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From: MUKHOP%RCSJJ%gmr.com@CSNET-RELAY.ARPA
Newsgroups: mod.ai
Subject: Creativity and Analogy
Message-ID: <8607071752.AA26740@ucbvax.Berkeley.EDU>
Date: Thu, 3-Jul-86 18:07:00 EDT
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Posted: Thu Jul  3 18:07:00 1986
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Jay Weber makes some interesting observations:

> 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.


   I agree with your reasoning and the conclusion that analogies map ONTO
abstractions--in fact, I think they map ONTO and ONE-TO-ONE (in other words
there is a one-to-one correspondence).  Also, EACH analogy (and abstraction)
partitions the space of categories into two subspaces.  However, the SPACE
of analogies does not partition the space of categories because the world
can concurrently be modeled by multiple abstraction lattices (not necessarily
hierarchies) in which the transitivity property may not hold. Consider the 
following:

       a) "A battery is like a reservoir"  (storage capability)
  AND  b) "A reservoir is like a pond"     (body of water)

DO NOT IMPLY:
       c) "A battery is like a pond"  


> ...
> 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.  

    I am glad that scientists, by and large, have not let "slipperiness" in
some linguistic sense (as you define it) discourage them from carrying on 
their research. Of course, all research issues are "slippery" in a conceptual 
sense, by definition. (I would also expect a high degree of correlation 
between linguistic and conceptual "slipperiness").
    There has been some discussion now (in AIList) on the relationship 
between "creativity" and "making-interesting-analogies".  Is it mere 
empirical association or are there stronger causal links?  One extreme 
view is that the definition of creativity is "making interesting analogies".
Some recent illuminating discussions in this forum suggest that the ability
to synthesize concepts from partial concepts in other domains is a key 
ingredient of a great number of creative activities.
    Is there some creative task that could not be performed by a machine 
capable of making complex analogies in an interesting manner--a complex
analogy being defined as a many-to-one transformation between domains (as 
opposed to a simple analogy which is a one-to-one mapping)? 

Uttam Mukhopadhyay
Computer Science Dept.
General Motors Research Labs