Psychol. Res. 38, 283-302 (1976)

© by Springer-Verlag 1976

The Structure of Haptic Space in the Blind and Sighted * **

MICHAEL BRAMBRING

Fachbereich Psychologie, Universit~t Marburg, D-355 Marburg/Lahn,

GutenbergstraBe 18, Federal Republic of Germany

Received March 3 / September 8, 1975

SUMMARY. The purpose of the present experiment was to analyse

the metric of haptic space. The subjects were shown a goal-point,

after having felt the sides of a right triangle with differing

lengths. The subjects were then required to estimate the posi-

tion of the goal-point in one of two ways, either along the

hypotenuse from the starting point (a cognitive spatial orienta-

tion task) or via the sides touched previously (a perceptual

spatial orientation task). They were asked to do this either by

making a hand movement which would approximate the distance

(motor estimate) or verbally (verbal estimate). There were four

groups of subjects: congenitally blind (CB), adventitiously blind

(AB), sighted under blindfold (SB), and sighted people with visual

pre-orientation (SV). 10 subjects were in each group. The major

results of the experiment were: (I) With all groups but SV a

distortion was observed in the estimates of the shortest distance

from the Euclidian metric to the city-block-metric. (2) The groups

AB and SB produced the largest distortion from the Euclidian

metric. (3) In the case of motor estimates, both cognitive and

This investigation was supported in part by the German Research Association

(Deutsche Forschungsgemeinschaft) ; head of the research project

Prof. Dr. F. Merz.

** I thank the staff of the "Blind Mobility Research Unit" of the University

of Nottingham for the support in correcting the English translation.

283

perceptual spatial orientation tasks led to congruent metrics.

(4) With the exception of group SV verbal and motor estimates

led to divergent metrics. The results are considered from the

points of view of (a) empiricist theories, (b) theories of equal

laws of structure for all sensory modalities, and (c) the hypothe-

sis of transposition.

INTRODUCTION

Blind people are restricted through loss of vision mainly in their

ability to read and to move around independently. The introduc- tion of Braille many years ago has partially compensated for

the inability to read visually. In contrast, however, efforts

have only recently been made to improve the mobility of blind

people through systematic mobility training (Hoover, 1950).

The locomotion of blind people in the street or in open spaces is

chiefly restricted by two difficul~ies: first by their lack of

ability to perceive and identify satisfactorily objects at a dis-

tance, and secondly by their inability to orient themselves. Only

in the last few years research workers and teachers of the blind

have become more intensively concerned with the orientation prob-

lems of the blind. Tactual maps have been developed in order to

improve their geographical orientation (Leonard and Newman, 1970;

Bentzen, 1972; Kidwell and Greer, 1973; James, 1973). Yet, the

cognitive picture or mental map that blind people possess of their

environment and how they orient themselves to it is largely un-

known. Furthermore, it is not clear whether geographical represen-

tations in the haptic and in locomotive space are similar, or how

the transformation from a tactual map into locomotion occurs.

The present paper seeks to analyze the metric of haptic space from

the point of view of the geographical orientation of the blind.

The term geographical orientation refers to a person's ability to

establish his actual position in relation to a not directly visible

topographical space, for example, the ability to maintain a sense

of direction when moving about in familiar and unfamiliar surround-

ings. Thus, geographical orientation requires first the establish- ment of one's actual position relative to the immediate environment

(estimation of distance and direction), and secondly the establish- ment of one's actual position in relation to a topographical refer-

ence system (cognitive and perceptual spatial orientation).

The differentiation between cognitive and perceptual spatial orienta- tion is important, from both theoretical and practical points of view: theoretically, because it is beyond question that perceptual spatial orientation is possible for blind people, whilst opinions

284

differ as to whether this applies to cognitive spatial orienta-

tion; practically, because each aspect involves a different type

of orientation task. Perceptual spatial orientation refers to

the ability to recognize a previously walked route, or to find a

route independently from tactual or verbal information; cognitive

spatial orientation refers to the ability to return on the shortest

route after a detour or different alternate detours. Thus, cogni-

tive spatial orientation refers to orientation in a topographical

space without previous experience of the route; perceptual spatial

orientation to orient with previous inforamtion about the route.

In other words, in the case of perceptual spatial orientation it

is necessary to reproduce a spatial relationship; in case of cog-

nitive spatial orientation one mustproduce a new spatial relation-

ship.

GENERAL THEORETICAL CONSIDERATIONS

It is possible to sum up the previous theories and research re-

lating to orientation problems of blind people under the following

headings:

I. Empiricism - Nativism

The philosophical controversy (e.g. Locke, 1632 - 17o4) over,

whether blind people are able to develop spatial imagery at all, has

been replaced by the psychological question of, how sighted people

perceive and how people without vision are able to give non-

visual experience a spatial representation.

The philosophical issue was particularly strongly discussed in

Germany in the 193Os, especially as a results of v. Senden's case

studies (1932) of congenitally blind people who had been operated on

for cataract in adulthood. Following these reports, v. Senden

came to the conclusion that owing to a lack of visual experience

the congenitally blind are unable, or hardly able, to develop

spatial imagery. This conclusion has been contested by several

authors on theoretical, empirical, and methodological grounds

(Hebb, 1949; Wertheimer, 1951). Present-day psychological research

has no doubt that, on the one hand fundamental, that is, bio-

logically determined perception, such as figure-ground perception

or rudimentary depth perception, is innate, but that on the other,

man's perception depends to a great extent on factors of learning.

More recent case studies on congenitally blind people who have

undergone surgery (Gregory, 1966; Valvo, 1968) justify the criti-

cism of v. Senden's conclusions. Gregory (1966) even doubts

whether such cases can give information on the philosophical isSue

at all, as the congenitally blind adult who has been operated upon

285

is not comparable with a sighted infant owing to his previous

non-visual experience and his different ability to learn. For example, immediately after the operation, Gregory's patient was able to recognize visually things which he knew tactually, such

as capital letters. These findings suggest that spatial modalities could be acquiredby all sense modalities, even though varying

in intensity and extent.

2. Geographical Orientation

Most of the psychological research into geographical orientation

of blind or sighted people has investigated their ability to give estimates of the distances and directions from their vantage point of geographical places, e.g. places in a town, or well-known towns

within a country; little research has been directed towards in-

vestigations of geographical orientation after walking given routes (cf. Howard and Templeton, 1966, p. 262/3). Howard and Templeton (1966) indicate that patients with certain brain lesions exhibit typical and systematic distortions in the drawing of their geographical surroundings; different processing of information

in the brain leads to different cognitive pictures of geographical lay-out. Another example of systematic distortion of the geograph- ical representation of one's surroundings is given by Gould and

~ite (1974): differing ethnic populations in Los Angeles (whites, blacks, and Spanish-Americans) possess quite different mental maps

of their town; the different geographical pictures obviously depend on the differences in locomotion as well as in the different

experience of the groups. Analogously, one may ask what kind of

cognitive picture blind people possess due to their restricted locomotion and distinctive method of information collection and

processing.

The earliest investigation into geographical orientation with blindfolded sighted subjects after having walked given routes was carried out by Liebig (1933). This revealed that deviation from the correct goal point depends on the kind of route: errors of estimation are greater after having followed a route involving curves than after a route somposed of linear movements. Worchel

(1951) compared the performance of two samples of 33 subjects -

one sample of blindfolded sighted people and the other congenitally

and adventitiously blind people. After having walked figures of triangular shape, blindfolded sighted people achieved significantly higher accuracy at reaching the goal point than did blind people and no significant difference was revealed between performance of the congenitally and adventitiously blind groups. The superior accuracy of the sighted people, however, was based on a more accurate estimate of direction, rather than of distance.

In contrast, Juurmaa (1965) failed to discover any significant

286

difference between blindfolded and blind groups with similar

tasks. However, his figures were more complicated than Worchel's

and this may explain the contrary results. Both investigations

used only the accuracy of the fixation of the goal point of certain

routes as the dependent variable. They did not record the manner

in which the performance was achieved. One might postulate that

differences exist in the cognitive approaches of the two groups

no matter whether the two groups achieve similar or dissimilar

accuracy in reaching the goal point.

3. The Structure of Space

The structure of any space may be described by characteristics

such as boundaries, volume, metric, isotropy, and so on. In the

present study especially the termmetric is important. Mathemati-

cally, the term metric means a specific function which passes

through any pair of points in the space. A well-known metric

is the Euclidian metric which means that the shortest distance

between any pair of points in the space can be described by a

striight line, i.e. a linear function. Luneburg (1947, 1950) was

able to show that for visual space the Euclidian metric is not

valid. Visual space is non-Euclidian and the shortest distance

between any pair of points corresponds to the geodates on a

hyperboloid according to Riemann's spaces. Nevertheless, a mathe-

matical formulation of the metric of haptic space has not yet

been formulated.

However, the investigation by Kosslyn, Pick and Fariello (unpub-

lished) points out that significant deviations from the Euclidian

metric can be observed when vision is restricted. In their ex-

periment children and adults had to distribute objects in a large

room so that the shortest distance between any pair of objects

was equal. The room contained barriers, some transparent and

some opaque, around which the Ss had move in order to perform the

task. In addition, the Ss had to estimate the shortest distances

between each pair of objects verbally by means of the multidimen-

sional scaling method by Kruskal. Children estimated these dis-

tances to be longer when barriers of either type were present;

adults did so only in the presence of opaque barriers. Thus,

both restricted vision and the distance travelled in order to

perform the task influenced the estimates.

The investigations by Luneburg and by Kosslyn, Pick and Fariello

show that one can calculate the metric by means of motor or ver-

bal estimates. So far, it is not known whether both kinds of estimate lead to congruent results.

The purpose of the present experiment was to analyze the metric

of haptic space in the sighted and blind. In this connection two

287

different types of orientation tasks were chosen together with

two different types of estimates. The main interest of the present

study was to analyze the process of cognitive spatial orientation,

that is, whether people without vision are capable of producing

new spatial relations and how they achieve this. However, in

contrast to previous investigations (Worchel, 1951; Juurmaa, 1965)

this study attempted to analyze the cognitive information process

of orientation and not the accuracy of orientation tasks.

METHOD

General Procedure

In order to observe the process of spatial orientation in haptic

space, the right triangle was chosen as the simplest figure (e.g.,

Fig. I). The figures were produced legibly on manila paper used

for braille writing. According to the choice of the distances

very long and very short distances were avoided in order to prevent

a 'ceiling effect'. The directions for the movements in all three

stimulus conditions were in the first quadrant.

During the presentation of the figures the sheets of paper were

lying in the median plane of the body of the S. The left index

finger of the S was lying at the starting point A; with the right

index finger the S touched the raised detour distances as many

times as he wanted. During the motor estimates the S had to tap

ten times with a pencil from the starting point A to the goal point

B, while he raised his arm and put it down where he believed

that the goal point was situated. After each tap he stretched his

arm so that he did not simply copy his previous movement. During

the verbal estimates the S guessed the distances. The estimates

of the distances for motor movements were measured as a vector

from the starting point A as well as by Cartesian coordinates to

the nearest millimeter; the verbal estimates were given to the

nearest centimeter. The Ss were not given any feedback about their

estimates.

Experimental Condi ti ons

Four experimental conditions were chosen: two different types of

orientation tasks (I. cognitive and 2. perceptual spatial orienta-

tion) and two different types of estimates (I. motor and 2. verbal

estimates). Both orientation tasks were carried out with both

kinds of estimates. The main interest of the present study was

the analysis of the cognitive spatial orientation with motor estimate. For, theoretically, it was important to analyze how

people without vision were able to produce new spatial relations

after alternate detour routes. The motor estimate was chosen

288

because it was likely that the performance of all people would

be more comparable with this kind of estimate than with verbal

estimate. Therefore, only this experimental condition was carried

out with all three stimulus conditions; the other three experimen-

tal conditions: (1) cognitive spatial orientation with verbal

estimate, (2) perceptual spatial orientation with motor estimate,

and (3) perceptual spatial orientation with verbal estimate were

carried out with one stimulus condition. The restriction was nec-

essary in order to avoid overloading the Ss. Even under these re-

stricted conditions each S had to give a thousand motor estimates.

The whole investigation was divided into six individual sessions;

during the first three sessions the cognitive spatial orientation

tasks with motor estimates were carried out, each lasting approxima-

tely three quarters of an hour. The other three experimental

conditions were then conducted, the motor estimates lasting three

quarters of an hour and each verbal condition half an hour.

Subjects

Four groups of 10 subjects participated in the experiment:

I) Congenitally blind persons who were blind at birth and there-

fore did not possess any visual experience (congenitally blind

= CB).

2) Adventitiously blind persons who were blinded after the age

of five. In regard to the onset of blindness they possessed more

or less visual experience (adventitiously blind = AB).

3) Sighted persons who wore a blindfold during all sessions and

therefore this was carried out under similar experimental condi- tions as the blind people (sighted under blindfold = SB).

4) Sighted persons who viewed the figures first and then wore

a blindfold only during the motor estimates (sighted with visual

pre-orientation = SV). The experimental groups were matched concerning sex, age, and edu-

cational background. Each group consisted of five male and five female subjects; age ranged from 14 to 27 years; the younger Ss

were pupils of the German High School for the Blind (Deutsche

Blindenstudienanstalt) or comparable High Schools in Marburg; the

older Ss were students of the University of Marburg. All experimen-

tal and all stimulus conditions were carried out by the same Ss.

Stimulus Conditions

In the first stimulus condition (Fig. I), the distance of the

shortest line between starting point A and goal point B was

constant while the detour distances varied.

289

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l e n g t h o f t h e d i r e c t o r s h o r t e s t d i s t a n c e (c) b e t w e e n s t a r t i n g p o i n t A a nd

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After tactually inspecting representations of the detour distances

(b i + ai) , the task of the Ss was to estimate the shortest distance

(c i) between starting point A and goal point B each time.

In the second stimulus condition (Fig. 2), unlike the first stimu-

lus condition, the lengths of the detour distances (b i + a i) were

always equal, however, the lengths of the direct distances (ci)

were varied.

The figures of the first and second stimulus condition were so

arranged that a reciprocal control of the results was possible

because one could cross-validate them. Overall, 20 figures were

constructed in both stimulus conditions: in the first stimulus

condition there were for each direct distance four different detour

distances; overall, there were five different direct distances.

In the second stimulus condition there were for each detour dis-

tance four different direct distances; overall, there were five different detour distances.

In the third stimulus condition (Fig. 3) the lengths of the detour

distances (b i + ai) and the lengths of direct distances (c i) were always equal.

In the third stimulus condition, the figures were rotated by -30 °,

- 10 ° , O °, +10 ° and +30 ° according to the horizontal axis of the

sheet of paper. Through this condition it was possible to discover

290

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Fig. 2. Arrangement of the figures of the second experimental condition. The

lengths of the dircet or shortest distances (ci) between starting point A

and goal point B i are always different; the lengths of the detour distances

(h i + ai) between starting point A i and goal point B i are always constant.

The dash-dot-line shows the horizontal axis of the sheet of paper for the

figures

B 5

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Fig. 3. Arrangement of the figures of the third experimental condition. The

leng~s of the direct or shortest distances (ci) between starting point A i and

goal point B i are always constant; the lengths of the detour distances (b i + ai)

between starting point A i and goal point B i are always constant. The dash-

dot-line shows the horizontal axis of the sheet of paper for the figures

291

whether the estimates of distances were invariant against a rota-

tion in the space. Furthermore, it was possible to check the accuracy of the estimates because detour distances and direct dis-

tances were varied together four times. In all, this gave 20

figures for the third stimulus condition.

Types of Spatial Metric

This experiment was concerned with three different types of spatial

metric of how subjective estimates were made, and what effects different detour distances would have on these estimates. These

suggest, for example, for the four triangles in Fig. I (I) that

in spite of the differences in the lengths of the two sides of

the detour distances, the direct distance will all be estimated

as equal; (2) that as the lengths of the two sides of the detour

distance increase, the direct distances will be estimated as :corre-

spondingly longer; (3) that as the longer side of the detour

distance increases in length, the length of the direct distance

will be estimated as correspondingly longer. These three different

types of estimates each correspond to a different metric: In

the first case the type of estimate corresponds to Euclidian

metric; in the second case to a city-block-metric and finally, in

the last case to a supremum-metric. Mathematically, all three

metrics are special cases of the Minkowski p or r metrics. Accord-

ing to the Minkowski-metrics the shortest distance between starting

point A and goal point B can be calculated by:

I rl I/r (Ix =1

X,Y = Cartesian coordinates of the space; n = dimensions'of the

space; r = weighting factor (exponent)

Mathematically, it is possible to demonstrate that with r = 1.0

the city-block-metric, with r = 2.0 the Euclidian, and with

r -- ~ the supremum-metric occurs.

RESULTS

The statistical analysis consisted of comparisons of averages and

standard deviations of the motor and verbal estimates for indepen-

dent and dependent populations. In addition multiple statistical

tests were applied (cf. Sachs, 1969). The metric was calculated

for the first and second stimulus condition at which detour and direct distances were varied separately. This section deals first

with the main question of the investigation. That is, how far are the estimates of the shortest distance in haptic space

292

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influenced by the length of the detour distances? Secondly, the

accuracy of these estimates were calculated and are shown in Table I.

An analysis of Table I shows, first, that the standard deviations

for all four of the experimental groups and for the three stimulus-

conditions are approximately equal. Sighted people with visual

pre-orientation (SV) show the lowest standard deviations. Second,

the third stimulus condition is the best condition to compute the

accuracy of the motor estimates because the detour and direct

distances had been co-varied. A sign test for trend in location

and dispersion (Cox and Stuart, 1955) demonstrates that the esti-

mates can be described by linear functions; these linear functions

in turn point out deviations from m = 1.O with regard to the linear

coefficients (m). These deviations are significant for three of

the four experimental groups (Groups CB, AB, and SB: 8 values of

the linear coefficients less than m = 1.O, p < .05; group SV pro-

duced 6 values less than m = 1.O, p > .05). A Kruskal-Wallis test

was used to discover differences between the groups; this shows the

following result: H = 9.05, df = 3, p < .05. Subsequently, Mann-

Whitney U-tests were used which showed that the congenitally blind

group (CB) gave a significantly lower linear coefficient than the

other three groups (U-tests: critical values for n I = 10, n 2 = 10,

two-tailed test U < 23, p < .05. CB vs AB: U = 18, p < .05; CB vs

SB: U = 19, p < .05; CB vs SV: U = 14, p < .05).

In the first two stimulus conditions one can observe the influence

of independent variation of the detour distance and the direct

distance: a) The first stimulus condition holds the direct dis-

tance constant while detour distances are varied. With the excep-

tion of the group of sighted people with visual pre-orientation

the variation of the detour distances has a systematic influence

on the estimates of the direct distance. The effect is strongest

for adventitiously blind people (AB); there is 2.7 cms difference

in the estimates of the constant direct distance between the

shortest and the longest detour distance (20.9 cms - 18.2 ems).

If one considers the fact that all motor estimates are too short,

which can be seen from the linear functions, and corrects the

observed differences with the reciprocal values of the linear

coefficient (m-l) - comparable to a correction for attenuation -

one would then get a corrected value. For example, if we take the

case above, the corrected value is 3.8 cms which results from 2.7

cms x 0.71 -I . This correction is necessary i T order to level the

systematic underestimation of distances in haptic space as well as

to equalize the differences in the underestimation of the different

experimental groups. The statistical analysis compares the esti-

mates of the direct distance (Xc') for all the different detour

distances (b+a) by means of the Wilcoxon-Wilcox-test for multiple

comparisons of dependent samples (cf. Sachs, 1969, p. 532). For

example, the comparison between x c' =20.6 cms and 19.8 cms yields

a value of 17.O in the Wilcoxon-Wilcox-test which is higher than

294

the critical value of 14.8, p < .05 (Wilcoxon-Wilcox-test: critical

values for n = 10 and k = 4 are 14.0 = p < .05, 18.O = p < .O1.

CB: 17.0 s between 20.6 cms and 19.8 cms; AB: 20.5 ss between 20.4

cms and 18.2 cms, 24.5 ss between 20.9 cms and 18.2 cms, 17.5 s

between 20.9 cms and 19.4 cms; SB: 15.0 s between 21.7 cms and

20.3 cms). Thus, the statistical analysis yields significant re-

sults for three of the four groups; it is the SV-group whose esti-

mates were not influenced by the different long detour distances

and whose data are non-significant.

b) In the second stimulus condition, in which a constant detour

distance was combined with varied direct distances, the results

showed significant differences for most of the distances of the

SV-group. However, significant differences appeared rarely in the

distances of the other groups (Wilcoxon-Wilcox-test: critical values

for n = 10, k = 4: 14.8 = p < .05 and 18.O = p < .O1. CB: 14.O s

between 22.8 cms and 21.7 cms; AB: 18.O ss between 20.3 cms and

19.2 cms; SB: 15.0 s between 21.3 cms and 20.0 cms, 16.5 s between 21.3 cms and 19.9 cms; SV: 15.5 s between 19.4 cms and 17.5 cms,

23.0 ss between 20.2 cms and 17.5 cms, 21.5 ss between 20.2 cms and

18.1 cms).

Overall, the results indicate that a confident statement is only

possible for sighted people with visual pre-orientation who ex-

clusively use the yardstick of direct distance, unlike the other

three groups who use some sort of mix between direct and detour

distances as a yardstick for their estimates.

In Table 2 the estimates of the direct distance are shown in an

analogous manner for the control experimental conditions.

Table 2 shows (1) that it is striking that the standard deviations of the congenitally blind people under cognitive spatial orienta-

tion with verbal estimates are much higher than the standard

deviations of the other groups; for all of the distances there are

differences at the O.O1 level of significance. Furthermore, the

standard deviations of the sighted people with visual pre-orienta-

tion are significantly less than those of the adventitiously blind

at the 0.05 level of significance. Between the sighted groups a

significant difference does not exist (F-tests: critical values

for df = 9/9 are F = 3.18, p < .05 and F = 5.35, p < .O1).

(2) The linear coefficients (m) of the linear functions only deviate

significantly from m = 1.O. For congenitally blind people (Signtest

for trend by Cox & Stuart: 8 values greater than m = 1.O, p < .05).

(3) With reference to the first two stimulus conditions it

is again possible to observe the influence of the separate varia-

tion of detour and direct distances; however, it was carried out

with only one stimulus condition for each experimental condition:

a) In the first stimulus condition, the statistical analysis

yields significant differences only for adventitiously blind and

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blindfolded sighted people (Wilcoxon-Wilcox-test: critical values for n = 10, k = 4: 14.8 = p < .05 and 18.O = p < .01. AB: 17.O s

between 21.8 cms and 19.7 cms; SB: 15.O s between 22.7 cms and 21.2

cms). b) In the second stimulus condition there are significant

differences with the exception of congenitally blind people

(wircoxon-Wilcox-test: critical values for n = 10, k = 4: 14.8 =

p < .O5 and 18.0 = p < .O1. AB: 15.O s ~etween 20.3 cms and 17.5

cms; SB: 18.0 ss between 23.0 cms and 20.3 cms, 15.O s between

21.6 cms and 20.3 cms; SV: 22.O ss between 22.0 cms and 19.1 cms,

16.5 s between 20.6 cms and 19.1 cms).

Table 3 shows the values of the analysis for the various experi-

mental conditions. The values of the differences (c 4' - ci') are

all corrected by the reciprocal values of the linear coefficients

(l/m). By means of this correction one can get comparable values

for the various groups and figures.

Theoretical differences for the various figures have been obtained

by calculating the values of the objective differences of all

r-exponents of the Minkowski-metrics from r = 1,O to ~o according

Eq. I (p.6). Then, the actual observed differences have been

found.

Three findings of significance are to be read from Table 3:

1) Looking at the r-values for the cognitive spatial orientation

task with motor estimates these show a high agreement between

both stimulus conditions. Sighted people with visual pre-orienta-

tion always exhibit estimates according to the Euclidian metric.

In contrast, adventitiously blind people exhibit the strongest

distortion from the Euclidian metric in favour of the city-block-

metric. The statistical analysis (Table 4) indicates that sighted

people with visual pre-orientation do not show any significant dif-

ferences from the Euclidian metric under both cross-validated stimu-

lus conditions; however, both adventitiously and blindfolded sighted

people show significant distortion under both stimulus conditions,

whereas congenitally blind people do this only under the first

stimulus condition.

2) Looking at the r-values for perceptual and cognitive spatial

orientation with motor estimates, the results show a high level

of agreement. A significant distortion from the Euclidian metric

is found only for the adventitiously blind people (Sign-trendtest

by Cox and Stuart: AB: 8 values < r = 2.0, p < .O5s).

3) Looking at the Verbal estimates only the congenitally blind

group shows a significant distortion from the Euclidian metric

(Sign-trendtest by Cox and Stuart: CB: 8 values < r = 2.0, p < .O5s).

298

Table 4. Significances for the exponents (r) of the Minkowski-metrics for

the experimental groups and the stimulus conditions

~ stimulus

dition

Experime~

tal group

I st 2 nd

s ns CB 8 values < r = 2.0 4 values < r = 2.0

s s AB iO values < r = 2.0 9 values < r = 2.0

s s SB 8 values < r = 2.0 8 values < r = 2.0

SV 6 values < r = 2.O ns 4 values < r = 2.O ns

Sign-test for trend in location and dispersion by Cox and Stuart;

s = p < .05; ns = p > .05

CONCLUSIONS

Interpretation of the present results leads to some interesting

conclusions:

I) If one considers the variance of the estimates of the various

groups involved in cognitive and perceptual spatial orientation

with both motor and verbal estimates, then the much higher variance

of the verbal estimates of congenitally blind people is noticeable.

Under all the other conditions this group displays approximately

the same variance as the other groups. Obviously, the congenitally

blind person has difficulty in estimating verbally those spatial

relationships which he cannot directly perceive. This reveals

the obvious unfamiliarity of this task to the congenitally blind

person and suggests a lack of sufficient feedback to enable him

to achieve congruence between motor and verbal estimates. It is

possible to characterize such a behavior as a form of "verbalism".

The question arises whether appropriate feedback will improve

congruence of motor and verbal estimates. Furthermore, this re-

sult may explain the statements of previous investigators about the

difficulties that congenitally blind people have in spatial orien-

tation tasks. It seems very important to be aware of the kind of

measurements used in these types of experiments.

2) In view of the present results, it seems unquestionable that

the metric of the haptic space is non-Euclidian. As the length

of the detour distances increases, the estimate of the shortest

distance deteriorates from the Euclidian metric to the city-block-

metric. This result is valid for adventitiously blind people,

sighted people under blindfold, and also to a certain extent for

congenitally blind people. However, sighted people with visual

pre-orientation produce estimates equivalent to the Euclidian

metric. This result confirms the expectation that, after visual

pre-orientation, the shortest distances are estimated according

299

to the Euclidian metric even under non-visual testing. Had this

group shown a distortion from the Euclidian metric, this would

have implied that either the perception of the shortest distance

in the near range of visual space is unable to be described by

means of a Euclidian metric - which would be contrary to previous findings - or that visual perception and the succeeding non-visual

motor estimation of the shortest distance are not equivalent.

Adventitiously blind people and almost to the same extent blind-

folded sighted people show significant distortions from the

Euclidian metric. In the case of cognitive spatial orientation

the shortest distance must be deduced, and these subjects are

searching for information on which to base their estimate. For

this , they use the detour distance to a great extent. This is

understandable because they know, from their prior visual ex-

perience, that a longer detour usually implies a longer direct

distance between the starting point and goal point of a path. The

fact that adventitiously blind people give results comparable to

those of the blindfolded sighted subjects shows that the internal

cognitive process for spatial orientation is identical in all

people who possess visual experience but are unable to use vision.

Furthermore, the duration of the loss of vision does not affect the type of orientation process but merely the variability of the

estimates.

The congenitally blind exhibit only to a restricted extent a distor-

tion away from the Euclidian towards city-block-metric. The reason

may be found in the inconsistency of the estimates. There seems

to be no clear strategy employed in problems of cognitive spatial

orientation. However, the results demonstrate that it is impossible

to deny that the congenitally blind possess spatial imagery. It

is worthwhile to investigate the reasons for this lack of a

consistent strategy, and whether the ability to make consistent

estimates could be acquired through appropriate feedback.

3) The congruence of the metric for both perceptual and cognitive

orientation might be expected for sighted subjects with visual

pre-orientatio~ Indeed, this differentiation does not arise, for

with this experimental group it is in both cases a matter of re-

production of the spatial relationship due to the visual pre-

orientation.

However, this congruence could not be expected for the groups without visual pre-orientation because, whereas perceptual spatial

orientation merely requires reproduction of the spatial relation- ship, cognitive spatial orientation requires its production. The

congruence of the metrics obtained shows that the "calculated" relationship is isomorphous with the perceived relationship.

4) Only with sighted people with visual pre-orientation do motor

300

and verbal estimates result in congruent metrics. This is to be

expected as the subjects of this experimentai group were allowed

to perceive the figures before the motor estimates and during the

verbal descriptions. The divergent results of the other groups

show that under nonvisual conditions motor performance and verbal

descriptions do not correlate highly. However, when interpreting

these results it is necessary to take heed of a possible methodo-

logical artefact. Verbal estimates by adventitiously blind and

sighted people under blindfold were mostly given in whole numbers,

with an interval of two or three centimeters. Thus, comparatively

large differences occur leading to higher values of r for the

metric. In the case of congenitally blind people, however, the

much higher variance leads to apparent leveling of the estimates

of length and this goes some way towards explaining the lower

values of r for the metric.

5) The present results lead to several theoretical conclusions:

a) It seems certain that congenitally blind people can produce

new spatial relationships in haptic space, although with less

stability than people with visual experience. This result is in

direct disagreement with older empiricist theories (e.g.v. Senden,

1932) which tried to verify that the congenitally blind are not

capable of this. b) The difference in the parameters of the structure of haptic

orientation (by congenitally and adventitiously blind and blind-

folded sighted people) and the structure of visual orientation

(by sighted people with visual pre-orientation) indicates that

the opinion of Blumenfeld (1937) concerning similar laws of struc-

ture for all sensory modalities is not valid. An alternative

view is that specific characteristics of the various modalities

occur under various conditions.

c) Contrary to previous investigations concerning cognitive

spatial orientation tasks (Worchel, 1951; Juurmaa, 1965) the

present results show that differences between congenitally and

adventitiously blind people and sighted people with and without

visual pre-orientation do not primarily concern the accuracy but

rather the manner of spatial orientation. d) The fact that adventitiously blind and blindfolded sighted

people have approximately equivalent structures of haptic space is

interesting with regard to the transposition hypothesis of R~v~sz

(1934) and Worchel (1951). It seems obvious to explain the con-

gruence of their metrics and simultaneously the differences be- tween them and each of the other groups by suggesting the inter-

vening variable of transposition. However, transposition does

not lead to laws of structure analogous to those of sighted peo- ple. In contrast, people with visual experience but lack of visual

control develop apparently specific strategies by means of which they are capable of orienting themselves spatially; this strategy

is clearly distinct from that of sighted people with visual control.

301

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302