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The role of left--right symmetry in the encodement of spatial orientations.

J. B. Deregowski [*]

Three experiments investigated a hypothesis, suggested by studies of the difficulties of discriminating between shapes forming symmetrical pairs, that spatial orientations of thin flat plates (lamellae) may be encoded in a plane, the encodement consisting of two enantiomorphs. The results indicated that participants encoded the spatial orientation of lamellar stimuli in terms of the difference in cogency between their two enantiomorphic elements (Expt 1). The difference in the cogency of the two enantiomorphs is related to the orientation of the plane containing the lamellar stimulus with respect to the participant's fronto-parallel plane (Expt 2). The two possible orientations of a lamella which yield the same difference of cogency, but which differ in spatial orientation (e.g. lamella 'b' set at 30[degrees] or set at 150[degrees]) are distinguished by the manner in which the two enantiomorphic elements are arranged with respect to their axis of symmetry (Expt 3). The results suggest that the orientation of a lamella may be encoded as a two-dimensional representation and hence that three dimensions may he encoded by two by means of enantiomorphs. Implications of this finding for the encodements of three-dimensional solids, wherein pronounced contours may fulfil the same role as do the edges of lamella, are discussed briefly.

The ability to discriminate among distinct shapes has been a matter of psychological interest for considerable time. It is well established that certain shapes are more mutually confusable than others, in particular that shapes presented on a flat surface and forming arrangements symmetrical about the observer's median plane are likely to be mistaken for each other. Letters 'b' and 'd' and letters 'p' and 'q' form such highly confusable pairs. They are often used to demonstrate the problem the persistence of which is said to be responsible for the difficulties experienced by children when learning to read and write (Frith, 1971). Mach (1898) was probably the first to draw attention explicitly to the problem. Corballis and Beale (1976), who explored it thoroughly, regard it as arising out of left/right confusions which are a consequence of the structure of the perceiving organism.

The present study is concerned with the perceptual significance of the confusability of enantiomorphic stimuli (i.e. stimuli which are identical to each other except that right and left, say, are interchanged). The method by which this notion is examined is, in part, the traditional technique of discrimination learning used by Rudel and Teuber (1963) in their developmental studies. The study does not, however, concern developmental changes; it concerns the nature of the perceptual phenomenon from which difficulties of discrimination arise. The phenomena ot mutual confounding of symmetrically arranged stimuli and of perception of symmetry, although frequently investigated in children, are not confined to any age group or unique to the human species (Bradshaw, Bradley, & Patterson, 1976; Giurfa, Eichmann, & Menzel, 1996).

The traditional testing procedure concerned with discrimination learning uses two stimuli. The stimuli are presented either side by side on a vertical screen or horizontally on top of a table in front of the participant. The procedure ensures that the plane containing them is orthogonal to the participant's median plane. In studies concerned with reading difficulties the resulting elimination of the other spatial orientations and presentation of the stimuli in orientations in which the participant is likely to encounter letters is clearly legitimate, since it removes irrelevant influences. It is not, however, a measure free of cost as far as understanding of the perceptual mechanisms is involved. It does not, obviously, reveal how discrimination learning would progress if the stimuli were presented in planes non-orthogonal to the median plane.

Consider lamellar stimuli (flat stimuli having virtually no thickness) made of uniform material, such as shapes cut out of paper. Such stimuli are primarily encoded in terms of projections of their outlines onto the retina. Corballis and Beale's (1976) notion implies that discrimination between any two stimuli which project enantiomorphic images onto the eye should be equally difficult. Such stimuli need not be either co-planar or in a plane orthogonal to the participant's median plane (see Fig. 1). If the light flux reaching the eye from the two stimuli forms enantiomorphic patterns at the eye, these stimuli will be, according to the theory, mutually confusable. Arrangements of stimuli yielding such light patterns are shown in Fig. 2. One would expect discrimination learning between such stimuli to proceed at the same rate in the context of all the arrangements--the orientation of the planes containing the stimuli with respect to the observer's fronto-parallel plane being of no consequence. However, empiric al evidence suggests that this is not the case and that stimuli presented in the observer's fronto-parallel plane are recognized with greater ease than those presented in other planes (Deregowski & McGeorge, 1998b; Deregowski, Parker, & Dziurawiec, 1996).

Confusions, which studies of discrimination learning demonstrate, can be conceptualized as resulting from the fact that every lamellar stimulus is encoded not simply as its own facsimile but by means of two elements, its own facsimile and its derivative, the two elements forming a symmetrical pair (i.e. being enantiomorphic). The facsimile fosters correct recognition of the stimulus; the derivative element fosters the erroneous response of mistaking the stimulus's enantiomorph for the stimulus. The tendency to confuse enantiomorphs is therefore a function of the relative 'strengths' of the two elements of encodement.

The first experiment is intended to provide preliminary data for exploring the above simple model of enantiomorphic confusions. Its purpose is to determine whether these enantiomorphic confusions are, as these studies suggest, more likely when the stimuli are presented in non fronto-parallel planes. If so then it would appear that mental representations of stimuli incorporate their orientations in such a manner as to affect enantiomorphic confusions. That is to say they enshrine differences in the balance of power between competing enantiomorphs. The perceptual mechanism involved in enantiomorphic confusions is thus involved in the encodement of orientation. Further, if such a balance between enantiomorphs can indeed be used to encode the orientation of the stimulus then the stimulus's orientation can be encoded on a plane of the enantiomorphs. An encodement of the third dimension in a plane can thus be achieved and the unelucidated and puzzling notion of three-dimensionality of representations whether in th e form of generalized cones (Marr & Nishihara, 1978) or in the form of geons (Biederman, 1987) can be put to question.

Figure 2(a) presents an arrangement of stimuli which are both co-planar and orthogonal to the participant's median plane as they were used in the earlier investigations (e.g. Rudel & Teuber, 1963; Serpell, 1971). In the arrangement presented in Fig. 2(b) both of these characteristics are absent: the stimuli are in parallel planes that are non-orthogonal to the participant's median plane. The range of stimuli used was extended by the addition of two further arrangements of stimuli. In one (Fig. 2(c)) the stimuli are co-planar but non-orthogonal; in the other (Fig. 2(d)) they are orthogonal but non co-planar.

In the traditional discrimination task the participant is presented with two coplanar stimuli (say, two plaques placed flat on a table), one of which is arbitrarily designated by the experimenters as 'the correct one', The participant's task is to learn to recognize 'the correct one', the pair of stimuli being repeatedly presented in the same two locations but with the stimuli allocated at random to these locations. On each presentation the participant indicates which of the two stimuli is 'the correct one' and is told whether his or her choice is correct. A criterion for successful learning is defined in terms of a run of correct choices. The following example demonstrates the procedure: the stimuli are A and B, of which A has been designated as 'the correct one'. They are presented in either AB or BA arrangement. Underlining indicates the participant's putative response. The criterion of learning has been arbitrarily set as a run of five correct responses. Consider the following run:

A[underline{B}]; [underline{A}]B; [underline{B}]A; [underline{A}]B; B[underline{A}]; B[underline{A}]; B[underline{A}]; [underline{A}]B

By the adopted criterion learning was achieved in three presentations since a run of five correct responses begins at the fourth presentation. This traditional procedure was used in the first experiment.

EXPERIMENT 1: THE INTRODUCTORY EXPERIMENT

Method

Materials

Two pairs of enantiomorphic lamellae in the form of random hexagons served as the main experimental stimuli. In addition, a pair of introductory stimuli, a rectangular lamella and a trapezoidal lamella, was used. All the stimuli were made out of 2-mm thick stiff board and were about 100 mm tall. The stimuli used were mounted vertically on circular bases 95 mm in diameter. Both the stimuli and the bases were painted uniformly grey. The stimuli are shown in Fig. 3. The figure shows the stimuli as they appear when placed in the fronto-parallel plane--a mode of presentation involving minimal perception of depth since in this presentation all the elements of the vertical hexagonal lamellae are about equidistant from the participant. When the lamellae are placed in a non fronto-parallel plane their perception necessarily involves depth.

Participants

The participants were 34 schoolchildren from a Scottish city. All were aged between 7 and 8 years.

Procedure

Participants were tested individually. The participant was seated at a table and the stimuli were presented in pairs (as shown in Fig. 2). The two stimuli were presented so that their bases were 200 mm apart. The participant was told that the task was to find our which of the two stimuli the experimenter liked and that in the beginning it would be necessary to guess. Pairs of stimuli were presented to participants in the following four arrangements (shown in Fig. 2):

(A) Co-planar stimuli (presented to 18 participants):

(i) Fronto-parallel: both stimuli in the participant's fronto-parallel plane (Fig. 2(a)).

(ii) Non fronto-parallel: both stimuli in a plane inclined at 45[degrees] to the participant's fronto-parallel plane (Fig. 2(c)).

(B) Non co-planar stimuli (presented to 16 participants):

(i) Fronto-parallel: stimuli in two planes parallel to the participant's fronto-parallel plane (Fig. 2(d)).

(ii) Non fronto-parallel: stimuli in two planes inclined at an angle of 45[degrees] to the participant's fronto-parallel plane (Fig. 2(b)).

In order to ensure that the participants understood the instructions the introductory pair of stimuli was presented to them first. These stimuli were always presented as a co-planar and fronto-parallel plane (i.e. in arrangement 2(a)). All participants were able to discriminate between the introductory stimuli after three presentations; however, they were always given six trials to ensure that the procedure was understood.

Presentation of a pair of test stimuli followed immediately on completion of the introductory task. Each participant was randomly allocated either to the group responding to the co-planar stimuli or to the group responding to non co-planar stimuli. Order of presentation of the two versions of the stimuli (fronto-parallel and non fronto-parallel) within each group was systematically alternated between participants. The two arrangements of the stimuli within a pair were presented in a random sequence. Testing was brought to an end when one of the following occurred:

(1) A participant identified the 'correct' stimulus on eight consecutive presentations. Such a participant was deemed to have learned the discrimination. The participant's score was defined as the number of trials needed to reach the run of eight consecutive correct responses. Thus a participant, whose testing ended after the fourteenth trial, would be awarded a score of 6.

(2) Thirty presentations were made and the criterion for learning had not been reached. Such participants were awarded a score of 30.

Results

Scores gained by participants reaching the criteria, defined above, were used in the final analysis. The data were evaluated by means of the Wilcoxon matched pairs signed ranks test, comparing responses of each participant to fronto-parallel and non fronto-parallel plane stimuli. As anticipated, participants required fewer trials to learn to discriminate between stimuli in the fronto-parallel plane (mean number of trials = 7.4) than they did to do so when the stimuli were in the non fronto-parallel plane (mean number of trials = 10.1). The test shows that this difference is significant (p = .05). The effect therefore warrants further investigation.

Discussion

Learning to discriminate between fronto-parallel stimuli is shown to be easier than learning to discriminate between stimuli in a non fronto-parallel plane. Since the angular setting of the stimuli affect the results, it follows that the participants encode the orientation of the lamellae. Furthermore, as the sloping stimuli are more readily confused, the two postulated enantiomorphs by means of which each stimulus is encoded must differ much more markedly in the case of stimuli in the fronto-parallel plane than in the case of the stimuli in inclined planes. This suggests that this discrepancy in strength varies with the orientation of the plane containing the stimulus, declining with the decrease of the angle which this plane makes with the participant's median plane. This effect should also be demonstrable when only one stimulus is presented at a time. Verification of the hypothesis just stated is particularly desirable because it is known (Braine & Fisher, 1988) that the difficulties of discrimination decl ine when the stimuli are presented singly and because, as shown by Deregowski and Ellis (1974), participants do not treat elements of symmetrical displays (such as are used in discrimination learning tasks) in isolation: their judgments are dependent on the shape of the elements as well as on the relationships between elements.

Further, the difference in ease of learning to discriminate between enantiomorphic stimuli suggests that the facsimile encodements of the lamellae set at an angle to the fronto-parallel plane are relatively 'weaker' than those of the lamellae in the fronto-parallel plane. If this conclusion is correct then similar differences in strength should be observable when participants are simply required to remember a single lamella. This leads to the following hypotheses:

Hypothesis 1. That participants will perceive the facsimile of a stimulus lamella as more similar to the lamella than they would the enantiomorph of this facsimile.

Hypothesis 2. That the discrepancy between the perceived similarity of the facsimile and its enantiomorph will vary with the orientations of the lamella with respect to the fronto-parallel plane. That it will be particularly pronounced in the case of stimuli presented in the fronto-parallel plane and less pronounced in the case of the stimuli presented at an angle to the fronto-parallel plane.

EXPERIMENT 2

Method

Materials

The materials consisted of a set of irregular, pentagonal lamellae, mounted on circular (95 mm diameter) bases. The lamellae were made of cardboard 2 mm thick, and they were about 35-60 mm high. Stimuli were painted grey.

The response stimuli were black-on-white silhouettes of the lamellae as they would appear to the observer if placed in the fronto-parallel plane. Both possible orientations of each lamella were depicted. Each figure was drawn on stiff rectangular card 5 cm x 7.5 cm in size. Examples of response stimuli are shown in Fig. 4.

Participants

The participants were 24 University of Aberdeen students, 12 men and 12 women.

Procedure

Each participant was presented with a set of 15 lamellar pentagons, five in each of the following orientations: (1) in the participant's fronto-parallel plane; (2) the vertical plane inclined at an angle of 30 [degrees] to the participant's fronto-parallel plane; and (3) the vertical plane inclined at an angle of 1500 to the participant's fronto-parallel plane. These arrangements are shown in Fig. 5. The lamellae were presented in front of the participant, one at a time on the table, in random order, each figure remaining on display for about 7 s.

After presentation of the last lamella the participant was presented with a set of 60 cards, 15 of which bore depictions of the stimulus pentagons as they would appear in the fronto-parallel plane, 15 of which bore enantiomorphs of these depictions, and 30 of which portrayed pentagons unrelated to the pentagons used as stimuli. The cards were shuffled thoroughly to ensure a random order. Participants viewed the cards one by one and indicated whether they had seen the depicted pentagon and also indicated (on a 5-point scale) how certain they were of their judgment. The participants were permitted to look at each card for as long as they wished.

Results

Each participant made 60 responses of which 30 were to pictures related to the stimuli. In order to gain an assessment of the effectiveness of the procedure used, participants' responses to the 'related' and 'unrelated' stimuli were compared by simply considering the score of identifications as 'seen before' in each category. This score could range from 0 to 15 for the responses made to stimuli related to the initiating stimulus and from 0 to 30 for the responses to the control stimuli. The latter score was converted into a 0 to 15 score for the purpose of statistical comparison.

Analysis of variance yielded a highly significant difference (F(2,46) = 66.4, p [less than] .0001) between the responses. The means for the three categories of response were: facsimile representations = 10.1; enantiomorphic representations = 8.5; control figures = 4.5. All the differences between means are significant (p = .003; LSD test). This confirms that the participants attended to the task and justifies further analysis which concerns responses to 'related' stimuli only. Of the 30 responses of this kind made by each participant, 10 were made to stimuli derived from lamellae presented in each of the three orientations. In each set of 10 responses, five were made to the response stimuli 'facing left' and five to response stimuli 'facing right'. Therefore the largest attainable number of consistent responses was five, and each of these responses was associated with a confidence rating. For each condition, the participant's score was taken to be the sum of the confidence ratings for stimuli identified as h aving been encountered before. Thus three scores were obtained in response to the facsimile depictions and three to their enantiomorphs. Table 1 presents the mean group scores obtained.

The hypotheses put forward lead one to expect that:

Hypothesis 1. Scores obtained with facsimile response stimuli should be higher than those obtained with enantiomorphic response stimuli.

Hypothesis 2. The difference between the 'facsimile' and 'enantiomorphic' scores obtained in response to three Orientations of the initial stimuli will differ. It will be more pronounced in the case of responses to the fron-to-parallel stimuli than in the case of responses to the stimuli in other planes.

Analysis of variance yielded a highly significant difference between responses evoked by facsimile response stimuli and the enantiomorphic stimuli (F(1,23) = 17.2, p [less than] .0004). The facsimile response stimuli evoked higher scores. Planned comparisons between pairs of responses made to the two kinds of response stimuli (facsimile and enantiomorphic) concerning the same orientation of the initial stimulus were also carried out. Only the difference between the responses made to the stimuli presented in the fronto-parallel plane was significant (F(1 ,23) = 7.6, p [less than] .02). The differences within the other two pairs of responses were not significant.

Discussion

The literature available does not enable one to define the perceptual functions of the two postulated enantiomorphic elements of the encodement, the facsimile and its derivative. It is unlikely that they exist solely to deceive or to entertain psychologists. It is more plausible that they fulfil some other role in perception of lamellar stimuli and that the difficulties in discrimination learning to which this contributes are unwanted sequelae of this. There are two characteristics to which someone participating in a discrimination learning task involving non co-planar stimuli must attend: (1) the shape of the stimuli, and (2) the orientation of the stimuli. The encodement of the shape of stimuli lies outwith the scope of this study. The encodement of the orientation of the stimuli (and therefore depth) is at its very core.

A possible scheme for the encodement of both the shape and the orientation of lamellae in a plane is presented below. It incorporates an assumption that the confusability of enantiomorphs indicates that enantiomorphs are used to encode the orientation of planes of stimuli with respect to the fronto-parallel plane. The proposed device makes it possible to represent all three dimensions of the stimulus (their two planar dimensions and the inclination of the plane containing them) within a notional plane of representation.

Consider Fig. 6. It shows, schematically, settings involving four different stimuli. The corresponding postulated encodement of the stimuli is presented beneath each setting. The following rules were followed in deriving these putative encodements:

(1) The facsimile element of the encodement is that element which is projected onto the fronto-parallel plane when a stimulus is rotated so as to render it parallel to the fronto-parallel plane, through the smaller of the two angles (angle [alpha] in Fig. 5(a) and (c)).

(2) The derivative element of the encodement is the enantiomorph of the facsimile element.

(3) The elements of an encodement are arranged so that the edges of the facsimile element which are nearer to the observer are close to the axis of symmetry of the encodement.

Application of these rules results in distinctive encodements shown in Fig. 6.

Initiating stimuli (symbolized here by 'b' and 'd') yield different encodements depending on their orientation. Thus with the participant looking northwards the following facsimiles obtain:

(i) stimulus 'b' in the SW-NE plane is encoded as: facsimile element 'b'; derivative element 'd'.

(ii) stimulus 'b' in the NW-SE plane is encoded as: facsimile element 'b'; derivative element 'd'.

(iii) stimulus 'd' in the SW-NE plane is encoded as: facsimile element 'd'; derivative element 'b'.

(iv) stimulus 'd' in the NW-SE plane is encoded as: facsimile element 'd'; derivative element 'b'.

The proximity of the edges of the stimuli to the observer is encoded by the appropriate placement of the elements relative to the axis of symmetry. In consequence this feature is the same in the case of stimulus settings (i) and (iv) (in both cases the 'stem' of the letter is closer to the observer than its 'belly') and of settings (ii) and (iii) (in both cases the 'belly' of the letter is the part nearest the observer). Combination of the two measures just described ensures that the four encodements are quite distinct.

Since, when stimuli are presented in the circumstances exemplified above, both their shape and their orientation are recognized, these characteristics must be unambiguously encoded. The resulting encodements must therefore differ depending on the orientation of the stimuli: that is, on both the orientation of the planes containing the stimuli and the orientation of the stimuli within those planes. The method of encodement described in the discussion of the results of Expt 1 concerns solely the orientation of the plane. It does not distinguish between stimuli exemplified in Fig. 6(i) and 6(u) since both of these are equivalently encoded as 'bd' or 'db' with 'b' as the facsimile element. This confusion can be clarified if the stimuli in the SW-NE plane tend to evoke predominantly one of these alternative forms of encodement while those in SE-NW plane evoke the other. This is plausible because, when a lamella is presented to a participant in a plane which is at an angle to the participant's fronto-parallel plan e, the relationship between the observer and the stimulus gains another dimension: that of differential proximity. Thus, as shown in Fig. 6, letter 'b' has its 'stem' close to the notional fronto-parallel plane when placed in the SW-NE plane, but away from the fronto-parallel plane when placed in the NW-SE plane. This yields, according to the postulated model, two equally legitimate encodements which differ from each other solely by the manner in which their elements are arranged with respect to the axes of symmetry. The encodement of the stimulus in this form is likely, there being no obvious alternatives. That is to say, as shown in Fig. 6, the encodement of stimulus (i) is more likely to be in one of the alternative forms than in the other and so is that of stimulus (ii); and the more favoured form of encodement of stimulus (i) is likely to be the less favoured form of encodement of stimulus (ii). Furthermore, studies of artistic depictions in 'splitstyles' (Boas, 1927, Deregowski, 1984; Petrie, 1930), whe rein two profiles of animals are drawn side by side, suggest that the elements closer to the observer are likely to be encoded as closer to the axis of symmetry and therefore the corresponding form is likely to be favoured. This postulated effect is investigated in the next experiment.

EXPERIMENT 3

Method

Participants

Fourteen participants drawn from the university panel (seven men and seven women) took part in the experiment. They were paid for participation.

Materials

The initiating stimuli were 30 grey lamellar models mounted on 90 mm diameter circular bases, similar to those used in the two previous experiments. They were random hexagons about 60 mm tall.

The response stimuli were full-size portrayals of the models as black silhouettes on A8 sheets of stiff cardboard. On each sheet a model was portrayed twice by a symmetrical arrangement of its enantiomorphs. Two arrangements of the enantiomorphs which are referred to as 'bd' and 'db' and which differed in positioning of the axis of symmetry were used for construction of the response stimuli (see Fig. 7). There were therefore 60 response stimuli.

Procedure

The models were randomly divided into five sets of six models each. Within each set randomly selected pairs of models were allocated to three different orientations at which they were later presented to the participant: at 30[degrees] to the participants' fronto-parallel plane, at 150[degrees] to the fronto-parallel plane and in the fronto-parallel plane. (The angles given are the angles between the participants' fronto-parallel plane and the plane of presentation.)

The participants were shown the models and told that they would he shown pictures of models and required to recognize the models they had been shown previously. They were also shown an example of a response stimulus. They were further told that they would have to identify which of the two silhouettes within each picture reminded them of a stimulus that they had been shown, and to indicate on a 1-5 scale the degree of their confidence in the accuracy of their identification.

Each participant was presented one by one in a random sequence with all the models, in sets of six. Each model, placed in the appropriate orientation, remained on display for about 3 s, Presentation of a set of stimuli was immediately followed by presentation of the 12 related response stimuli, in a random sequence, one by one. These were laid flat on the table in front of the participant. A new stimulus was presented as soon as the response to the stimulus on display was gathered.

A new set of models was presented about 3 min after the last representation of the preceding set. This procedure was repeated until responses to all five sets were obtained.

Results

For each participant six scores were computed, one for each combination of the orientation of the model (30[degrees], 0[degrees], 150[degrees]) with each of the two arrangements of response silhouettes ('bd', 'db'). These scores were the totals of the confidence ratings given to correct identifications of the silhouettes. (The correct silhouette, as defined in the discussion following Expt 2, is that which is obtained by rotation of the stimulus figure through 30[degrees].) The scores thus derived take account of both the number of correct responses and the participant's confidence in them. Table 2 shows the resulting Pearson correlation matrices. A correlational analysis was used to investigate whether the two measures (obtained by means of the two arrangements of 'bd' and 'db') correlate differently, depending on the orientation of the plane of the models (SW-NE and SE-NW), with measures obtained in the fronto-parallel plane. The latter are regarded as datum measures. One would expect the two datum measures obtained to correlate, thus confirming the reliability of the datum. Therefore the following correlations are of relevance in the present context: (1) correlation between scores relating to the models presented in the fronto-parallel plane, and obtained using the two alternative response arrangements ('bd' and 'db'); and (2) correlations among the scores related to the three orientations of the models and obtained with the same measuring device (i.e. arrangement 'bd' or 'db').

Scores obtained with the two arrangements of response stimuli and pertaining to the fronto-parallel presentations were correlated at .66 (p [less than] .02). This suggests that the relevant scores are related, as one would expect datum scores obtained with different measuring devices to be.

Furthermore, when the 'db' arrangements of silhouettes are used the scores relating to the stimuli in the SW-NE (/) plane correlate highly with the scores relating to the fronto-parallel plane (r = .87, p [less than] .01), while the scores relating to the stimuli in the SE-NW (\) plane do not do so (r = .50, p [greater than] .05). Therefore responses made to 'db' configurations after presentation of stimuli in the / setting appear to be related to the responses made to stimuli set in the fronto-parallel plane, while there is no evidence that responses to the stimuli set in the \ orientation are so related. A symmetrical set of results is furnished by responses to 'bd' arrangements. The stimuli in the \ setting yield scores highly correlated with those yielded by the stimuli in the fronto-parallel plane (r = .82, p = .001) while those in the / setting are not so associated (r = .51, p [greater than] .05). All other paired correlations were equivocal. Within each arrangement of response silhouettes, correlatio ns between scores obtained to the fronto-parallel stimulus and the two other stimuli were compared using the formula for dependent correlations (Cohen & Cohen, 1975) and were found to differ significantly in the expected directions. For the 'bd' settings the comparison yielded t(11) = 2.54,p [less than] .02, and for the 'db' setting t(11) = 1.81, p [less than] .05 (one-tailed tests).

Discussion

The results clearly show that orientation of the stimulus affects the relative strength of the encoded enantiomorphs. For the stimuli in the fronto-parallel plane both manners of encodement ('bd' and 'db') yield clearly related scores. But when stimuli are presented at an angle to the fronto-parallel plane only one of the two possible manners of encodement is related to that of the stimuli in the fronto-parallel plane; this manner appears to be related to the orientation of the stimulus. This relationship is best illustrated by reference to Fig. 6. On one of the measures used (say 'db'), participants presented with the arrangement shown in Fig. 6(i) are likely to make responses similar to those made to 'b' presented in the fronto-parallel plane; not so participants presented with the arrangement shown in Fig. 6(ii). This effect enables the observer to distinguish between two orientations of the lamellae that are symmetrical about their median plane, for example a lamella pointing towards the north-east and th e same lamella pointing towards the north-west.

GENERAL DISCUSSION

The three experiments reported derive their impetus from studies of shape-discrimination learning and are particularly concerned with the mechanism involved in encodement of spatial orientation of random and unfamiliar shapes of lamellae. It is postulated that the mechanism in question encodes the orientation of the planes containing the lamellae principally by means of a difference in the cogency of their enantiomorphic images, and that these very images hinder the process of shape discrimination. Such an unsought perceptual effect (whereby a perceptually advantageous act becomes, in changed conditions, a hindrance) is not unique to the present circumstances. Similar effects are known to occur in other perceptual processes. For example, Gregory (1969) makes a strong case that certain figures are misperceived because they trigger the mechanism normally involved in perception of depth, and thus well-known visual illusions arise.

The experiments endeavoured to investigate the tentative suggestion that a lamella's spatial orientation is fully encoded by two enantiomorphic 'images' of the lamella and their mutual relationship, notably their arrangement about their axis of symmetry. Thus, it was put forward that a lamella of shape 'b' is encoded by two enantiomorphs, 'b' and 'd', which are arranged in either 'bd' or 'db' manner depending on whether the 'belly' of the lamella or its 'stem' is closer to the viewer. The results of the experiments were as follows. Expt 1 suggests that participants may indeed encode the spatial orientation of lamellar stimuli in terms of the difference in cogency between their two enantiomorphic elements. Expt 2 shows that such difference in cogency is related to the orientation of the plane containing the lamellar stimulus with respect to the participant's fronto-parallel plane. Expr 3 shows that the two possible orientations of a lamella which yield the same difference of cogency, but which differ in spati al orientation (e.g. lamella 'b' set at 30[degrees] and lamella 'b' set at 150[degrees]) are distinguished by the manner in which the two elements of the postulated encodement are arranged with respect to their axis of symmetry.

In sum, the results show that the spatial orientation of a lamella contained in a vertical plane may be encoded in terms of two parameters:

(1) the relative strength of the two enantiomorphic elements which each lamella evokes (the presence of two elements does not imply that a lamella is encoded twice; the two elements jointly contribute to the encodement of the lamella and its spatial orientation); and

(2) the position of the dominant element (the facsimile) with respect to the axis of encodement.

It is parsimonious to postulate that a planar encodement is used to describe the orientation of a lamella in space. Bearing in mind that all the data obtained concerned stimuli which were, in the main, presented in vertical planes and that this may have unknown implications for any extrapolation as to the nature of the perceptual mechanism, one can but tentatively speculate about the implications of the present findings for perception of non-lamellar stimuli, which are those generally encountered. The resulting speculation might run as follows.

These findings have obvious relevance for encodement of solids, if a link between encodement of orientation of lamellae and that of solids can be demonstrated. Such a link is most likely to be found in the features which lamellae share with solid objects. These features are the typical contours (Deregowski & Dziurawiec, 1996; Deregowski & McGeorge 1998a, 1998b; Dziurawiec & Deregowski, 1992). It is plausible that an observer encodes the orientation of the solid in the same terms as he or she would encode the orientation of a lamella: the typical contour of the solid is detected and treated as if it were the edge of a lamella.

The implicit system of encodement of orientation of objects is, since it entails only planar encodement, preferable to any system that relies on the existence of prototypical shapes in the perceptual system which are said to serve as 'building material'. The dubious validity of the suggestion that such a system reliant on a store of such shapes exists is cogently demonstrated by considering random lamellar shapes such as used in the present experiments. Two geometrically unrelated lamellar hexagons are readily discriminated from each other, and readily recognized. If they owe this to perceptual prototypes stored in memory, then one can legitimately ask: How many prototypes are there to deal with random hexagons? The tentatively postulated system has the advantage of dispensing with such props. It proposes instead a purely zetetic process--a process proceeding by systematic enquiry involving no prototypical shapes.

Acknowledgements

The authors would like to thank Professor Chris McManus and Mr John Shepherd for their helpful comments on an earlier version of this article.

(*.) Requests for reprints should be addressed to Professor J. B. Deregowski, Department of Psychology, University of Aberdeen, King's College, Aberdeen AB24 2UB, UK (e-mail: psy022@abdn.ac.uk).

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            Mean group scores obtained in response to the three
                         orientations of lamellae
                         Orientation of stimulus
                                SW-NE (/)        Fronto-parallel (-)
Facsimile responses               10.3                  12.3
Enantiomorphic responses           9.6                   9.2
                         SE-NW (\)
Facsimile responses         9.8
Enantiomorphic responses    8.0


Correlations among responses made to lamellae in three orientations. Table 2(a) responses made to 'db' arrangements of pictures, Table 2(b) diagonal responses made to 'bd' arrangements. Stimulus settings are indicated by short marginal lines. Thus '/' indicates SW-NE setting, '-' indicates fronto-parallel setting, and '\' indicates SE-NW setting
  (a) db           (b) bd
    /     -    \     /     -    /  1.00   .87  .50  1.00   .51  .41
-        1.00  .50        1.00  .82
\             1.00             1.00
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Author:Deregowski, J. B.; McGeorge, P.; Wynn, V.
Publication:British Journal of Psychology
Geographic Code:4EUUK
Date:May 1, 2000
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