibility seems to be necessary for learning--else what
is there to learn? Is fallibility necessary for intelligence? (See Turing's
comments quoted on Pg. 378.) How does Deep Blue (the IBM system that beat
Kasparov) meet with Turing's expectations about programs that play chess well?
(As a digression) it is often stated that Turing claimed that within 100 years
a computer would be able to play a creditable game of chess. But, at least in
the claim reported in the Times (Pg. 349), he seems only to be claiming
that the question of whether good chess requires judgment might be possible to
settle within 100 years. Both claims are evidently redeemed by Deep Blue. How
are the questions resolved?
- 6.
- At the outset we noted that Turing's claim that TMs correctly
characterized the class of all computable problems depends on an argument that
every computable problem could, in principle, be computed by human cognitive
processes--that the area Computation-Cognition,
in the figure, is
empty. The Big Questions about artificial intelligence seem to be whether it is
possible for a machine to exhibit intelligent behavior, whether it is possible
for a machine to possess, in some sense, intelligence, and whether there is any
aspect of human cognition that is, in principle, not computable. How do these
questions differ from each other? What are they asking in terms of the figure?
Which of the questions are addressed by Turing's Imitation Game thought
experiment (the ``Turing Test'') (Pg. 415ff)? By chess playing computers? By
programs that learn?
- 7.
- The structure of the Turing Test forces one to restrict arguments about
intelligence to the Input/Output behavior of the agents involved, but arguments
that dismiss, for instance, Deep Blue as an example of intelligence on the part
of computers are based not on the external behavior of the system but rather on
its internal structure. Is intelligence properly a question of external
or internal behavior (or both)? To what extent does the notion of intelligence
depend on (human) introspection? Is it even possible to develop concrete
criteria for intelligence on such a foundation?
In one of his arguments for the plausibility
of the TM as a model of computation (and, in particular, as a model of human
computation) Turing argued that at any given time a (human) computer might
choose to write out a set of notes detailing their position in the computation
so that they might lay it aside and pick up again where they left off later.
(Thus justifying the finite configurations of the TM as analogs of the state of
mind of the computer.) This seems to make an explicit connection between
internal operation and (at least potential) I/O behavior. It also seems to
be limited to those processes for which the human has sufficiently accurate
introspection. What (if any) is the relationship between such accurate
(or, perhaps, quantifiable) introspection and computability? Certainly, every
computation is such a process. Is every behavior
that is a result of such a process necessarily computable? Does intelligent
behavior require ignorance of the process responsible for the behavior?
CS80--Senior Seminar
Discussion Questions--Hodges
This document was generated using the
LaTeX2HTML translator Version 98.1p1 release (March 2nd, 1998)
Copyright © 1993, 1994, 1995, 1996, 1997,
Nikos Drakos,
Computer Based Learning Unit, University of Leeds.
The command line arguments were:
latex2html hodges.
The translation was initiated by James Rogers on 2000-10-13
Footnotes
- ...
program.1
- There is actually a theoretical result that establishes that
the class of machines that are equivalent in computing power to Turing Machines
is characterized by Universality and the ability to specialize programs by
binding arguments to fixed values. Remarkably, this latter capability is just
as necessary as the first.
James Rogers
www.cs.earlham.edu/jrogers
2000-10-13