Concepts

Developmental aspects

Most laboratory and field studies of human behaviour involve taking a situational snap-shot at a given time in a given place. It is easy to overlook the continuously changing nature both of people and of work situations.

When the skilled manager encounters what, on the face of it, is an intolerable set of work practices, attitudes and performance he does not necessarily take drastic action, he identifies the natural processes of change and accelerates them. In a remarkably short time changes in procedures, products and workload, promotions, resignations, retirements and so on can transform any situation.

The changes within an individual are even more inexorably continuous. Again it is easy to develop the illusion that a worker is a constant factor in a changing situation particularly for a person in the middle period of working life. This was encouraged by the traditional view of a skilled man as one who learned his trade by the age of 21 and thereafter practised it for more than forty years until he retired at 65. This was never the case and in the current working world it is even less so because of developing technology which has its impact on almost all jobs and also on the social context of work. For example, because of employment levels there is currently an emphasis on earlier retirement from and later entry into the working world.

Concepts

The human contribution

The human role as a system controller

The business of designing machines, processes and systems can be pursued more or less independently of the properties of people. Nevertheless people are always involved, the designer himself is a human being and his product will shape the behaviour of many workers and other users. More fundamentally, the design activity will be meaningless unless it is directed towards serving some human need. In spite of all this, the design process itself is often thought about and executed without any formal considerations about people. Inevitably the engineer, architect or other designer devotes most of his attention and expertise to devising mechanisms, buildings and so on which support some human activity more effectively than those currently available. The new machine or system must not be very different from the old one for a variety of reasons. The old one did its job, not perfectly but well enough to justify its existence. The new one is usually designed on the basis of copying the old one but removing as many as possible of the faults. There are other reasons such as commonality of components and, of course, shortage of imagination which lead to most design and development being a progressive iterative process. This happens to suit the human operators because most of their skills will transfer along the line of development of the machines and systems.

Few would disagree that analogy is an important tool in the acquisition of new knowledge. Indeed, work in cognitive science and educational psychology in the last dozen years provides ample evidence of the usefulness of analogy in learning and has substantially advanced our understanding of the psychological mechanisms responsible for that utility (e.g., Burstein, 1986; Carbonell, 1986; Collins & Gentner, 1987; Gentner, 1983; Gentner & Gentner, 1983; Gick & Holyoak, 1980; Rumelhart & Norman, 1981; Vosniadou & Ortony, 1983). Yet, as this chapter will demonstrate, the use of analogies in learning is far from straightforward and, surprisingly, often results in deeply held erroneous knowledge.

Our intention is to offer a more temporized and cautionary alternative to the general enthusiasm for learning by analogy, especially in its most common form: the use of a single mapping between a source and a target concept (the “topic”) – what we shall refer to as a single analogy. (For exceptions that address more complex uses of analogy, see Burstein, 1986; Collins & Gentner, 1987). We argue that simple analogies that help novices to gain a preliminary grasp of difficult, complex concepts may later become serious impediments to fuller and more correct understandings. Specifically, although simple analogies rarely if ever form the basis for a full understanding of a newly encountered concept, there is nevertheless a powerful tendency for learners to continue to limit their understanding to just those aspects of the new concept covered by its mapping from the old one. Analogies seduce learners into reducing complex concepts to a simpler and more familiar analogical core.

The contributions included in Part III focus on developmental and instructional aspects of similarity and analogy. In her chapter, Ann Brown argues that young children can transfer knowledge across analogous domains and that findings that they can not are an artifact of the paradigms used to assess transfer. Stella Vosniadou also argues that children are capable of using analogical reasoning to acquire new knowledge and that what develops is not analogical reasoning per se but the content and organization of the knowledge base to which analogical reasoning is applied.

Brian Ross discusses the role that remindings play in acquiring knowledge about unfamiliar domains and suggests using surface similarity as a way to enhance analogical access. In their contribution, John Bransford, Jeffery Franks, Nancy Vye, and Robert Sherwood offer several proposals about how to make the knowledge base more flexible. They suggest teaching people in problem-oriented environments, rather than teaching facts, and they mention various instructional techniques for promoting the noticing of similarities and differences. Rand Spiro, Paul Feltovich, Richard Coulson, and Daniel Anderson discuss the advantages and disadvantages of using instructional analogies to acquire knowledge in ill-structured domains. Finally, William Brewer offers a commentary on the contributions to Part III, focusing on the role of analogical reasoning in knowledge acquisition.

The contributions to this volume are extensively revised versions of papers delivered at a Workshop on Similarity and Analogy held at the Allerton House of the University of Illinois, Urbana-Champaign, in June 1986. The purpose of the workshop was to bring together scientists working on similarity and analogy to explore current theoretical developments in this area and to consider the practical implications of this work for learning and instruction. The group was interdisciplinary in character and included scientists looking at similarity and analogy from psychological, computational, and educational points of view. The workshop was exciting, enjoyable, and rewarding, and we would like to take this opportunity to thank all the participants for helping to make it so.

Much of the workshop's original structure survived in the transition to this edited volume. The contributions in the first part deal with the issue of similarity. The second part includes the contributions dealing with analogical reasoning. Because analogies are fundamentally concerned with similarity at the level of representational structure, the chapters in the second part provide a theoretical context for those dealing with analogical reasoning by examining a number of questions about the nature of similarity and its relation to conceptual structure. The contributions in the third part discuss analogical reasoning in relation to learning and instruction. All three parts end with one or more chapters that offer commentaries, providing quite detailed discussions of most, although not all, of the other chapters in the book.

For the past several years my colleagues and I have been analyzing what we call parallel distributed processing (PDP) systems and looking at what we call the microstructure of cognition (cf. McClelland, Rumelhart, & the PDP Research Group, 1986; Rumelhart, McClelland, & the PDP Research Group, 1986). In this work we developed computational models of cognitive processes based on principles of “brainstyle” processing. The major focus of this work has been in perception, memory retrieval, and learning. The question remains as to how this work extends to the domains of “higher mental processes.” We have made one attempt to show how our PDP models can be used to account for schemalike effects (Rumelhart, Smolensky, McClelland, & Hinton, 1986). This chapter is designed to push those ideas further and to sketch an account of reasoning from a PDP perspective. I will proceed by first describing the basic theoretical structure of the PDP approach. I will then give a brief account of the reasoning process and finally show how it can be seen as resulting from a parallel distributed processing system.

Parallel distributed processing

Cognitive psychology/information processing has become the dominant approach to the understanding of higher mental processes over the past 25 years or so. The computer has provided, among other things, the primary conceptual tools that have allowed cognitive psychology to succeed. These tools have been powerful and have offered a conceptualization of mind that has proven both more rigorous and more powerful than any that have preceded it.

Wittgenstein's admonition “don't think, but look” has had the important effect of stimulating psychologists to reconsider their common practice of equating concept formation with the learning of simple definitional rules. In the early 1970s, psychologists like Eleanor Rosch (e.g., Rosch, 1973), responding to the difficulty of identifying necessary and sufficient conditions for membership of all kinds of categories, proposed alternative models of category representation based on clusters of correlated features related to the categories only probabilistically. Without denying the importance and impact of this changed view of concepts (reviewed, e.g., by Smith & Medin, 1981), we think that in certain respects the “don't think, but look” advice may have been taken too literally. There are problems with equating concepts with undifferentiated clusters of properties and with abandoning the idea that category membership may depend on intrinsically important, even if relatively inaccessible, features. For example, on the basis of readily accessible properties that can be seen, people presumably will not judge whales to be very similar to other mammals. However, if they think about the fact that whales are mammals not fish, they will probably acknowledge that with respect to some important, although less accessible property or properties whales are similar to other mammals.

Introduction

Suppose we asked someone how to get to some place in the city we were visiting and received needed instructions in response. Clearly, we would say that this person knew the answer, no matter whether the person knew the place personally or just had to figure out its location on the basis of general knowledge of the city, that is, by conducting inference. We would say this, of course, only if the answer were given to us in a reasonable amount of time.

The above example illustrates a general principle: One knows what one remembers, or what one can infer from what one remembers within a certain time constraint. Thus our knowledge can be viewed as a combination of two components, memorized knowledge and inferential extension, that is, knowledge that can be created from recorded knowledge by conducting inference within a certain time limit.

The main thesis of this chapter is that individual concepts – elementary components of our knowledge – parallel such a two-tiered nature of knowledge. We hypothesize that processes of assigning meaning to individual concepts recognized in a stream of information, or of retrieving them from memory to express an intended meaning are intrinsically inferential and involve, on a smaller scale, the same types of inference – deductive, analogical, and inductive – as processes of applying and constructing knowledge in general. This hypothesis reflects an intuition that the meaning of most concepts cannot, in principle, be defined in a crisp and context-independent fashion.

In our studies of human reasoning (Burstein, 1986; Collins, 1978; Collins & Loftus, 1975; Collins & Michalski, 1989) we have found that the processes of comparison and mapping are central to all forms of human inference. For example, comparison underlies categorization (Smith & Medin, 1981) in that the very act of categorizing involves a comparison between an instance and a concept. Categorization is of use to humans because it allows us to make inferences (mappings) about what properties the categorized instances will have (e.g., they may fly away, they can be turned on, etc.). As the chapters in this volume amply illustrate, analogies and metaphors are also heavily dependent on these processes of comparison and mapping.

The literature on similarity, analogy, and metaphor ranges over many different kinds of comparison and mapping processes. Our goal is to clarify the issues being addressed and the critical distinctions that need to be made. We will attempt to consider the entire territory over which the discussion of comparison and mapping arises, but no doubt we will miss some of the critical distinctions and issues.

Some of the disagreements arise because researchers are talking about different kinds of comparisons or the different contexts in which comparison and mapping processes are used. Indeed, one common confusion is due to the use of the term mapping to describe either a functional correspondence between conceptual entities, the process tjiat establishes such correspondences (which we will refer to as comparison), or the process of transferring properties of one conceptual system to another, “similar” one.

Introduction

Artificial intelligence has a long and continuing interest in analogy (Burstein, 1985; Carbonell, 1985; Evans 1968; Forbus & Gentner, 1983; Kedar-Cabelli, 1985; Winston, 1980). From a computational point of view, more controversy surrounds analogy than any other single topic in the cognitive arena. From the perspective of an outsider, researchers appear to be doing wildly different things, all under the rubric of analogy. Perhaps this is just the natural result of a healthy diversity of thought. On the other hand, it may be a manifestation of the seductive name analogy. Somehow, “analogy” and “intelligence” seem to go hand in hand. The notion of researching analogy conjures up the illusion, at least, that one is directly addressing the problems of thinking and reasoning. Why is this? One possible reason is that analogy truly is central to thought. Several researchers have advanced the claim that thought is primarily metaphorical or analogical. A more cynical view is that analogy is a fuzzy concept that means different things to different people. But so is intelligence. Though researchers do not agree on what either term means, they can concur with abstract claims like “analogical reasoning is a fundamental component of intelligence”. It is perhaps this view that prompted Saul Amarel at the 1983 International Machine Learning Workshop to propose a moratorium on the term analogy in machine learning. Perhaps the field has fallen prey to a seductive term.

The power of human intelligence depends on the growth of knowledge through experience, coupled with flexibility in accessing and exploiting prior knowledge to deal with novel situations. These global characteristics of intelligence must be reflected in theoretical models of the human cognitive system (Holland, Holyoak, Nisbett, & Thagard, 1986). The core of a cognitive architecture (i.e., a theory of the basic components of human cognition) consists of three subsystems: a problem-solving system, capable of drawing inferences to construct plans for attaining goals; a memory system, which can be searched in an efficient manner to identify information relevant to the current problem; and an inductive system, which generates new knowledge structures to be stored in memory so as to increase the subsequent effectiveness of the problem-solving system.

These three subsystems are, of course, highly interdependent; consequently, the best proving ground for theories of cognition will be the analysis of skills that reflect the interactions among problem solving, memory, and induction. One such skill is analogical problem solving – the use of a solution to a known source problem to develop a solution to a novel target problem. At the most general level, analogical problem solving involves three steps, each of which raises difficult theoretical problems (Holyoak, 1984, 1985). The first step involves accessing a plausibly useful analog in memory. It is particularly difficult to identify candidate analogs when they are concealed in a large memory system, and when the source and target were encountered in different contexts and have many salient dissimilarities. These theoretical issues are closely related to those raised in Schank's (1982) discussion of “reminding.”

A central goal of cognitive science is to characterize the knowledge that underlies human intelligence. Many investigators have expended much effort toward this aim and in the process have proposed a variety of knowledge structures as the basic units of human knowledge, including definitions, prototypes, exemplars, frames, schemata, scripts, and mental models. An implicit assumption in much of this work is that knowledge structures are stable: Knowledge structures are stored in long-term memory as discrete and relatively static sets of information; they are retrieved intact when relevant to current processing; different members of a population use the same basic structures; and a given individual uses the same structures across contexts. These intuitions of stability are often compelling, and it is sometimes hard to imagine how we could communicate or perform other intelligent behaviors without stable knowledge structures.

But perhaps it is important to consider the issue of stability more explicitly. Are there stable knowledge structures in long-term memory? If so, are they retrieved as static units when relevant to current processing? Do different individuals represent a given category in the same way? Does a given individual represent a category the same way across contexts? Whatever conclusions we reach should have important implications for theories of human cognition and for attempts to implement increasingly powerful forms of machine intelligence.

Introduction

This chapter discusses the issues of similarity and analogy in development, learning, and instruction as represented in the chapters by John Bransford, Jeffery Franks, Nancy Vye, and Robert Sherwood; Ann Brown; Brian Ross; Rand Spiro, Paul Feltovich, Richard Coulson, and Daniel Anderson; and Stella Vosniadou. The following anecdote illustrates many of the themes that appear in the discussion of these chapters.

I was in a seminar recently where we were trying to set up an overhead projector for the first time. There was no screen in the room, and the one patch of wall of reasonable size was crossed with pipes. So I said to one of the other faculty members, “Let's try aiming the projector at the blackboard.” This individual said, “No, that's crazy.” I immediately gave in and began helping to aim the projector toward the wall. Then I said, “Wait, let's try the blackboard – I think it will work”. We did try the blackboard, and it did work reasonably well.

What was going on here? First, why did the other person immediately reject my original suggestion, and why did I give in? I think it is clear that the other person had a causal model for light which included the assumption that black surfaces absorb all the light that falls on them. As applied to the example at hand, this meant that it would be stupid to try to project the overhead on the blackboard, since no light would reflect off it and we would not be able to see the transparencies.

Introduction

We compare objects to each other in a variety of ways. We experience our world in terms of a complex system of distinct kinds of perceptual similarities. We judge objects to be similar or different. We also judge objects to be similar and different in part – to be, for example, similar in color and different in size. We categorize objects by their attributes and in so doing judge them to be similar; for example, we categorize objects as red, as blue, as big, as small. We compare objects in terms of their direction of difference – judging, for example, one object to be smaller than another. This variety of kinds of judgments clearly indicates that perceptual similarity is not one thing but is of many interrelated kinds. In brief, we seem to possess a complex system of perceptual relations, a complex system of kinds of similarity. The concern of this chapter is with the development of a system of knowledge about such relations.

The evidence suggests that an understanding of perceptual relations develops quite slowly during the preschool years. Indeed, working out a system of perceptual dimensions, a system of kinds of similarities, may be one of the major intellectual achievements of early childhood. The evidence for an emerging dimensional competence is widespread – and includes developments in Piagetian conservation tasks (e.g., Piaget, 1929), in seriation and transitive inference tasks, in classification tasks (e.g., Inhelder & Piaget, 1958, 1964), in transposition learning (e.g., Keunne, 1946) and discriminative learning tasks (e.g., Kendler, 1979).

Here is a simple and appealing idea about the way people decide whether an object belongs to a category: The object is a member of the category if it is sufficiently similar to known category members. To put this in more cognitive terms, if you want to know whether an object is a category member, start with a representation of the object and a representation of the potential category. Then determine the similarity of the object representation to the category representation. If this similarity value is high enough, then the object belongs to the category; otherwise, it does not. For example, suppose you come across a white three-dimensional object with an elliptical profile; or suppose you read or hear a description like the one I just gave you. You can calculate a measure of the similarity between your mental representation of this object and your prior representation of categories it might fit into. Depending on the outcome of this calculation, you might decide that similarity warrants calling the object an egg, perhaps, or a turnip or a Christmas ornament.

This simple picture of categorizing seems intuitively right, especially in the context of pattern recognition. A specific egg – one you have never seen before – looks a lot like other eggs. It certainly looks more like eggs than it looks like members of most other categories. And so it is hard to escape the conclusion that something about this resemblance makes it an egg or, at least, makes us think it's one.

The subtitle of this chapter is borrowed from an article published in 1940 by Charles L. Cragg. He begins with the following quotation from Balzac:

So he had grown rich at last, and thought to transmit to his only son all the cut-and-dried experience which he himself had purchased at the price of his lost illusions; a noble last illusion of age.

Except for the part about growing rich, we find that Balzac's ideas fit our experiences quite well. In our roles as parents, friends, supervisors, and professional educators we frequently attempt to prepare people for the future by imparting the wisdom gleaned from our own experiences. Sometimes our efforts are rewarded, but we are often less successful than we would like to be and we need to understand why.

Our goal in this chapter is to examine the task of preparing people for the future by exploring the notion that wisdom can't be told. Our arguments are divided into four parts.

First, we consider in more detail the notion that wisdom cannot be told. The argument is not that people are unable to learn from being shown or told. Clearly, we can remind people of important sets of information and tell them new information, and they can often tell it back to us. However, this provides no guarantee that people will develop the kinds of sensitivities necessary to use relevant information in new situations.

It is widely accepted that similarity is a key determinant of transfer. In this chapter I suggest that both of these venerable terms – similarity and transfer – refer to complex notions that require further differentiation. I approach the problem by a double decomposition: decomposing similarity into finer subclasses and decomposing learning by similarity and analogy into a set of component subprocesses.

One thing reminds us of another. Mental experience is full of moments in which a current situation reminds us of some prior experience stored in memory. Sometimes such remindings lead to a change in the way we think about one or both of the situations. Here is an example reported by Dan Slobin (personal communication, April 1986). His daughter, Heida, had traveled quite a bit by the age of 3. One day in Turkey she heard a dog barking and remarked, “Dogs in Turkey make the same sound as dogs in America.… Maybe all dogs do. Do dogs in India sound the same?” Where did this question come from? According to Slobin's notebook, “She apparently noticed that while the people sounded different from country to country, the dogs did not.” The fact that only humans speak different languages may seem obvious to an adult, but for Heida to arrive at it by observation must have required a series of insights. She had to compare people from different countries and note that they typically sound different.