MUKHOP%RCSJJ%gmr.com@CSNET-RELAY.ARPA (06/10/86)
At a recent talk in Ann Arbor, Roger Schank observed/implied that a distinct characteristic of many creative people is the ability to analogize. My understanding of analogizing is to define transformations between two domains so that entities and relationships in one domain can be mapped into corresponding entities and relationships in the other domain. It appears that the greater the disparity in the "physics" of the two domains, the higher is the creative effort demanded. Not all transformations produce interesting results. Good analogies must be interesting from the perspective of the particular creative activity. Is this model of creativity--making interesting analogies--valid across the spectrum of creative actvities, from the hard sciences (Physics, Chemistry, etc.) to the fine arts (painting, music)? Is there more to creativity than making interesting analogies? I am inclined to believe that making interesting analogies is at the heart of all intelligent activity that is described as creative. Uttam Mukhopadhyay General Motors Research Labs. (313)575-2105 Net address: mukhop@gmr.com
jay@ROCHESTER.ARPA.UUCP (06/16/86)
> At a recent talk in Ann Arbor, Roger Schank observed/implied that >a distinct characteristic of many creative people is the ability to >analogize. My understanding of analogizing is to define transformations >between two domains so that entities and relationships in one domain >can be mapped into corresponding entities and relationships in the >other domain. It appears that the greater the disparity in the "physics" >of the two domains, the higher is the creative effort demanded. > Not all transformations produce interesting results. Good analogies >must be interesting from the perspective of the particular creative >activity. True. Every pair of "things" is analogous in *some* sense, i.e. there exists a mapping between them. The utility of an analogy is how it leads one to use those things more successfully. > Is this model of creativity--making interesting analogies--valid >across the spectrum of creative actvities, from the hard sciences >(Physics, Chemistry, etc.) to the fine arts (painting, music)? >Is there more to creativity than making interesting analogies? I am >inclined to believe that making interesting analogies is at the heart >of all intelligent activity that is described as creative. I believe that one could give a reasonable definition of analogy that encompasses all intelligent activity, or at least inductive learning (which is a biggie as far as intelligence goes). I question, however, how useful it is in AI to relate a slippery word like "analogy" to an even slipperier word like "creativity". A formal approach with those two terms will satisfy very few people, and an informal approach will only give us an inflated opinion of the value of our own research, which is largely why people make such comparisons. Jay Weber Department of Computer Science University of Rochester jay@rochester.arpa
colonel@buffalo.CSNET.UUCP (06/16/86)
This is a brief reply to U. Mukhopadhyay's article. > At a recent talk in Ann Arbor, Roger Schank observed/implied that > a distinct characteristic of many creative people is the ability to > analogize. [...] > Is this model of creativity--making interesting analogies--valid > across the spectrum of creative actvities, from the hard sciences > (Physics, Chemistry, etc.) to the fine arts (painting, music)? > Is there more to creativity than making interesting analogies? I am > inclined to believe that making interesting analogies is at the heart > of all intelligent activity that is described as creative. "Creativity" is often idealized as the missing ingredient in computer consciousness, but what exactly does it mean? In most of the examples drawn from science, it means advantageously overriding the usual categories and compartments, since categorizing and compartmentalizing knowledge are characteristically scientific habits. Of course, making analogies is one way to achieve this. In art, creativity is much more straightforward! One creates a work of art where there was none before. The essence of this kind of creativity is to be able to perceive what _is not._ This follows in an essential way from the ability to perceive what one is taking for granted, in order to stop taking it for granted. A good reference is F. Perls et al., _Gestalt Therapy._
MUKHOP%RCSJJ%gmr.com@CSNET-RELAY.ARPA (06/20/86)
Gordon C Joly asks: > A friend described another friend as a potentially good novelist, >because ``she always has a radically different view in the situation; >she always has a new angle''. But is there analogy tucked away in her >reasoning? ... The description suggests a person who makes interesting analyses (or abstractions) of situations, i.e. she "understands" situations in terms of unusual world models. While this quality, by itself, might enable her to make good commentaries and write fine essays, there must be something more to make her a good novelist: the ability to find an expression for (instantiate) this world model in the medium of language. To abstract and then instantiate is but one way to make transformations (analogies) between domains. Uttam Mukhopadhyay GM Research Labs
MUKHOP%RCSJJ%gmr.com@CSNET-RELAY.ARPA (06/20/86)
Jay Weber states: >I believe that one could give a reasonable definition of analogy that >encompasses all intelligent activity, or at least inductive learning >(which is a biggie as far as intelligence goes). I think inductive learning is only half of the story. The other half is to instantiate what is learned, in another domain. >I question, however, >how useful it is in AI to relate a slippery word like "analogy" to an >even slipperier word like "creativity". A formal approach with those >two terms will satisfy very few people, and an informal approach will >only give us an inflated opinion of the value of our own research, >which is largely why people make such comparisons. 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. 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? Uttam Mukhopadhyay GM Research Labs
jay@ROCHESTER.ARPA (Jay Weber) (06/27/86)
> 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
MUKHOP%RCSJJ%gmr.com@CSNET-RELAY.ARPA (07/04/86)
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
MUKHOP%RCSJJ%gmr.com@CSNET-RELAY.ARPA (07/15/86)
I believe that Jay Weber and I mostly agree on the relation between an abstraction and an analogy as well as the relation between the respective spaces of abstractions and analogies (linguistic "slipperiness" notwithstanding). What I disagreed with is the notion of some absolute abstraction hierarchy implicit in Jay's comments: > ... 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,..... The distinction between an absolute abstraction hierarchy and multiple abstraction lattices (the term I used in an earlier communication) is central to the discussion of creativity, that is if you accept that creativity is the art of making INTERESTING analogies (or abstractions). Implicit in this definition is a choice between candidate analogies--a choice not available in an abstraction hierarchy. In all fairness, Jay never states explicitly that the world can only be represented by a single abstraction hierarchy. > Proper scientists (by definition) do not construct theories about things > that cannot be empirically examined, e.g. using structure mapping functions > to model the communal descriptive definition of the English word > "creativity". Scientists pick testable domains such as problem solving > where you can test predictions of a particular theory with respect to > correct problem solving. I am surprised by Jay's definition of "proper scientists". As to modeling the communal descriptive definition of "creativity", how else could one begin to emulate this elusive property? I am surprised at his choice of a model problem for "proper scientists"--something as general as problem solving. If problem solving by induction or by analogy are proper domains, why isn't problem solving by "creativity" acceptable? The fact that the word means slightly different things to different people does not justify its exclusion from the class of "proper domains". It is fairly obvious that we have similar perceptions about what the word "creativity" means--how else could we be having this discussion? > In the past, scientists have left debate over > such concepts as "truth" and "beauty" to philosophers, and I think we > should do the same with "creativity" and "intelligence". Who are the "we" in this sentence? If "we" refers to the AIList, doesn't that include philosophers interested in AI? > In Cognitive Science, researchers have too often exaggerated the impact > of their work through the careless and unscientific use of such terms. What is the lesson to be learnt here? Do not use words like "creativity" that sound pompous? If I want to develop a program that has this interesting property I will need to give this property a name. What would be more natural than "creativity"?