Path: utzoo!attcan!uunet!ncrlnk!ncr-sd!hp-sdd!hplabs!otter!kers
From: kers@otter.hpl.hp.com (Christopher Dollin)
Newsgroups: comp.ai
Subject: Re: RE: Artificial Intelligence and Intelligence
Message-ID: <2070023@otter.hpl.hp.com>
Date: 16 Nov 88 13:01:02 GMT
References: <484@soleil.UUCP>
Organization: Hewlett-Packard Laboratories, Bristol, UK.
Lines: 52

Dave Peru says:

| Human beings KNOW the "halting problem for Turing machines", my point is
| that machines can NOT know the "halting problem for Turing machines".
|
| Please describe how you would give this knowledge to a computer.

The same way I would give the knowledge to a student. Oh, machines aren't
intelligent? But isn't that what we're discussing already?

| All uncomputability problems come from dealing with infinity.

Hm. Wouldn't "unboundedness" be a better term to use than "infinity"? [Since
you have elsewhere claimed said "zero = infinity" isn't against your
intuition, doesn't it follow that computability problems come from dealing
with zero too?]

| Like naive set theory, naive Artificial Intelligence does not deal with
| paradoxes and the concept of "infinity".

But does that matter?

| Human beings understand the concept of "infinity", most of mathematics would
  ^^^^^^^^^^^^
| be meaningless if you took out the concept of "infinity".  Mathematicians
| would be quite upset if you told them that they were really fooling themselves
| all this time.  Physicists use "infinity" for predicting reality.

*Some* human beings do. Some don't. Some mathematicians have a downer on
"infinity".

| Finite machines cannot understand "infinity".

Hm. I claim human beings are counterexamples, but you don't believe that
humans are machines. [Probably none of us agree on what "machine" means
anyway. We might have better agreement on "human".] Do you claim that an
infinite concept can't be captured in a finite way? I would have thought that
many of our early notions of infinity were derived by a uniform extension of
finite patterns ... to borrow the book title, "One ... Two ... Three ...
Infinity".

| For the concept of "infinity" to have any meaning at all you MUST have the
| computational strength of reality.

Is reality finite? ["Is there an odd or even number of elementary particles in
the universe?" - no I *don't* propose to reopen that flamefeast.] What is
"computational strength"? Are machines unreal? Is the filling in my sandwiches
determined only when I bite through the bread? When will the long dark teatime
of the soul be a paper back?

Regards,    | "Once   I would have been glad   to have made your acquaintance
Kers.       | Now   I feel the danger   brought about   by circumstance."