Lederman (1985) Spatial and movement-based heuristics for ......for encoding spatial information...

Journal of Experimental Psychology: General1985, Vol. 114, No. 1,33-49

Copyright 1985 by Ihe American Psychological Association, Inc.0096-3445/85/S00.75

Spatial and Movement-Based Heuristics for Encoding PatternInformation Through Touch

Susan 3. LedermanQueen's University at Kingston, Kingston,

Ontario, Canada

Roberta L. KlatzkyUniversity of California at Santa Barbara

Paul O. BarberQueen's University at Kingston, Kingston, Ontario, Canada

Seven experiments investigated the heuristics people use to encode spatial patterninformation through touch. Observers traced a tangible pathway with one handand then answered questions about either the euclidean line between the pathwayendpoints or the pathway itself. Parameters of the euclidean line were heldconstant, while characteristics of the felt pathway were manipulated. Experiments1-4 showed that blindfolded sighted and blind observers increasingly overestimatedthe length of the euclidean line as the length of the explored pathway increased.This indicates a movement-based heuristic for encoding distance. Experiments5-7 indicated that judgments of the position of the euclidean line did not varywith the position of the felt pathway or the extent to which it deviated from thatline. Instead, the results indicated that observers relied on implicit spatial axes,which are movement independent, to judge position. These and other results haveimplications for theories of haptic encoding of spatial pattern and for theconstruction of tangible graphics displays.

In the past few years there has been con-siderable interest in how people encode layoutinformation in large-scale space (i.e., spacethat surrounds the observer, Ittelson, 1973)and how they update this information as theymove about in their environment (e.g., Liben,Patterson, & Newcombe, 1981; Rieser, Guth,& Hill, 1982; Reiser, Lockman, & Pick, 1980).These same questions are also importantwhen considering how people interpret small-scale spatial layouts, which include variousforms of graphics (maps, pictures, graphs,etc.) and three-dimensional objects or models.

This research was supported by Natural Sciences andEngineering Research Council of Canada Grant A9S84to the first author and by National Institute of MentalHealth Grant MH25090 to the second author. Theauthois thank Cheryl O'Neill, Kathy Yeigh, and GeorgiaManolakos for running Experiments 2 and 3 and DebbieRedding-Stewart for running Experiments 5-7. We alsothank the Canadian National Institute for the Blind formaking their facilities available to us in Toronto, and allthe participants in Experiment 4 who gave us their timeand suggestions.

Requests for reprints should be sent to S. J. Lederman,Department of Psychology, Queen's University, Kingston,Ontario, Canada K7L 3N6, or to R. L. Klatzky, Depart-ment of Psychology, University of California at SantaBarbara, Santa Barbara, California 93106.

Although the role of movement has been animportant concern in studies of large-scalespatial encoding, it has been given relativelylittle attention in research on small-scalespace, which has concentrated more on thecontribution of vision. As a result, we do notknow a great deal about how sighted andblind observers encode spatial patterns hapti-cally; that is, through purposive touch.

Much of the earlier work on haptic patternencoding focused on the relative accuracy oftouch and vision, emphasizing the superiorityof the latter (e.g., Cashdan, 1968; Lobb,1965). Other research merely compared ac-curacy levels of blind and sighted observerswithout regard to qualitative processing dif-ferences between them (e.g., Cleaves & Royal,1979; Dodds, Howarth, & Carter, 1982; Wor-chel, 1951). Only recently have more analyticapproaches been adopted (e.g., Brambring,1976; Kerr, 1983; Millar, 1975, 1981). Inkeeping with this more recent work, thecurrent research also investigates the natureof haptically perceived spatial patterns insighted and blind observers.

An important theoretical question is, whatheuristics do people use in constructing arepresentation of a spatial layout from haptic

33

34 S. LEDERMAN, R. KLATZKY, AND P. BARBER

input? The haptic system commonly, althoughnot exclusively, gathers information by meansof a sequence of exploratory contact move-ments over surfaces and contours. One po-tential heuristic, then, is to use aspects of themovements directly to infer the nature of thespatial layout. Evidence for this heuristic canbe found both with small-scale patterns thatare felt with the finger (Brambring, 1976;Millar, 1975, 1976, 1981) and with large-scale layouts that are explored through move-ment (e.g., Book & Garling, 1981; Kosslyn,Pick, & Fariello, 1974; Rieser, Lockman, &Pick, 1980; Sherman, Croxton, & Smith,1979). In general, these studies show thatcharacteristics of the movements used inexploration of a display influence reproduc-tion of or judgments about its spatial prop-erties, such as the relative or absolute locationof points or distances between them.

The influence of movement on spatial lay-out representation can be related to the car-tographic distinction between two kinds ofphysical maps: route maps and survey maps(Downs & Stea, 1977). A survey map is anoverview in which all parts of the layout aredirectly accessible. A route map codes thelayout as a set of temporal and spatial se-quences. If a haptically explored layout isencoded in terms of the sequence of explor-atory movements, its internal representationmay be more like a route map. The speedand accuracy of access to such a representa-tion are potentially tied to the particular setof movements used during the initial explo-ration; such effects are found in the studiescited earlier.

The literature on "cognitive mapping" ofviewed displays is relevant to the question ofhaptic spatial representation because it iden-tifies a number of heuristics that might beused to achieve a spatial representation.Clearly, at least some of these may be usedfor encoding spatial information obtainedthrough the haptic system as well. Tversky(1981) has described heuristics that referpoints on a map to natural spatial axes(horizontal and vertical). Explicit landmarksand reference points can also be used torepresent locations (e.g., Lederman & Taylor,1969; Nelson & Chaiklin, 1980; Sadalla, Sta-plin, & Burroughs, 1979; Taylor, 1961). An-other heuristic is to convert the density of

points in space as an estimate of spatialextent—the "filled space illusion" (Thorn-dyke, 1981; Woodworm, 1938).

Whereas a movement-based heuristic canbe used to produce an internal representationsimilar to a route map, the other heuristicsjust described can be used to produce a staticspatial representation more like a survey map.Can these other heuristics be used with onlyhaptic input? Prior research suggests that theuse of external referents is possible. Theability to identify referents is severely de-creased when the observer is deprived ofsight, of course, but it is still possible to usediscriminative tactual features (Lederman &Taylor, 1969), spatial axes, or body parts(Millar, 1981; Wong, 1977). Congenitallyblind individuals appear less able to makeuse of such referents than sighted or adven-titiously blind individuals (for small-scale lay-outs, Millar, 1981; for large-scale layouts,Rieser et al., 1980). Thus, it appears to bemore difficult for the blind to achieve aninternal survey representation of a hapticinput.

The use of heuristics in cognitive mappinghas an important consequence: systematicdistortions in the resultant representation.The strategy of using natural axes results inerrors in relative location because peoplementally align points along an axis (Tversky,1981). Similarly, the use of filled space toestimate distance leads to overestimation ofsmall filled spaces and underestimation oflarge unfilled ones (Thorndyke, 1981; Wood-worth, 1938).

The study of haptic space perception hasrelevance for applied as well as theoreticalissues, particularly for the effective design oftangible graphics displays for the blind. Al-though tangible graphics have been used ona fairly informal basis for educating youngblind children, there has been relatively littlesystematic evaluation of these aids (see Schiff& Foulke, 1982). Tangible graphics are usuallyraised replicas of original visual masters, ap-parently based on the assumption that what-ever works for vision should be optimal fortouch (see Berla, 1982; Lederman, 1979).However, this assumption should not be ac-cepted without reservation, because modality-specific encoding mechanisms have beenfound (e.g., O'Connor & Hermelin, 1978).

HEURISTICS FOR HAPTIC SPATIAL ENCODING 35

The present research begins with the as-sumption that haptic perceivers of small-scaledisplays adopt encoding heuristics to convertmovement to spatial representations. If dis-plays are such that a direct translation tovisual imagery is not readily achieved (forexample, they are larger than a finger spanand unfamiliar in shape), movement-basedstrategies are particularly likely. For example,movement duration could be translated intoan estimate of linear extent; a shape couldbe represented by the muscular actions neededto trace it, or a contour's extent could bemeasured by considering the joints that mustbe activated in order to move a finger alongit (involvement of more proximal joints sug-gests longer contours). Such heuristics shouldlead to systematic and predictable patternsof error when exploratory movements do notdirectly reflect the to-be-reported attributesof a spatial display.

A different strategy is to adopt static ref-erence points or axes and locate points onthe pattern relative to those referents. Weconsider, in particular, pinpointing a positionwith one hand while judging other positionsrelative to it, and using natural spatial axes.These heuristics should not produce errorsthat are directly related to exploratory move-ments.

The principal concern of the present studiesis with judgments of portions of a spatiallayout that were not directly explored by thehand. The general task required observers totrace a tangible pathway with one hand andthen to answer questions about an inferredpath, consisting of the straight line betweenthe pathway's endpoints (and in some casesabout the explored pathway as well). Thisprocedure made it possible to hold constantthe parameters of the implicit line that wouldbe judged while varying features of the ex-plicitly felt pathway. If movement plays a rolein encoding the inferred line, variations inthe felt pathway should affect the reports.The first series of studies concerns judgmentsof the length of the inferred line, and thesecond series concerns judgments of its po-sition.

Haptic Perception of Distance

The following studies investigated whetherthe judgment of the euclidean distance be-

tween the start and end points of a tangiblepathway would increase with the length ofthe pathway itself, as would be consistentwith a movement-based heuristic. In additionto manipulating the length of the pathwayand the euclidean distance between its end-points, we used two modes of exploration. Inthe anchor mode, subjects kept one finger onthe starting point of the pathway throughoutexploration; in the no-anchor mode, the non-exploring hand was not used. This manipu-lation was intended to determine whether theprovision of a static reference point (theanchor hand) would eliminate the movement-based heuristic.

Experiments 1-3

In Experiment 1, subjects judged either thelength of the felt pathway or the euclideandistance on each trial, not knowing in advancewhich would be required. Pathway estimateswere used primarily to focus observers' atten-tion on their exploration of the entire pathwayconfiguration. This study used a static place-ment response to indicate the judged distance.Experiment 2 used the same response, butrequired observers only to judge the euclideandistance, in order to determine whether theycould ignore their movements and just focuson the pathway endpoints, thus eliminatingeffects of pathway distance. Experiment 3was identical to Experiment 2 except for theuse of a dynamic tracing response, moresimilar to the movements used in explorationthan a static placement response.

Method

Observers. In each experiment, 12 men and 12women participated for payment. The observers weredifferent in each experiment. All were normally sighted,right-handed members of psychology classes at Queen'sUniversity and were naive as to the purpose of theexperiment.

Apparatus and stimuli. For each of five euclideandistances (2.5, 4.1, 6.7, 11.0, and 15.2 cm), five pathwaydistances were designated (1, 2, 4, 6, and 8 times theeuclidean distance). At pathway distance level 1, thepathway was a straight line. The configurations of the 20curved pathways corresponding to the other pathwaydistances were curved lines that could be traced with onehand while the other remained on the starting point.(The two hands never touched beyond the start.) Eachpathway was pressed into a Brailon plastic sheet with astylus (Letraset Canada Model B-l), creating a pathwayof raised dots about 2 mm in diameter and separated by


about 3 mm. The start and end points of the pathway

were marked with small sandpaper squares. The resulting

25 patterns were oriented so that the euclidean (straight)

line between the pathway endpoints was oriented across

a variety of vertical, horizontal, and oblique positions

(relative to the horizontal table edge in front of the

subject).

A board 194 cm in length was mounted 23 cm above

and parallel to the table edge. In Experiments 1 and 2,

observers indicated their distance estimates by anchoring

their left hand on a small marker toward the left end of

the board and placing their right index finger to the right

(without sliding it along the board) so that the internnger

distance represented their judgment of extent. In Exper-

iment 3, the observer placed the left index Anger on the

marker and the right index finger was placed beside it.

The right index finger was then moved along the board

until the distance moved matched the euclidean estimate.

Procedure. Observers were blindfolded. On no-anchor

trials, the experimenter placed the observer's right index

finger on the start square. The observer traced the

pathway to the end and could then retrace it back and

forth as often as desired. On anchor trials, the observer's

left index finger was placed on the start and the right

index finger slid over it and traced the pathway as in no-

anchor trials. Immediately after exploration, the observer

made either a euclidean judgment (i.e., of the length of

the straight line between start and end points) or (in

Experiment 1 only) a judgment of the length of the

actually explored pathway. In Experiment I, half of the

observers of each gender made both judgments about all

stimuli by using an anchor in the first session and no

anchor in the second session; the remaining observers

had sessions in the reverse order. In Experiments 2 and

3, observers made euclidean judgments about all 25

stimuli by using both modes of exploration in a single

session. The 50 trials in a session were randomly ordered

and lasted about 1 hr.

Results

Euclidean errors. All three studies showedthat judgments of euclidean distance increasedwith pathway length, even when subjects usedone finger as an anchor, for both static anddynamic responses. The magnitude of thiseffect was reduced when observers knew in

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EUCLIDEAN DISTANCE (e)

NO ANCHOR

FELT PATHWAY DISTANCE

(in multiples of e )

Figure 1. Experiment 1: Mean signed errors in euclidean judgments as a function of pathway distance, for

each euclidean distance and mode of exploration (anchor, no anchor). (When pathway distance = le, the

pathway is the euclidean line.)


advance that they were to judge the euclideandistance.

Figure 1 shows the euclidean errors (re-ported distance minus true distance) in Ex-periment 1 for each combination of pathwayand euclidean distance, by exploratory mode.Tables 1 and 2 show the corresponding resultsfor Experiments 2 and 3 as well as the averageerror for each euclidean distance and eachpathway distance.

Table 3 reports F values for significanteffects (p < .05) in the analysis of euclideanerrors. (This table is not intended to addressthe magnitude of the effects.) The trends areas follows: In all three studies, euclideanerrors increased with increasing pathway dis-tance. The effect of pathway distance onabsolute errors was greatest in Experiment 1,where either euclidean or pathway distancewas tested. However, Experiments 2 and 3showed strong relative effects (8e: le errorvalues), particularly for the 15.2-cm euclideandistance.

In Experiment 1, signed euclidean errorswere higher in the no-anchor than in theanchor condition. However, in Experiments2 and 3, errors were higher in the anchorcondition than they were in the no-anchor

Table 1Experiment 2: Errors on Euclidean DistanceJudgments by Euclidean Distance, PathwayDistance, and Mode of Exploration

Table 2Experiment 3: Error on Euclidean DistanceJudgments by Euclidean Distance, PathwayDistance, and Mode of Exploration

distance

Pathway distance

e 2e 4e 6e 8e Ave.

Anchor

2.54.16.7

11.015.2Ave.

2.842.112.672.282.522.48

3.503.32

3.373.120.442.75

2.013.71

4.952.982.693.27

2.954.562.001.452.872.76

2.734.893.660.124.323.14

2.813.723.331.992.57

No anchor

2.54.16.7

11.015.2Ave.

2.942.733.281.200.812.19

2.812.552.851.79

-1.191.76

1.652.974.18

2.050.212.21

2.765.083.021.41

-0.232.41

3.454.084.65

-0.553.403.00

2.723.483.60

1.182.31

Euclideandistance

Pathway distance

e 2e 4e 6e 8e Ave.

Anchor

2.54.16.7

11.015.2

Ave.

1.961.85

1.131.090.361.28

2.022.37

1.451.58

0.201.52

0.622.52

2.781.45

1.561.79

1.342.71

0.88-0.88

1.821.17

1.523.92

2.39-0.88

3.132.00

1.492.67

1.730.47

1.41

No anchor

2.54.16.7

11.015.2Ave.

2.201.650.940.94

-0.930.96

1.661.731.170.48

-1.600.69

0.712.04

2.421.280.141.32

1.963.702.011.02

-0.181.70

2.052.97

2.68-0.95

3.982.15

1.722.42

1.840.350.28

Note. Ave. = average error.

Note. Ave. = average error.

condition, but were significant in Experiment2 only. The important point is that the anchortherefore did not consistently reduce error.

The main effect of euclidean distance wassignificant in all three studies, but the effectswere inconsistent. In Experiment 1, signederror increased with euclidean distance,whereas in Experiments 2 and 3 the fivefunctions relating euclidean judgment errorto pathway distance were more tightly clus-tered together.

There were also several two-way interac-tions that should be considered. First, esti-mated euclidean distance tended to decreaseanomalously with pathway distance when the11-cm euclidean distance stimuli were pre-sented. We cannot explain the reasons forthis, other than that it may reflect a stimulusartifact. Second, the pathway distance effecttended to increase with euclidean distance inExperiment 1; the effect was somewhat lessregular in Experiments 2 and 3, but in allthree cases the pathway distance by euclideandistance interaction was statistically signifi-cant. Third, the pathway by mode interactionwas significant in Experiments 1 and 3, in-dicating a reduction in the magnitude of thepathway distance effect when an anchor wasused.


Table 3

Experiments 1-3: F values for Significant Effects on the Euclidean Error Measure

Experiment

123

Pathwaydistance,F(4, 88)

20.454.105.31

Euclideandistance,F(4, 88)

15.179.158.50

Mode ofexploration,

F(l, 22)

22.675.81

PX E,F(16, 352)

4.829.978.99

P X M ,F (4, 88)

4.23

4.02

M X E ,F(4, 88)

7.943.74

Gender,F(\, 22)

7.51

Note. P X E = Pathway X Euclidean Distance; P X M = Pathway X Mode of Exploration; and M X E = Mode ofExploration X Euclidean Distance.

Pathway errors. Errors (reported minustrue distance) in judgments of the pathwaydistance in Experiment 1 were affected onlyby pathway length, as denned by the com-bination of euclidean distance, F(4, 88) =10.12, and pathway distance, F(4, 88) =23.84; for the interaction, P(16, 352) = 13.03,ps < .0001. Figure 2 shows that the pathwayestimates tend to follow Weber's law.

Experiment 4

Experiments 1-3 support the hypothesisthat a movement-based heuristic is used toestimate distances in a haptically exploredpattern. One might expect similar strongeffects of pathway exploration with blindsubjects, who may have even less recourse to

nonmovement-based heuristics that make useof external referents (Millar, 1981). Accord-ingly, Experiment 4 assessed whether blind(congenital and adventitious) subjects wouldsystematically overestimate euclidean extentas a function of increasing length of anexplored pathway.

Method

Observers. Thirty totally blind (i.e., only perceptionof light, but not of form or movement) adults participated.Ten of these observers were congenitally blind and theother 20 lost their sight some time after birth. Table 4shows their attributes on several variables. Causes ofblindness included diabetic retinopathy, retrolentalfibro-plasia, retmoblastoma, cataracts, glaucoma, encephalitis(uncertain), unknown fungus, iritis, detached retina,macular degeneration, accident, cone disturbance, andmicroopthalmus. Only one observer had irregular periph-

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2 3 4 5 6 7 B 9 10 2O 30 40 90 «0 TO M90IOO 200

FELT PATHWAY DISTANCE (cm)

Figure 2. Experiment 1: Mean signed errors in pathway judgments as a function of pathway distance; barsindicate one standard error of the mean.


eral neuropathy, and he had normal sensation at the timeof testing. Only three observers had not completed high

school.Procedure. The apparatus and stimuli were like those

used in the previous experiments. Observers were run atthe Canadian National Institute for the Blind in Torontoor in their homes, in one session for about 2 hr. Itconsisted of a number of practice trials and 72 test trials:3 euclidean distances (2.5, 6.7, and 15.2 cm), 3 pathwaydistances (I , 4, and 8 times euclidean), 2 modes ofexploration (anchor, no-anchor), 2 judgments (euclideanor pathway distance), and 2 types of instruction (subjectswere told which judgment to make either before or afterexploring the stimulus pathway). The order of conditionswas random. A tracing response was used, as in Experi-ment 3.

Results

The blindness data were variable enoughthat it seemed unwise to use multiple regres-sion techniques in the analysis. Instead, sub-jects were split into two groups according towhether they were congenitally blind (i.e.,

Table 4Experiment 4: Characteristics of Subjects

Subjectnumber

,

23456789

101112131415161718192021222324252627282930

Sex

MFFFMMMMMMMMFMMMMMMFMFMFFFMFFF

Age

(yrs)

382920455233356342333532322818485425273130652345302432352933

Age

at onset

29birth

2birth

25251248

11816

birth2

birthbirth44452425

birth6

6420

birth11

birthbirthbirth

281

Yearsblind

9291845278

231541151932302818490.52

31240.753

4519

243235

132

blind from birth, n = 10) or adventitiouslyblind (n - 20). Analyses of variance (ANOVAS)(signed euclidean errors; signed pathway er-rors) included this 2-level factor along withpathway distance, euclidean distance, time ofinstruction, and exploration mode.

Euclidean errors. As in Experiments 1-3,judgments of euclidean distance increasedwith pathway length, regardless of the modeof exploration (anchor vs. no-anchor). Thisresult is indicated by the highly significantpathway effect, F(2, 56) = 16.77, p < .0001.The effect of euclidean distance was alsostatistically significant, but tended to vary bygroup. Thus, distance estimates increasedwith increasing euclidean distance for thecongenitally blind, F(2, 18) = 6.56, p < .01;however, distance estimates initially increasedand then slightly decreased as a function ofeuclidean distance for the adventitiously blind,F(2, 38) = 5.31, p < .01. This is because ob-servers tended to increasingly underestimatethe 15.2-cm euclidean distances. The inter-action term, pathway length by euclideanlength, was also significant, f\4, 12) = 4.04,p < .005, indicating as before that the pathwayeffect tended to increase with increasing eu-clidean distance. These results have beenplotted in Figure 3. The left panel showssigned errors in euclidean judgments for thecongenitally blind as a function of pathwaydistance and euclidean distance and the rightpanel shows the corresponding data for theadventitiously blind. Errors were greater over-all for the congenitally blind than they werefor the adventitiously blind, F(l, 28) = 4.17,p < .05. The pathway distortion effect wasclearly evident in both groups, althoughmore pronounced in the congenitally blind ob-servers.

The effect of anchor was not statisticallysignificant, although the pattern of resultswas similar to that of Experiment 1; that is,the anchor condition resulted in fewer errorsand less variability. Knowledge about thetype of judgment to be made interacted sig-nificantly with euclidean distance, f[2, 56) =5.22, p < .01. In general, prior knowledge ofthe response type reduced error, but only forthe 15.2-cm euclidean distances.

Pathway errors. Errors (reported minustrue distance) in judgments of the pathwaydistance were affected by pathway length, as


CONSENITAU.Y BLIND ADVENTITIOUSLY BLIND

FELT PATHWAY DISTANCE(In multiples of euclidean distance)

Figure 3. Experiment 4: Mean signed errors in euclidean judgments as a function of pathway distance, fen-

each euclidean distance and each group (congenitally and adventitiously blind).

defined by the combination of euclidean dis-tance and pathway distance as a single vari-able, F(8, 224) = 30.12, p < .0001. As inExperiment 1, errors tended to be overesti-mates for the shorter extents up to about 20-40 cm and underestimates beyond that range.These results are shown in Figure 4; errorsin pathway distance judgments are plotted asa function of felt pathway distance for bothblindness groups. Observers were more ac-curate when told which of the two judgmentswould be required before (as opposed toafter) the exploration phase, but particularlyfor the two longest pathways; this was indi-cated by a significant Pathway Distance XTime-of-Instruction interaction, F(8, 224) =3.70, p < .0005. There were no differencesin the accuracy with which the two blindnessgroups estimated the length of the pathwaystraced. No other effects in either analysiswere statistically significant.

Haptic Perception of Position

Experiments 1-4 demonstrated that ob-servers used a movement-based strategy whenestimating the extent of inferred euclideandistance. Specifically, they increasingly over-

estimated the length of an inferred straight-line path as the extent of the pathway tracedincreased. Experiments 5-7 investigated thepossibility that observers also used a move-ment-based heuristic when judging inferredposition. Experiment 5 was intended to trans-late the variables of the distance experimentsdirectly into manipulations of position. Effectsof movement-related varibles on judgmentsof position did not, however, parallel thoseof corresponding variables in Experiments 1-4. In fact, only one movement-related effectwas obtained, and that was potentially attrib-utable to the use of static spatial referentsthat varied with exploratory movements. To-gether, Experiments 6 and 7 verified that theobtained effect was due to a spatial-referentrather than to a movement-based heuristic.

Experiment 5

In this study, subjects judged the position(cf. euclidean distance in Experiments 1-4)of the inferred straight line joining the startand end points of each dotted line configu-ration that they explored. The direction and"detour" (maximum perpendicular) distanceof the pathway (cf. pathway distance in pre-


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O ADVENTITIOUSLY BLIND

2 3 4 5 6 7 8 9 10 20 30 *> » 60 70 9090100 200

FELT PATHWAY DISTANCE (cm)

Figure 4. Experiment 4: Mean signed errors in pathway judgments as a function of pathway distance, foreach group (congenitally and adventitiously blind).

vious experiments) from the inferred linewere manipulated. If a movement-based heu-ristic were used, judgments of inferred posi-tion would be distorted in the direction ofthe movements used to explore the pattern.Further, the magnitude of the distortionshould increase with the detour distance ofthe pathway from the inferred line.

Method

Observers. The normally sighted observers were 10male and 10 female students in introductory psychologyat the University of California, Santa Barbara (UCSB).They received credit toward a course requirement orwere paid for participating.

Stimuli. The stimuli were raised dot pathways formedas in the previous studies. Figure 5 depicts a typicalstimulus. The start (S) and end (E) points were always6.7 cm apart in a straight line and were marked withsandpaper circles. The end point bisected a 3.8-cmreference line made of fine dots (1 mm in diameter and2 mm apart); it was positioned parallel to the table edgein front of the observer. There were 24 stimuli, eachrepresenting a unique combination of levels of threefactors.

The first factor was the region of the hemiplane abovethe reference line in which the direct line (SE) fell. Itsposition is specified by direct angle (SER). (All angles

are measured relative to the right horizontal vector ER.)The direct angle was randomly selected within the region31-70°, 71-110°, or 111-150°. The second stimulus-denned factor was the direction in which the pathwaydeparted from the start of the direct line. It could be

path

S ..•"

directline

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z SER * "direct angle"

4. FER = "detour angle"

reference line \;

(horizontal axis) E

[table edge)

Figure 5. Experiment 5: Sample pathway configuration.(Points PI and P2 were not in the actual displays.)


either clockwise (as in Figure 5) or counterclockwise.The stimuli with clockwise pathways were reflectionsalong a vertical axis of those with counterclockwisepathways. The third factor was detour distance (FL): themaximum perpendicular distance of the pathway fromthe direct line. The dot F (unmarked on actual displays)on the pathway, which was farthest from the direct line,was located so that its perpendicular projection intersectedwithin the middle 50% of SE. The detour distance factorhad four levels in geometric increments: 2.5, 6.7, 11, and17.9 cm. A pathway can be schematized as a perturbationabout the trapezoid S-P1-P2-E in Figure 5. The pointsPI, P2, and F lie along a line parallel to SE; PI and P2are perpendicular to the 1/4 and 3/4 points of SE,respectively. The length of each pathway was arbitrarilyset as twice the distance S-P1-P2-E. Thus pathwaylengths for the four levels of detour distance were 18.7,34.3, 51.1, and 78.7 cm. There were also three straight-line stimuli, for which the pathway was in fact the directline SE, one in each region.

Procedure. Observers were blindfolded. On each trial,the observer examined a stimulus as in Experiments 1-4. As previously, he or she was allowed to feel the pathway

from end to end as many times as desired. The experi-menter then instructed the observer to judge the positionof either the direct line (from the end point E to thestart point S) or the detour line (from E to F, the furthestpoint on the path).

Responses were made by setting a pointer, the fixedend of which was centered on a reference line mountedon a response board. The free end of the pointer toucheda circular protractor, from which response angles wereread. To prevent use of absolute spatial position inresponding, this apparatus was on a table to the observer'sright so that it was necessary to swivel rightward torespond. The observer was to pretend that the fixed endof the pointer was at the end of the pathway and thatthe reference line on the response board was the samereference line as originally examined. For the direct-linejudgments, the subject was to set the pointer toward thestart point on the pathway; for the detour-line judgments,the subject was to point toward the farthest detour pointon the pathway. The instructions and feedback duringpractice trials made it clear that the farthest point wasthe one that deviated most from the direct line along aperpendicular.

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Error'— .25 actual* 16

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30 40 50 60 70 80 90 100 110 120 130 140 ISO

DIRECT ANGLE (deg)

Figure 6. Experiment 5: Mean signed errors in judgments of angular position of the direct line (positiveerror is an overshoot; negative error is an undershoot) as a function of the true direct angle, for each modeof exploration (anchor, no anchor). (The symbol at the top of the graph indicates the detour distance forthe stimulus having the corresponding direct angle, Dl = 2.5 cm, D2 = 6.7 cm, D3 = 11 cm, D4 = 17.9cm. Bars indicate one standard error of the mean. Separate functions are shown for straight vs. curvedpaths.)


Both judgments were made for each of the 24 curved-pathway stimuli by using both the anchor and no-anchormodes of exploration. For each of the three straight-line

stimuli, only the direct-line judgment was made (becausethere was no detour from the straight line). Thus therewas a total of 102 trials, distributed over two to three 1-hr sessions in random order. The first session began with

two practice trials with feedback.

Results

In general, the results did not conform topredictions based on the use of a movement-based heuristic. Responses were not distortedin the direction that the pathway detouredfrom the euclidean line between its endpoints,nor did errors increase as the detour distanceincreased. Mode of exploration had littleeffect on these results.

Signed error was measured as the lesser ofthe two angular differences between the truestimulus angle and the observer's response.

Underestimations (responses within 180°clockwise of the true value) were signednegatively; overestimations were signed posi-tively. Figure 6 shows the errors for judgmentsof the direct line's angular position as afunction of true direct angle. Each pointcorresponds to a different stimulus. The strik-ing linearity of the function indicates whystimuli are not plotted separately for eachlevel of the region variable. Figure 7 showscorresponding results for detour-line judg-ments.

Clearly, error for both types of judgments(direct and detour line) is a linear functionof the true angle, with no effect on detourdistance. As a movement-based strategy didnot appear to be used in judging position,additional analyses were performed. Theslopes and y intercepts of the error versustrue angle functions were considered to eval-

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DETOUR ANGLE (deg)

Figure 7: Experiment 5: Mean signed errors in judgments of angular position of the detour line, as afunction of the true detour angle, for each mode of exploration (anchor, no anchor). (Detour distance is

indicated as in Figure 6. Bars indicate one standard error of the mean. Separate functions are shown forthe clockwise and counterclockwise pathway directions.)


uate the possibility that a nonmovement-based, spatial referent strategy was used. Forthe curved pathways, the effect of pathwaydirection depended on the type of judgment.For judgments of the direct line (Figure 6),error values for clockwise and counterclock-wise pathways fell along a single function.(The r2 values were .94 and .92 in the anchorand no-anchor conditions, respectively.) Theslope of that function was steeper in the no-anchor condition, F(l, 18) = 5.11, p < .05.In contrast, for the detour-line judgments(Figure 7) there were two distinct functionsrelating error to true angle, one for eachpathway direction. These functions had dif-ferent intercepts, F(l, 18) = 45.8, p < .001.(The r2 values for the clockwise and counter-clockwise functions were .88 and .81 in theanchor condition and .81 and .77 in the no-anchor condition.) There were no gendereffects.

To compare the straight pathways with thecurved ones, additional analyses were per-formed on the direct-line judgments (Figure6). This time the pathway direction factorwas replaced with "pathway type" (curvedclockwise vs. curved counterclockwise vs.straight). The straight-line paths lay along adifferent function from the curved; in theanalyses of slopes and intercepts, the pathwaytype factor produced Fs(2, 36) = 29.4 and34.9, ps<.001, respectively. Although thismay indicate an effect of movement, it seemslikely to be mediated by the greater memorydemands of following curved pathways.

Experiment 6

Experiment 5 generally failed to confirmthe expectation that movements involved inhaptic exploration would distort the percep-tion of inferred position, as they had theperception of inferred distance in Experiments1-4. Neither the distance that a pathwaydeviated nor its direction of deviation fromthe inferred direct line affected judgments ofthe orientation of that line. Instead, the resultsof Experiment 5 suggested the use of a non-movement-based, spatial-referent heuristic forencoding position information. The spatialheuristic is indicated, in particular, by thelinear functions relating error to the trueangle. In terms of this heuristic, the functions

in Figures 6 and 7 can be more meaningfullyexpressed as

Error = o(true angle — b),

where a is the slope of the function(s) in eachfigure and b is the corresponding x intercept(i.e., the judged angle that is perceived withzero error). As this expression indicates, errorwas roughly a constant fraction (given by theslope) of the departure of the true stimulusangle from another angle b. If subjects judgedposition by first computing the deviation ofthe judged line from an implicit axis at b,and then moved the pointer away from thataxis some constant fraction of that deviation,a linear error function like that observedwould be obtained.

By this reasoning, the slope of the errorfunction indicates the extent to which theimplicit axis was relied upon: the steeper theslope, the more the response deviated towardthat axis and the greater the error. The resultsof Experiment 5 indicate, then, that observersrelied more upon implicit spatial axes whenexamining curved as compared with straightpaths. Further, they indicate that in judgmentsof the direct line, an anchor produced slightlyless reliance upon a spatial axis. The x inter-cept of the error function indicates the posi-tion of the implicit axis that was used. Theabove analyses therefore suggest that the modeof exploration and pathway direction did notaffect the axis used to make direct-line judg-ments (which was at about 90°), but that theaxis used for judgments of the detour anglevaried with pathway direction (in the vicinity-of 45° and 135° for detour-line judgmentswith the clockwise and counterclockwisepathway directions, respectively).

One might conclude from this latter findingthat the direction of movement influencedperformance by dictating which spatial axisto use in judging the detour point's position.Experiment 6 tested an alternative to thismovement-based strategy. It derives from theobservation that the distribution of detourangles in Experiment 5 varied with pathwaydirection, that is, clockwise pathways weremostly less than 90° and centered around45°, and counterclockwise pathways weremostly greater than 90° and centered around135°. If subjects had learned about this verynatural arrangement (during practice trials


or early in the experiment), they might haveused implicit spatial axes in the mannerindicated by the results. (The low variabilityindicates that the arrangement was learnedearly and the spatial heuristic used consis-tently, if at all.)

To test this alternative explanation, therelative positions of direct and detour angleswere reversed in Experiment 6. Now thedetour angles were distributed around 90°,and the distribution of direct angles variedwith pathway direction; that is, clockwisepathways were associated with direct anglespredominantly greater than 90°, and coun-terclockwise pathways were associated withdirect angles less than 90°. If subjects tendto hone in on spatial axes that reflect thegeneral arrangement of judged angles and torefer to these axes when making their judg-ments, we should find that the functionsrelating error to direct angle now vary withpathway direction, and those measuring errorfor detour judgments do not—the reverse ofthe pattern in Experiment 5.

Method

The naive observers were 9 male and I I femalestudents in introductory psychology at UCSB; all subjectswere normally sighted. The stimuli were similar in designto those of Experiment 5, with the following changes.There were only two values of detour distance, 7.9 and15.2 cm. The corresponding pathway lengths were 29.3and 50.9 cm, which are 1.5 times (cf. 2 times inExperiment 5) the length of the S-P1-P2-E path shown

in Figure 5. Pairs of pathways differing in the directionfactor were related as shown in Figure 8. For each valueof detour angle, there was a clockwise and counterclock-wise path that were reflections of one another aroundthe FE axis. These had the same points E and F (andthus the same detour line), but approached it fromopposite directions.

The stimuli comprised 12 pathways (six mirror-imagepairs) whose detour angles fell within 0-90° and 12whose detour angles fell within 90-180°. The position ofthe direct lines varied within ±60-83° of the detourlines. (The detour and direct angles used and correspond-ing detour-distance values are shown in Figures 9 and10.) Each observer took part in 2 practice and 48 regulartrials over one or two sessions lasting approximately 1 to1 1/2 hr. Only the no-anchor mode of exploration was

used. Each stimulus was presented twice, once with thedetour-line judgment and once with the direct-line judg-ment, in random order. Observers were told which judg-ment to make after exploring the pathway.

Results

The results are shown in Figures 9 and 10.As in Experiment 5 (although the fits were

(F)

(Table Eda«l

(S|-E}= Potti I,clockwise^— ($2-E)« Path 2,counterclockwise

L FER » detour angle <IOO*IiS, E R • direct ongle.Path I (143')

LSZ E R * direct angle.Palh 2 ( 57° )

Figure 8. Experiments 6 and 7: Sample pair of configu-rations resulting from superimposition of stimuli that are

reflections about a common detour line.

weaker), error was a linear function of thetrue angle judged. More important, reversalof the distributions of detour and direct anglesled to a reversal of the previously obtainedresults. For the detour judgment, the valuesfor both pathway directions lay along a singlefunction (r2 = .72). For the direct judgment,the clockwise and counterclockwise pathwaydirections produced different functions (r2 =.41 and .49, respectively). These observationswere confirmed by ANOVA on the slopes andintercepts, with judgment (detour, direct),pathway direction, and gender as factors.There were no significant effects on slopes.The intercepts of the functions differed as afunction of pathway direction, F(l, 18) =6.25, p < .05, but only for the direct-linejudgments—F(\, 18) = 6.43, p < .05 for theJudgment X Direction interaction.

Together with Experiment 5, these resultsindicate that subjects use implicit spatial axesrather than a movement-based heuristic injudging position. A spatial axis represents thegeneral location of a group of angles (e.g.,detour angles on clockwise-directed pathways).The influence of movement is therefore quiteindirect. Where groups of angles associatedwith different directions of movement tendto have different locations in the plane, judg-ments of those angles will refer to differentspatial axes.


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DIRECT ANGLE (deg)

Figure 9. Experiment 6: Mean signed errors in direct-line judgments as a function of true direct angle;

bars indicate one standard error of the mean. (The symbol at the top indicates the detour distance value

for the corresponding stimulus, Dl = 7.9 cm, D2 = 15.2 cm. Separate functions are shown for clockwise

and counterclockwise pathway directions.)

Experiment 7

Experiment 7 attempted to eliminate theuse of the spatial heuristic just described, todetermine whether movement-related vari-ables (i.e., detour distance and pathway di-

rection) would then affect judgments of spatial

position. Both detour and direct angles weredistributed throughout the 360° plane, sothat it was impossible to approximate theirgeneral location with any one axis.

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DETOUR ANGLE (dag)

Figure 10. Experiment 6: Mean signed errors in detour-line judgments as a function of true detour angle;

bars indicate one standard error of the mean. (Detour distance is indicated as in Figure 9.)


Table 5

Experiment 7: Mean Error and Standard Error of

the Mean by Gender, Detour Distance (in

Centimeters), and Direction

Detour distance (cm)

Direction 4.1 SE 7.9 SE 15.2 SE

FemalesClockwise -3.8 4.2 3.9 1.8 7.6 3.7Counter-

clockwise 12.2 2.7 0.9 1.9 5.0 3.3Males.Clockwise O.I 3.5 1.5 3.4 0.7 2.7Counter-

clockwise -4.7 3.5 -0.8 3.0 -1.8 2.0

Method

Observers. The normally sighted naive observers were12 male and 8 female students in introductory psychologyat UCSB.

Stimuli. The stimuli were the same pathways used inExperiment 6, reoriented, plus six mirror-image pairshaving a detour-distance value of 4.1 cm and a pathwaylength of 18.3 cm. Pathways departed from the startpoint in either the clockwise or counterclockwise direction,where the end point was the center of the clock. Thestimuli were oriented so that the detour angles fell withinsix regions that divided the 360° plane into 60° segments.For each detour distance, one pair of stimuli with acommon detour line fell in each region. The direct angleswere within ±40-83° of the detour angles. Each observerwas given the 36 stimuli in a random order in one sessionthat began with two practice trials.

Procedure. The procedure was like that of the no-anchor, detour judgment trials of Experiment 5; neitherthe direct judgment nor the anchor condition was used.

Results

The results indicate that when a spatialheuristic is ineffective, the distance and direc-tion of movement still do not bias judgmentsof position. Table 5 shows the mean signederror over observers and the standard errorof the mean for each condition. Althoughthere were effects of critical movement-relatedvariables, that is, detour distance and pathwaydirection, these were unsystematic and attrib-utable to stimulus variations. Each combi-nation of direction, distance, and region cor-responded to a unique pathway, and differentpathways produced different values of signederrors, leading to a three-way interaction,FllO, 180) = 4.68, p < .001, a Direction XDistance interaction, F(2, 36) = 3.46, p <.05, and a region effect, F(5, 90) = 2.35, p <

.05. The very tight configurations resultingfrom a detour distance of 4.1 cm were par-ticularly error-prone. This was especially trueof one such configuration, in which the po-sition of the detour point was clearly ambig-uous. When these stimuli were eliminatedfrom the analysis, there were no significanteffects whatsoever. Effects of gender and theGender X Distance X Direction interaction,F(l, 18) = 5.23 and f\2, 36) = 5.80, ps <.05, were also observed in the overall analysisbut vanished with the elimination of the 4.1-cm detour pathways.

General Discussion

The results of the current experimentsindicate that haptic perceptions of distanceand position both rely on encoding heuristicsand that these perceptions, as a result, aresubject to different forms of distortion. Thenature of the heuristic appears to vary withthe encoded spatial attribute.

Experiments 1-4 indicate the use of move-ment-based heuristic when inferring the eu-clidean distance between two points on acurved line. As pathway extent increased, theeuclidean distance between the start and endpoints was increasingly overestimated by bothsighted and blind observers. This pathwaydistortion effect was more pronounced incongenitally blind observers than adventi-tiously blind, suggesting that visual experienceaids in inferring spatial extent from hapticexploration.

One interpretation of the distance distor-tion effect is that observers based their esti-mates of length on the duration of their fingermovements. Such temporal influences onjudgments of extent have been noted previ-ously (Wapner, Weinberg, Click, & Rand,1967; Wong, 1977), particularly in the "tau"effect (e.g., Scholtz, 1924), which is a tendencyfor judgments of the spatial distance betweentwo stimuli to increase with their temporaldistance. Another interpretation, similar toaccounts of the filled-space illusion, is thatsubjects used the spatial extent of the exploredpathway to infer the euclidean distance. Thepresent data cannot, however, discriminatebetween distortions mediated by time or spaceand those attributable more directly to move-ment.


In contrast to the distance judgments, peo-ple appeared to use a heuristic that is notbased on movement when judging position;that is, they used one that referred positionsto implicit spatial axes in the pattern plane.Similar heuristics have been found with visualdisplays (Tversky, 1981). Errors resulted be-cause observers' judgments were pulled to-ward these axes by some roughly constantproportion of the departure of the direct linefrom the implicit axis. Variables manipulatingobservers' exploratory movements had onlyindirect effects on their errors, influencingtheir choice of spatial referents.

What can be said regarding the route versussurvey map distinction from these results? Ifobservers built up a route map of the pathwayfrom haptic exploration and used that mapto answer questions about the inferred euclid-ean line, their judgments should be directlyrelated to the route of exploration; that is,movement-related distortions should occur.The experiments on position judgments areclearly inconsistent with this account; in fact,the use of implicit spatial axes segregatingregions of the plane suggests a survey repre-sentation. The judgments of distance, however,appear more in line with a route map inter-pretation. Alternatively, it remains possiblethat observers built up a distorted surveymap from their movements. With the currentdata, caution must be exercised when consid-ering a route map versus survey map inter-pretation. Whether surveylike or routelike,what is clearly indicated is that movementplayed a role in building the representationused for judging distance by both sighted andblind individuals and implicit reference axesplayed a role in the representation used forestimating position.

Further work is needed to clarify the con-ditions under which movement-dependentand movement-independent strategies will beused. However, the results of the presentstudies are immediately relevant to tangiblegraphics displays. In revealing certain sourcesof errors, our results have implications bothfor the design of such graphics and for theiroptimal use.

It should be noted that the present infer-ences about tangible graphics must for nowbe restricted to the curved, irregular sort offigures used here. However, despite this caveat,we have demonstrated specific sources of

distortion in haptic spatial perception andcan suggest means by which they might bereduced in an applied setting.

With regard to design, one message is thatthe size of a graphics configuration is ofcritical importance in determining the accu-racy with which it communicates spatial in-formation; moreover, optimal size may varywith the nature of the information to becommunicated. In Experiments 1-4, smallerdisplays were less conducive to errors indistance estimation, which may be becauseof their making smaller demands on memoryor may simply reflect Weber's law. However,in Experiment 7, smaller tightly curved path-ways yielded markedly high errors in positionjudgments, which may reflect limits on "hap-tic acuity." Thus, size may trade off withother factors, and optimal size should beempirically determined in the context of ap-plication. A second message from the exper-iments on position is that tangible graphicsshould provide explicit referents (points,lines), to reduce distortions resulting from anarbitrary spatial-referent strategy (see alsoLederman & Campbell, 1982).

With respect to the most effective meansof exploring tangible graphics displays, thepresent experiments suggest first that the userof a display should not be asked to ascertaina variety of spatial information simulta-neously. This is indicated by the reductionin (but note, not elimination of) error whensubjects had to prepare for one versus twojudgments in Experiments 1-4. Surprisingly,the use of an anchor in both sets of studiesdid not consistently reduce overall error, andit certainly did not eliminate (although itsometimes reduced) the distortions due toeither movement-based or spatial heuristics.Furthermore, when the use of an anchor didhave a positive effect, it extended only tojudgments about the straight line between thefingers and not the pathway actually traversed(i.e., judgments of euclidean but not pathwaydistance in Experiments 1-4; direct-line butnot detour-line position in Experiment 5).Thus, use of an anchor should be recom-mended only when information about itsposition is directly relevant to the judgmentbeing made, and even then it appears oflimited value.

In conclusion, our results suggest that thereis flexibility in the heuristics used to encode


pattern information from haptic exploration.When judging distance, our observers ap-peared to use a movement-based strategy;when judging position, they relied on implicitspatial axes. The latter strategy has also beendemonstrated with visual pattern encoding,suggesting that vision and touch can haveencoding heuristics in common. Could vision,like touch, also make use of a movement-based heuristic? It is possible that movementmight play a strategic role in visual encodingof large-scale patterns that require multiplefixations and eye movements in order to beviewed. In this case, vision would more closelyresemble haptic processing of small-scalespace, in that movement would be intrinsicto pattern exploration.

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Received March 16, 1984Revision received June 5, 1984 •

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