According to structure-mapping theory, the process of comparison is
one of alignment and mapping between representational structures. This
process induces a focus on commonalities and alignable differences (i.e.,
those related to the commonalities). Nonalignable differences (i.e., those
not related to the commonalities) are held to be neglected. The theory
thus predicts increased focus on the corresponding information, whether
these are commonalities or differences. In this paper, we explore the implications
of this claim for memory: Specifically, we test the prediction that alignable
differences are more likely to be processed and stored than nonalignable
differences. We present a study in which people made similarity comparisons
between pairs of pictures and then were probed for recall. The recall probes
were figures taken from the pictures and were either alignable differences
between the pairs or nonalignable differences. The alignable differences
were better memory probes than the nonalignable differences, suggesting
that people were more likely to encode and store the corresponding information
than the noncorresponding information.
Daily experience bombards us with a wide array of information, only some of which is worthy of further attention. In order to make sense of the world, we must filter out some aspects of the incoming information and focus on others. How do we determine which aspects to attend to and store?
One important determinant of what will be processed and remembered is consistency with prior schemas or mental models (Brewer & Dupree, 1983; Bransford & Johnson, 1972, 1973; Rumelhart, 1980). For example, Bransford and Johnson (1973) gave subjects titled paragraphs to read. Sentences that were consistent with the schema suggested by the title of the paragraph were better remembered than were sentences that were inconsistent with that schema. Anderson and Pichert (1978) asked subjects to read a description either from the perspective of a homebuyer or from the perspective of a burglar and then recall the description. Each group recalled details consistent with their perspective. Bower, Black and Turner (1979) demonstrated effects of the restaurant script (Schank & Abelson, 1977) on subjects' recall of restaurant descriptions. Thus, there is abundant evidence that information in a complex situation will be remembered based on its consistency with stored knowledge. But what happens when no clear schema applies, or (perhaps more commonly) when many schemas could apply?
For example, in the scene shown in Figure 1a, a number of events are occurring: there is a pig spraying mud on a tractor, a farmer shouting angrily, a helicopter causing a breeze, a hayloft blowing over, a barn, a pigsty, fences, grass, and so on. When presented with such a situation, how is it determined which information will be processed deeply enough to be recalled later?
In this paper, we suggest that one determinant of the information people
attend to is the comparisons they make. We first review the structure-mapping
theory of comparison; then, we examine the implications of this view for
memory and present an experimental test of the predictions.
Figure 1: Sample triad of stimuli used in the experiment. The
base picture (a) could be compared with one of two other pictures (b or
c). Each comparison changes which objects are alignable differences and
which are nonalignable differences.
Structural alignment and mapping in similarity comparison
Comparison is a core cognitive process. It has typically been studied in the context of determining the similarity between two things (Gentner & Markman, 1995; Markman & Gentner, 1993b; Medin, Goldstone, & Gentner, 1993; Tversky, 1977), or in order to examine the impact of similarity on cognitive processes such as categorization (Goldstone, 1994a; Hampton, 1995), learning (Gentner, 1989; Kotovsky & Gentner, 1996) and decision-making (Medin, Goldstone, & Markman, 1995). However, comparison is equally important in determining which differences people find psychologically salient. The comparison of two scenes tells you what information to pay attention to: the aligned structure and its associated alignable differences. By the aligned structure we mean the system of matching predicates and corresponding objects, where objects can be placed in correspondence either on the basis of having shared attributes or by virtue of playing similar roles in the common relational structure. By alignable differences we mean nonidentical items that have been placed in correspondence (Gentner & Markman, 1994; Markman & Gentner, 1993a, 1996). Alignable differences contrast with nonalignable differences, which are differences that are not in correspondence: i.e., elements in one scenario that have no correspondence in the other. For example, referring to the pair of scenes in Figures 1a and 1b, the pig in Figure 1a and the baby in Figure 1b are an alignable difference: they can be placed in correspondence because both are making a mess and are the object of another individual's anger. In contrast, the helicopter in Figure 1a has no correspondence in Figure 1b and hence it is a nonalignable difference.
These distinctions emerge within the framework of structure-mapping theory. Structure-mapping casts similarity as a process of alignment and mapping of structured representations (Falkenhainer, Forbus & Gentner, 1989; Gentner, 1983, 1989; Gentner & Markman, 1995; 1997; Gentner & Toupin, 1986; see also Holyoak & Thagard, 1989; Keane, Ledgeway, & Duff, 1994). On this account, similarity is processed much like analogy (Gentner & Markman, 1995; 1997; Medin, Goldstone & Gentner, 1993; Markman & Gentner, 1993a, 1993b). This approach presupposes structured mental representations that contain explicit relations between their elements: e.g., in Figure 1a, CAUSE [MESS[pig, tractor], ANGRY(man, pig)]. To compare representations of this type, a process of structural alignment is carried out to find the maximal structurally consistent match. A match is structurally consistent when it observes both parallel connectivity and one-to-one mapping . Parallel connectivity states that the arguments to corresponding representational elements must also be placed in correspondence. For example, if we compare Figures 1a and 1b, the pig in Figure 1a corresponds to the baby in Figure 1b, because both are making a mess. Likewise, the tractor in Figure 1a corresponds to the wall in Figure 1b, because both are the receivers of this mess-making. One-to-one mapping requires that each element in one representation match with at most one element in the other. For example, if the pig in Figure 1a is placed in correspondence with the baby in Figure 1b, he cannot also be placed in correspondence with the mother.
The distinction between alignable and nonalignable differences discussed above is a result of this comparison process. Alignable differences arise when nonidentical elements are placed in correspondence (by virtue of playing the same role in a matching relational structure). In contrast, nonalignable differences are those that are either not related to the commonalities, or are related in different ways. Nonalignable differences may be different elements that occupy different roles, or that lack assignable roles (because they are not connected to the common structure); or (in a frequent operationalization) they may be elements in one scenario that have no correspondence in the other. Alignable differences are connected to the common system; therefore whether a difference is considered to be alignable or nonalignable depends on which two scenarios are aligned and on how they are aligned. Thus, what is considered to be an alignable or a nonalignable difference will vary across comparisons. In the comparison of Figures 1a and 1b discussed above, the pig in Figure 1a and the baby in Figure 1b are an alignable difference, while the helicopter in Figure 1a is a nonalignable difference. In contrast, the pair consisting of Figures 1a and 1c share a different set of relations. In this case, the pig has no correspondence at all in Figure 1c, and hence is a nonalignable difference. The helicopter in Figure 1a and the fan in Figure 1c are placed in correspondence because they are both blowing something over, and so they form an alignable difference.
A central assumption of the structural alignment approach is that comparisons
focus attention on the common system. This predicts both that commonalities
should be more focal than differences (Markman & Gentner, 1994; Tversky,
1977), and also that alignable differences should be more focal than nonalignable
differences (by virtue of their connection to the common system). To test
this second claim, Gentner and Markman (1994) gave subjects
word pairs and asked them to list one difference for as many pairs as possible under time pressure. Subject produced many more alignable differences than nonalignable differences, suggesting that the comparison process made the alignable differences salient. Markman and Gentner (1996) tested the prediction that alignable differences should have stronger effects on the perception of overall similarity than nonalignable differences. Using picture pairs, they found that a change in an item that played the role of an alignable difference in a comparison had a greater impact on rated similarity than did the same change when the item played the role of a nonalignable difference.
Thus there is evidence that comparison of two items draws attention to the commonalities and the alignable differences of the pair. Returning to the issue of memory storage, we now draw a further implication. When comparisons are available during encoding, the structural alignment view predicts that the greater degree of attention during the comparison process should manifest itself as greater memorability for commonalities and alignable differences of the pair than for nonalignable differences.
We tested this prediction in a straightforward experiment. Participants
were asked to rate the similarity of ten pairs of pictures like Figures
1a and 1b or Figure 1a and 1c. After a 30 minute delay, participants were
shown an item taken from one of the pictures. The item was either an alignable
difference (e.g., the pig from Figure 1a given the pair 1a and 1b) or a
nonalignable difference (e.g., the helicopter from Figure 1a given the
pair 1a and 1b). The participant was then asked to remember as much as
possible about the scene from which the cue came. If the cue was an alignable
difference of the scenes, then subjects should be able to remember more
about the scene than if the cue was a nonalignable difference. The results
need not come out this way. If comparisons do not focus on commonalities
and their associated alignable differences, then there will not be a systematic
advantage for alignable difference cues over nonalignable difference cues.
Participants in this study were 36 members of the Columbia University community. They were paid $8.00 for their participation.
Ten sets of picture triads like the one in Figure 1 were drawn. The general structure of these triads was that the base picture had two distinct relational scenes within it. Each comparison figure matched one of these relational scenes. For example, Figure 1a is a base in which there are both anger and blowing relations. Figure 1b matches the base on the anger relation, and Figure 1c matches the base on the blowing relation. One object from each relational structure in the base scene was used as a recall cue. For example, as shown in Figure 2, the pig and the helicopter from Figure 1a were used as recall cues.
Figure 2: Two recall cues used in the experiment. Depending on
which picture the base is compared to, the cue could either be an alignable
difference or a nonalignable difference.
For the similarity ratings booklet, pairs consisting of the base and
one comparison figure were placed on sheets of paper. Beneath each pair
was a similarity scale ranging from 1 (Highly dissimilar) to 9 (Highly
similar). Each booklet contained one pair from a given triad. For the cued-recall
booklet, one recall cue appeared at the top of each page. Below the recall
cue was a set of lines on which participants could write what they recalled.
Each booklet contained one recall cue from a given base scene. The booklets
were set up so that half of the cues were alignable differences of the
picture pairs in each similarity booklet and half were nonalignable differences.
For both tasks, a different random order of pages was constructed for each
This design yielded two similarity booklets and two cued-recall booklet. Each subject was given one of the similarity booklets and one of the cued recall booklets. Between subjects, all possible pairings of similarity booklets and cued recall booklets were run.
At the start of the experimental session, participants were given a similarity rating booklet. They were asked to look at the pairs of pictures and to rate their similarity on the nine-point scale provided. They were asked to give the pair a low rating if it was not very similar, and to give it a high rating if the pair was quite similar. Participants took approximately five-minutes to complete the similarity ratings task. After completing their ratings, participants took part in an unrelated study that took approximately 30 minutes to complete. After completing this task (and in no case before 30 minutes had elapsed since the completion of the similarity ratings task), participants were given the cued recall booklet. They were told that they would see objects that appeared in pictures from the similarity ratings task they performed earlier in the session. Participants were asked to write down as much as they could about the picture in which that object appeared. The cued-recall portion of the study took approximately 15 minutes to complete.
The main independent variable in this study is Cue type(alignable/nonalignable). This variable was run within-subjects, but between items. The primary dependent variable is the amount of information recalled.
The data were scored by two raters, neither of whom knew the hypothesis under study. Each rater scored the entire data set, and agreed on 95% of their scorings. Differences were resolved via discussion. When scoring the data, each new proposition about the pictures was counted as a piece of information. In general, this information consisted of objects that appeared in the pictures and relations between the objects. At times, the recall protocols also contained descriptive information (e.g., the dirty pig). Each new piece of information (including descriptive information) was counted as a piece of information recalled.
The data are summarized by item in Table 1. As expected, more information was recalled on average for each cue when the cue was an alignable difference in the pair (m=2.35) than when it was a nonalignable difference of the pair (m=1.32). There are two ways to assess the statistical reliability of this difference by item. One is to compare the amount of information recalled when a subject saw a particular base-comparison figure combination (i.e., Pair A or Pair B) when the cue was an alignable difference or a nonalignable difference. In this case, the cues are different, but the original pair of scenes seen by the subjects is the same. Done this way, a paired t-test reveals that the difference between alignable and nonalignable cues is statistically significant, t(19)=3.79, s.d.=1.22, p<.005. A second way to assess reliability is to compare the amount recalled for the same cue following the pair for which it was an alignable difference and following the pair for which it was a nonalignable difference. In this case, the cues are the same, but the original pair of scenes differs. Again, the difference between alignable and nonalignable cues is significant, t(19)=4.17, s.d.=1.11, p<.005. As one more way to look at this finding, overall, participants remembered at least one piece of information about a picture in memory on a higher proportion of trials when the cue was an alignable difference (m=0.55) than when the cue was a nonalignable difference (m=0.37), t(9)=5.04, s.d.=0.11, p<.005.
In contrast to the data for correct recall, on average more information
was recalled incorrectly given a nonalignable cue (m=0.64) than
given an alignable cue (m=0.40). Information incorrectly recalled
came from pictures other than the one containing the cue. As for the correct
recall data, these means can be analyzed holding the pair seen or the cue
constant. Holding the pair constant, the difference in incorrect recall
is statistically significant, t(19)=2.09, s.d.=0.52, p=.05.
Likewise, holding the cue constant, the difference in incorrect recall
is also statistically significant, t(19)=2.13, s.d.=.50,
p<.05. Thus, subjects were not only able to recall more information
about the scenes correctly given an alignable cue than given a nonalignable
cue, they were also less likely to recall information incorrectly given
an alignable cue than given a nonalignable cue. However, for both cues,
the amount of information incorrectly recalled was small.
Table 1. Amount of information recalled in cued recall task.
|Alignable Cue||Nonalignable Cue|
|Triad||Pair A||Pair B||Pair A||Pair B|
Finally, no systematic relationship between the rated similarity of
the pair and recall was observed. The rated similarity of pairs for which
at least one piece of information was recalled was no higher (m=4.84)
than for pairs for which nothing was recalled (m=4.86).
As predicted, people were more likely to recall pictures when probed with an alignable difference than when probed with a nonalignable difference. Further, subjects were less likely to incorrectly recall information given an alignable probe than given a nonalignable one. These results are consistent with prior findings that comparison processes create a focus on matching systems of knowledge. The new aspect of these findings is the extension to memory: It appears that the focus induced by the comparison process leads to better memory for the common system of information and for differences connected to it. Since the scenes were designed so that both the alignable and the nonalignable cues belong to rich relational systems in the base scene, the superiority of the alignable information reflects the importance of shared coherent knowledge.
This finding suggests one way in which the cognitive system deals with rich environments. By focusing on commonalities and differences between the current scene and other comparable scenes, the cognitive system can direct its processing efficiently towards information most likely to be relevant (Gentner & Markman, 1994; Markman & Gentner, 1993a; 1996). Further, alignable difference cues selectively increased the rate of correct recall (and not the rate of incorrect recalls), suggesting that the effect is not merely some sort of bias but rather the effect of a better-articulated representation of the common structure. We conjecture that this focus on common systems may promote expertise in two ways. First, it may lead a learner to form more detailed relational representations of the common systems (Gick & Holyoak, 1983). Second, as suggested by Forbus, Gentner & Law (1995), it may lead to increased uniformity of systems that are common across domain exemplars and thus contribute to the ability of experts to retrieve prior cases that share relational structure with the current case.
Is this focus on alignable differences limited to cases of explicit comparisons? We think not. Previous research on other cognitive processes that involve comparisons also reveals a focus on matching structure. In one study of judgment, Slovic and MacPhillamy (1974) asked people to decide which of a pair of students would have a higher grade-point average. Both students were described by pairs of test scores. One of the tests was taken by both students (i.e., it was an alignable difference), and the other was unique (i.e., nonalignable). People gave more weight to the common test than to the unique test in their judgments. In a related study, Markman and Medin (1995) asked people to make choices between pairs of video games. Some of the properties of the games were alignable differences, (e.g., one game had multiple levels, and another game had many different scenarios to be mastered). Other properties were nonalignable differences (e.g., one game had a practice session, and the other did not). People were asked to say which game would sell better and to justify their decision. The justifications were much more likely to contain alignable differences than to contain nonalignable differences. In a study of category acquisition, Wisniewski and Markman (in preparation) had people learn categories in which some features were values along a common dimension (i.e., they were alignable) and other features were values along unique dimensions (i.e., they were nonalignable). Following a brief delay, people were better able to recall alignable features in a free recall test than to recall nonalignable features, demonstrating another advantage for alignable differences over nonalignable differences in memory. In a related study, Zhang and Markman (in preparation) found that alignable differences of newly learned consumer products were better remembered than nonalignable differences after a one-week delay.
The impact of alignment on memory also has developmental implications. Kotovsky and Gentner (1996; Gentner, Rattermann, Markman & Kotovsky, 1995) found that 4-year-olds were better able to match higher-order perceptual relations, such as symmetry or monotonic increase, after repeated experience aligning within-dimension comparisons. We conjecture that the close within-dimension comparisons serve to focus the child on the common higher-order pattern, thereby increasing the likelihood of noticing this pattern in the more difficult cross-dimensional comparisons. Structural comparison has also been implicated in the development of taxonomic categories. In one study, Gentner and Imai (1995) taught preschool children a novel word (e.g., they pointed to an apple and said "This is a dax"). Then, the children were sequentially asked which others of a set of new items were also "daxes". When the chosen item was both taxonomically similar and shape-similar to the original, so that the pair aligned extremely well, children's subsequent extensions were far more taxonomic than in their baseline performance. These data suggest that comparisons which are facilitated by the presence of easily alignable perceptual information, can promote acquisition of more abstract categorical commonalities (see also Markman & Wisniewski, 1997; Namy, Smith, & Gershkoff-Stoew, 1997).
A focus on commonalities and differences among the available exemplars may provide a way for the cognitive system to filter information from the environment and to direct its processing towards information likely to be useful across a range of experiences. Our findings suggest that this focus on alignable systems influences what is stored in memory as well as what is salient in current processing. Although such a connection is to be expected, it cannot be taken for granted. Further, these findings invite new questions. Do comparisons between a present exemplar and past exemplars stored in memory have focusing effects similar to those we found for comparisons between two simultaneous exemplars? Do comparisons among multiple parallel exemplars create heightened focusing effects? Are there differences between relational comparisons and attribute comparisons? Further research should illuminate these issues.
Author Identification Notes
Please address all correspondence about this work to Arthur B. Markman,
Department of Psychology, Columbia University, 406 Schermerhorn Hall, New
York, NY 10027 (firstname.lastname@example.org). This work was supported by
NSF CAREER award SBR-95-10924 given to the first author and by National
Science Foundation Grant SBR-9511-757 and Office of Naval Research Grant
N00014-92-J1098 awarded to the second author. The authors would like to
thank Adalis Sanchez, Bozena Malyczko and Eloisa Mascarañas for
their help in constructing stimuli and scoring the data. Finally, the authors
thank Keith Holyoak, Doug Medin and the whole Similarity and Analogy group
for helpful comments about this work.
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More detailed descriptions of this process and of a computational model that can implement it can be found in Falkenhainer, Forbus and Gentner (1989) and Markman and Gentner (1993b). Other computational models with the same general characteristics have also been developed (Goldstone, 1994b; Holyoak & Thagard, 1989; Keane, Ledgeway, & Duff, 1994).
For this analysis the proportion of items for which something was remembered was compared for the alignable and nonalignable cues. Because only 36 subjects were run in this study, there was not enough data to meaningfully separate the proportions by the pair and cue.