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From: jay@ROCHESTER.ARPA (Jay Weber)
Newsgroups: mod.ai
Subject: Re: Creativity and Analogy
Message-ID: <8606271523.5@ur-seneca.rochester.arpa>
Date: Fri, 27-Jun-86 11:23:52 EDT
Article-I.D.: ur-senec.8606271523.5
Posted: Fri Jun 27 11:23:52 1986
Date-Received: Wed, 2-Jul-86 04:27:44 EDT
References: <8606250659.AA08024@ucbvax.Berkeley.EDU>
Sender: daemon@styx.UUCP
Reply-To: rochester!jay@ucbvax.Berkeley.EDU (Jay Weber)
Organization: U of Rochester, CS Dept, Rochester, NY
Lines: 62
Approved: ailist@sri-ai.arpa

>   Yes, I do want to understand "creativity" in terms of less slippery 
>concepts, such as "analogy".  We are forced to start with informal 
>approaches but hope to find more formal definitions.  I do not 
>understand why a formal approach would satisfy very few people or 
>why an informal approach would serve no useful purpose. 

Consider the following view of analogy, consistent with its formal
treatment in many sources.  A particular analogy, e.g. that which
exists between a battery and a reservoir, is a function that maps
from one category (set of instances) to another.  Equivalently we
can view this function as a relation R between categories, in this
case we have a particular kind of "storage capability".  This relation
is certainly

  1) reflexive.  "A battery is like a battery"  (under any relation)

  2) symmetric.  "A battery is like a reservoir" implies
                 "A reservoir is like a battery" under the same relation R

  3) transitive. "A battery is like a reservoir" and
                 "A reservoir is like a ketchup bottle" imply
                 "A battery is like a ketchup bottle" WHEN THE SAME
                 ANALOGY HOLDS BETWEEN THEM (same R).

Then any analogy R is an equivalence relation, partitioning the space
of categories.  Each analogy corresponds to a node in an abstraction
hierarchy which relates all of the sub-categories, SO THE SPACE OF
ANALOGIES MAPS ONTO THE SPACE OF ABSTRACTIONS, and so under these
definitions analogy and abstraction are equivalent.

Now to the point:  I recently presented this sketched proof to my peers
and they fought me whenever I tried to say "this is what analogy is"
rather than "this is what I define analogy to be" (with the latter claim
I probably should use a different term like R-analogy or XYZZY).  I fact,
no one could agree to a particular formal definition of the term "analogy",
since we all have individual formal definitions by virtue of the fact that
we will answer yes or no when given a potential analogy instance, so we
are formal language acceptors with our senses as input.  This is what I
mean by a "slippery" term, i.e. one that has drastically different
meanings depending on its user.   This is why I say a formal definition
of analogy would satisfy very few people.  Informal definitions are
useless because by defintion there is no notion of a valid inference
from the theory, we cannot make predictions with them and therefore
cannot do science with them (most "loose" defintions of things put
forward do have some formal properties, but one must be careful).
                  

>I am sure that you do not imply that an analysis (formal or informal)
>of >anything< is futile. What is it about "creativity" that makes its
>analysis a no-win proposition?

"Creativity" is VERY slippery, perhaps only slightly less slippery than
"intelligence".  Profit by Turing's example and keep your personal
definition of the slippery term in mind but define a new one, e.g.
Turing-test-intelligence instead of asking for a definition of the
word in usage.

Jay Weber
Department of Computer Science
University of Rochester
Rochester, N.Y. 14627
jay@rochester.arpa