The Interaction of the Processes of Mapping and Perception during Analogy Making

1. The Interaction of the Processes of Mapping and Perception during Analogy Making Svetoslav Bliznashki Scientific Advisor: Boicho Kokinov

2. Introduction • The top-down influence of analogical reasoning on high-level perception is investigated. • The methodology applied makes use of re-representation of ambiguous figures.

3. Structure of the presentation • Specifics of the analogy making phenomenon as well as some unresolved issues and controversies. • A brief outline of research on top-down influence on perception of ambiguous figures. • Hypotheses, methodology and results from two experiments dealing with top-down influence of analogy making on perception. • Implications for future studies.

4. Analogical Reasoning (AR) - definition • Analogical reasoning is a cognitive process through which new knowledge and insights are obtained for a novel domain or a particular problem on the basis of prior knowledge of familiar domains or problems.

5. AR - sub-processes • Perceptual stage – constructing a perceptual representation of the problem to be solved. This representation is called “target” for it comprises the problem which needs a solution. • Retrieval – retrieving a similar an episode similar to the target from Long Term Memory (LTM). • Mapping – establishing correspondences between objects in the base and the target domains. • Transfer – transferring knowledge from the base domain to the target domain in order to solve the particular problem. • Evaluation – the results from the transfer stage are evaluated and if the problem is solved correctly the new knowledge is incorporated (i.e. learning takes place).

6. AR – mapping mechanisms • Mapping is considered to be the central and most specific process of AR (e.g. Gentner 1983). • There are many possible matches between the objects of the target and the base domains. How are the particularly useful matches selected and the trivial or misleading ones discarded? The reduction of the number of possible matches is achieved by imposing several types of constraints on the mapping process. • These are: • the informational constraints (e.g. Keane 1994) - structural constraints, similarity constraints and pragmatic constraints. • the behavioral constraints - working memory (WM) constraints and background knowledge constraints.

7. AR – structural constraints • Objects are mapped to each other on the basis of a mapping between the relations which these objects serve as arguments to (Gentner 1983). Thus the mapping phenomenon relies primarily on the relational structure of the problem space. • Higher-order relations are more readily mapped than lower-order relations (the systematicity principle). • Only entities of the same type can be mapped. Thus objects are mapped with other objects only, attributes are mapped only with attributes and most importantly relations of a given order are mapped only with relations of the same order. • If two relations are mapped their corresponding arguments (objects) must also be mapped.

8. AR – similarity and pragmatic constraints • Similarity constraints – similar relations (and their corresponding objects respectively) are more likely to be mapped (Holyoak and Thagard 1989). • Pragmatic constraints – mappings which are more important in terms of goal relevance are preferred other things being equal (Holyoak and Thagard 1989).

9. AR – WM constraints • Analogical mapping can be obstructed in cases when WM capacity is overloaded. That’s why simpler structures result in fewer mapping errors (e.g. Keane 1990). • The limited WM capacity can result in subjects using mapping strategies which reduce the WM load. This strategies, however can lead to mapping errors. This constraint also results in different response latencies for more difficult problems to be mapped (Keane 1994).

10. AR – background knowledge constraints • Keane (1991) showed that mappings which are consistent with background knowledge are performed faster than those which are inconsistent or irrelevant with to background knowledge. These constraints can also effect the number of mapping errors the subjects produce with more errors taking place when some correct mappings are inconsistent with background knowledge.

11. AR – transfer. • What is most important about analogies is that they are a very important source of new knowledge about the target domain. This new knowledge about the target is supposed to be generated through a process called transfer (e.g. Keane 1994). The transfer mechanism transfers those relations in the base domain which have not been mapped to relations in the target. The arguments of the transferred relations are arguments from the target domain which are selected on the basis of the informational constraints (primarily on the basis of the structural constraints) outlined above.

12. AR – unresolved issues and controversies • Parallel vs. sequential processing. This controversy is related to the issue of whether the distinct processes involved in AR operate at least partially in parallel or are strictly consecutive. According to thesequential approach a particular sub-process begins operating only after the previous one has finished its work and has produced an output which serves as an input to the next process. On the other hand, the parallel account argues that different processes operate simultaneously.

13. AR – unresolved issues and controversies • Modular vs. interactionist views. This controversy is tightly related to the previous one. The interactionist account often assumes parallelism while the modular typically argues for sequential processing. The difference between this controversy and the parallel – sequential one is that the interactionist view supports the idea that different processes (e.g. representation building and mapping) can be decomposed to simpler steps which operate in parallel and participate in the production of both mapping and perception while the modular view holds that different processes don’t operate in parallel and can rely on potentially very different mechanisms (see Kokinov 2007 for a review). Thus this controversy seems to incorporate the sequential – parallel dispute and carry it even further. • The current work attempts to address empirically these controversial issues. As will be seen later it appears that the results from our experiments are more consistent with the parallel interactionist accounts.

14. Perceptual representations of ambiguous figures. • The top-down influence on perceptual representations has been repeatedly studied (see Long 2004 for a review). • Priming, context and motivational effects have been proven to shape perceptual experience of ambiguous stimuli (see Dunning 2006 for a review).

15. Perceptual representations of ambiguous figures. • The great majority of studies exploring top-down influence on ambiguous figures have explored this influence by placing subjects in particular contexts (in broad sense), presenting some ambiguous figures to them and asking them afterwards what they have actually seen. • Recently, however more implicit measures like reaction time (RT) and eye-tracking have been shown to correlate significantly with verbal reports and to verify reports’ accuracy. Dunning (2006) for example demonstrated that subjects who claim to have seen an ambiguous figure only in one way have their concept corresponding to that interpretation primed but no such priming effect is found with the concept referring to the non perceived interpretation.

16. Hypotheses • Both experiments explore two phenomena: • The influence of analogical mapping on perception. • The faith of the non perceived alternative.

17. Hypothesis 1 • Both experiments test the hypothesis that mapping can alter perception and cause re-representation . Moreover the experiments test this prediction with an ambiguous picture which is very hard to be seen both ways. The hypothesis is that even such a hard – to – re-represent picture will be seen both ways in the context of a particular mapping situation.

18. Hypothesis 2 • The concept which the non perceived representation refers to will be primed only for subjects belonging to groups which are likely to re-represent the stimulus but who for some reason failed to explicitly re-represent the ambiguous figure.

19. Hypothesis 1 - reasoning • Both the modular and the interactionist accounts assume that mapping can change perceptual experience although they differ on haw this influence is carried over. • The modular account assumes that the perceptual module can call back the perceptual module and ask it for a re-representation if no meaningful mapping has been found between the base and the target. Thus the interactionist view assumes that different modules can communicate their outputs to other modules, i.e. we have something as a loop structure.

20. Hypothesis 1 - reasoning • According to the interactionist view the different processes can be decomposed to relatively simple mechanisms which may be such that they participate in the production of both perception and mapping. Moreover, the elementary steps (sub-processes) which produce the macro-level processes are not separated in time and thus may appear in various orders making perception and mapping interleaved at all stages (Kokinov 2007). • Nonetheless as far I know no one has ever tried to explore the influence of mapping on perception empirically. A success in proving that this influence exists will further reveal the complexity and importance of AR as a cognitive phenomenon.

21. Hypothesis 1 - reasoning • Why re-representation? In our experiments we use an ambiguous figure which has one dominant and one “recessive” interpretation, i.e. it is very easy to see one way but very hard to be represented differently although the recessive representation is as meaningful as the dominant one. • On one hand this serves as a methodological trick by which we are sure that experimental subjects don’t simply report just one of the interpretations although they have seen them both. • On the other hand, however, we believe that such a situation is very close to AR in real world situations. It is widely accepted that AR is tightly linked to phenomena like creativity, problem solving and even scientific discovery. Such phenomena are often thought of as involving re-representation of the target problems in a novel, creative and useful ways. Little is known, however, on the processes which lie at the core of such re-representations. Our intent is to show that analogical mapping as a process crucial to creative thinking may be one of the factors which can cause ingenious re-representations of the problems encountered both in everyday settings and in the scientific laboratories.

22. Hypothesis 2 - reasoning • Our second hypothesis, namely that the non perceived (the “recessive”) alternative will prime its corresponding concept in an initial attempt to lay the modular and interactionist views on empirical ground. That is because it appears that these two alternative views would make different predictions about the faith of the non perceived for subjects in experimental settings in which the re-representation has a high probability of occurring.

23. Hypothesis 2 - reasoning • Modular view: According to the modular view the non perceived recessive interpretation should probably have no influence on further processing. That is because since this representation fails to be established and is not passed to the next module (for subjects don’t re-represent the stimulus) it should not influence further processing. Moreover the sequential nature of modular accounts prevents partial representations or full representations which the system for some reason does not eventually settle upon to have influence on further processing because this “further processing” begins only after the previous module (the perceptual stage in our case) has finished its work and has passed its outcome to the next processing stage (the mapping stage in our case). Thus since the alternative representation is not passed on to the mapping (or any other) stage and since partial or not settled upon representations can have no influence on later processes because these processes have not begun yet no such influence is assumed.

24. Hypothesis 2 - reasoning • Interactionist view: The interactionist accountsclaim that cognitive system operates in parallel. Also many such accounts (e.g. the COPYCAT cognitive model – Hofstadter 1994) assume that several alternative representations are constructed one of which the system gradually settles upon. The modular accounts are more likely to suppose that only one representation is fed forward to the mapping module. Because of the parallel nature of models influenced by the interactionist accounts partial representations and representations which the system does not for some reason settle upon can influence further processing. Moreover such views often claim that different processes rely on one and the same simple basic mechanisms which makes such influence a straightforward phenomenon for similar mechanisms are easy to influence each other.

25. Hypothesis 2 - reasoning • In our experiments we propose that subjects in groups likely to re-represent the stimulus who for some reason don’t do so will nonetheless exhibit priming effects on the concept the recessive interpretation refers to. That is because the high probability of re-representation probably results in those subjects constructing partial representations of the recessive interpretation or even full representations which are not settled upon. However, those (partial) representations are supposed to prime the concepts corresponding to the recessive interpretation of the ambiguous stimuli because of the parallelism in human cognitive system. • Less or no such priming is expected for subjects in groups which are unlikely to re-represent the stimulus because they are not supposed to have constructed even partial representations of the recessive interpretation of the ambiguous stimulus nor they are expected to have constructed entire but not settled upon representations.

26. Experiment 1 – stimuli, design and procedure • There are three groups in a between subjects design: • A control group • A condition called “strong mapping condition” • A condition called “weak mapping condition”

27. Experiment 1 – stimuli, design and procedure • The subjects from both the strong and the weak mapping conditions see slides in which a base and a target are presented in the form of simple line drawings. There are two drawings in the base and a single drawing represents the target. The subjects have to solve the target problem by choosing one of four alternatives, the one which best satisfies the relation in the base.

28. Experiment 1 – stimuli, design and procedure • The subjects in the control group see the same slides except that their slides do not contain a base (i.e. their slides contain only one target picture and four alternatives). All other pictures (the target and the four options) are equivalent across groups. The task in this condition is simply to say which of the four options presented is the most similar to the target picture. • In order to control for the differential complexity of the task all groups are obliged to watch each slide for at least 30 seconds.

29. Experiment 1 – stimuli, design and procedure • All groups experience four such slides with the first being defined as a trial slide in. The slides are presented in the same order for all groups. • Actually we are not interested in any of the reactions to the slides except for the last one, in which the target picture is ambiguous. This ambiguity results from the picture representing simultaneously a human face and an inscription. The inscription reads “cat”. This picture was designed to be easily seen as a human face but very hardly seen as an inscription. In a preliminary test only one out of twenty (5%) subjects saw the face and the inscription and this was achieved only after asking subjects to try to see something different than a human face. All target slides are shown in Appendix A at the end of the presentation.

30. Experiment 1 – stimuli, design and procedure • In the strong mapping condition only when the picture is seen as an inscription a plausible analogy exists. • After the experiment finishes all subjects are shown the target picture for one second and then are asked whether they have seen something different from a human face or not. Whether they have seen the inscription reading “cat” or not constitutes the first dependent variable in the experiment.

31. Experiment 1 – stimuli, design and procedure • The only difference between the strong mapping and the weak mapping condition was the background of the fourth option on the last slide. Although a small difference it was supposed to cause huge differences between these two groups for in the strong mapping case the fourth option embodied a salient relation depicted in the base while in the weak mapping condition this was not the case. Thus these two groups differed only in terms of the relational structures of the tasks.

32. Experiment 1 – stimuli, design and procedure • Here we expected that the subjects in the strong mapping condition would see the picture also as an inscription more often than those in the other two groups. Our reasons were that if no meaningful mapping existed between the base and the target there would emerge a pressure to re-represent the target in order to map it meaningfully to some part of the base. Moreover the fact that the fourth alternative was of textual nature and embodied a salient relation in the base is expected to cause subjects to try re-represent the target towards a textual interpretation or simply to make the concept of written text more relevant to the problem situation which in turn should make the re-representation in textual direction more easy. • None of these arguments holds true for the other two conditions and hence they were not supposed to differ from each other but were expected to cause significantly less re-representations than the strong mapping group. • The control group was included in the experiment in order to show that the relational structure of the task is what causes re-representation of the ambiguous stimulus rather than facts like the mere presence of a problem situation or more time, efforts, etc. invested in a problem solving tasks than in a simpler tasks like similarity judgments.

33. Experiment 1 – stimuli, design and procedure • In the same experiment, we also try to test our second hypothesis, namely that the concept which the non perceived representation refers to will be primed only for subjects belonging to groups which are likely to re-represent the stimulus but who for some reason failed to explicitly re-represent the ambiguous figure.

34. Experiment 1 – stimuli, design and procedure • In order to test our second hypothesis we included an additional task in the experiment. This is a version of the well known lexical decision task (LDT) in which the subjects are required to press a “yes” button if a string on a computer screen forms a word and the “no” button if the string is meaningless. • The subjects have to solve such a task five times – before and after the presentation of each slide. Thus there are 5 such trials in the experiment . Each trial consists of six strings.

35. Experiment 1 – stimuli, design and procedure • Each LDT trial contains three words and three non-words (except for the last trial in which there are four words and two non-words) and these are presented randomly to all subjects within trials. The same six strings are experienced by all subjects across trials, however. All strings consist of five letters and all words are controlled for subjective frequency. No words are repeated during individual trials as well as across trials. All strings are shown in Appendix A. • Again we are interested primarily in the last trial. It consists of two non-words and four words – the word “cat” (the inscription on the last slide which precedes the last word verification trial), two words which are presented in the options for answer in the last slide (which are thus primed during the presentation of the last slide) and a word which hasn’t occurred anywhere in the experiment which was supposed to be used as a base line indicator in the subsequent analyses.

36. Experiment 1 – stimuli, design and procedure • Our hypothesis here was that even the subjects in the strong mapping condition who don’t “see” the inscription (they haven’t explicitly re-represented the target) would probably be somewhat primed by it, i.e. they would respond to the word "cat” in the last session faster than the subjects in the control group and the weak mapping group, the majority of which also haven’t seen the inscription. In other words we hypothesize that some implicit (unconscious) and perhaps primitive and subtle re-representation has taken place in the experimental condition even in the case when no explicit re-representation has occurred. Thus the reaction time (RT) to the word “cat” constituted our second dependent variable in that study.

37. Results • Twenty subjects participated in each of the three conditions of this experiment. • First we will show the re-representation frequencies across the three groups and then we’ll discuss the RT results.

38. Results – re-representation

39. Results – re-representation

40. Results – re-representation

41. Results – re-representation

42. Results – re-representation

43. Results – re-representation

44. Discussion • Obviously our first hypothesis is completely justified for the strong mapping condition causing significantly more re-representations than both other conditions. • The weak mapping and the control conditions don’t differ significantly which implies that the relational structure of the problem space is what actually causes re-representation in that experiment. • The fact that the distribution of responses given is not affected by neither the experimental conditions nor from whether subjects re-represented or not the target stimulus implies that we were probably wrong when we hypothesized that re-representing the figure will lead to a correct mapping and correct solving of the task. This is probably due to the “sameness” relation in the base (there are two drawings in the first line as their should be two drawings or two inscriptions in the second) which appeared difficult to be recognized by most of the subjects. On the other hand the fact that we still obtain significant results with respect to our primary dependent measure implies that nonetheless the textual alternative has been recognized as a relevant one when it embodied the “negativity” relation (a white to a black frog) depicted in the base.

45. RT results • We compared the RTs to the word “cat” for four independent groups of subjects • Those who didn’t see the inscription in the control group. • Those who saw it in the strong mapping group. • Those who didn’t see it in the strong mapping group. • Those who didn’t see it in the weak mapping group. That is because too few subjects re-represented the target in the control and the weak mapping groups in order to fully cross the two variables - experimental condition (three levels) x re-representation (two levels).

46. RT results

47. RT results

48. RT discussion • Surprisingly it appeared that the word “cat” the “strong mapping no cat group” was primed as we expected but in a negative direction. The RTs to “cat” in that group are significantly longer than those of the other three groups (using the natural logarithm transformation of raw data and the Tukey HSD adjustment). • We suppose that the word “cat” was inhibited for some reason in that group rather than that it was primed in the control and the weak mapping groups because when the RT of the word “cat” was normed by the RT to the neutral word “tree” which was matched to “cat” on parameters like number of letters and subjective frequency it appeared that only the subjects from the “strong mapping no cat group” had reacted more slowly to “cat” than to “tree”. All other groups had reacted faster to “tree” than to “cat”. When this measure was used, again the overall effect was significant and the control group - “strong mapping no cat group” comparison was also significant. Nonetheless this issue had to be clarified in future studies.

49. RT discussion • Subjects reacted significantly faster to words than to non words. • The four groups produced no significant differences on any other words or non words included in the experiment except for the word “cat”. • These results are what should be expected from previous research and suggest that there were no substantial artifacts in our study.

50. RT discussion • Problems with the RT study: • Only a single stimulus (“cat”) is used in that experiment and most of the analyses conducted are not of repeated measurements type which is known to be more sensitive than traditional ANOVA. However other studies also use the same methodology (e.g. Dunning 2006) and succeed in obtaining significant results. • Levels of the independent variable are formed post hoc which makes this study resemble a natural rather than a random group design and thus prevents us from drawing causal inferences. However the fact that our independent variable caused no differences other than the expected ones makes it improbable that some unexpected confounding caused our results. • The results may be due simply to some specifics of the materials used in that experiments. For example it may be the fact the ambiguous stimulus consists of interpretations from different domains (i.e. pictorial vs. orthographic) which causes these results. Such a claim sounds a little unconvincing but there is nothing in these experiments which can explicitly rule it out.