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THE PERCEPTION OF A FORM IN AN
UNDIFI‘ERENTIATED FIELD A5 INDICATED BY
THE OBSERVER'S USE OF THE TILT-BOARD

Tho-is for flu Doom of M. A.
MICHIGAN STATE COLLEGE
Erwin Louis Haan
I953

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0-169

 

THE PERCEPTION OF A FORM IN AN UNDIFFERENTIATED
FIELD AS INDICATED BY THE OBSERVER'S USE OF
THE TILT-BOARD

BF

Erwin Louis Haan

A THESIS

Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements

for the degree of

MASTER OF ARTS

Department of Psychology

Year 1953

. I

6/} 2/53

DEDICATION

Grateful acknowledgment is made to
Dr. S. Howard Bartley in appreciation of
his critical advice and helpful counsel

throughout the course of this research.

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7

TABLE OF CONTENTS
Chapter Page
I INTRODUCTION . . . . . . . . . . . . . . . a o o 1
II STATEMENT OF THE PROBLEM . . . . . . . . . . . . 13
III EXPERIMENTAL PROCEDURE . . . . . . . . . . . . . 16
Subjects. . . . . . . . . . . . . . . . . . . 16
Apparatus . . . . . . . . . . . . . . . . . . 16
Instructions to Subjects. . . . . . . . . . . 18
Method. . . . . . . . . . . . . . . . . . . . 19

IV RESULTS AND INTERPRETATION . e e a . e o o o e a 22

<;

EESCUSSION . . . . . . . . . . . . . . . . . . . 31
VI SUMMARY. . . . . . . . . . . . . . . . . . . . . hl
VIIBIBLIOGRAPHY..................I45
VIII APPENDIX I . . . . . . . . . . . . . . . . . . . hb
Ix APPENDEX II.‘1 . . . . . . . . . . . . . . . . . So

LIST OF TABLES

Table Page

I Raw score tabulations of target observations
under naked and aided eye conditions . . o o o h?

II Analysis of variance of row degrees of freedom
for difference between 2x, 7x. and '
unaided vision 0 o o o o o o o o o o o o o o o “8

III Comparison of performance of aided and unaided
subjects on judgment of tilt o o o . . . . . . MB

IV Analysis of variance of the means of ten
trials for tilt dat‘ o o o o o o o o o o o o o #9

LIST OF FIGURES

Figure Page

I Geometry involved in unaided and aided
perception of a tilted plane surface . . . . . 11

II Graphical presentation of estimation of
tilt under unaided and two-power conditions. . 2h

III Graphical presentation of estimation of
tilt under unaided and seven-power conditions. 25

IV Relation of actual tilt of targets to
estimation of tilt (phenomenal tilt) . . . . . 30
Relation of geometric figures to estimation

Of tilt (phenomenal tilt). o o o e e e o o e o 30

V Overall physical features of experimental
env1r0nmento o o o o o o e e o o o o o o e o e 51

VI Physical features of observer's position . . . . 52
VII Close-up of tilt-board arrangement . . . . . . . 53
VIII Target construction. 0 o o e o o e e e o e e o 0 5’4-

IX EXperimenter's room and stage. . . . . . . . . . 55

Ie INTRODUCTION

Although they are universally experienced phenomena
of visual perception, the peculiar family of psycho-physio-
logical processes referred to as the constancies is yet
incompletely understood. While the natures of the various
phenomenalogies of the several kinds of constancy are
qualitatively different, the grosser psycho-physical aspects
of their separate origins and, in a more restricted sense,
the psycho-physiology of their action in terms of the per-
ceiving organism are very much the same.

Despite the kinship of the different kinds of constancy
in terms of origin and action, each of them is unique
enough, qualitatively, to be considered independently of
the others. In the course of deve10pment of sense psychology
these individual phenomenologies have come to be differ-
entiated into four main kinds: constancy of lightness, of
,color, of size, and of shape. Whereas it is the last of
these, shape constancy, which is the chief concern here, a
few things must be said concerning constancy in general to
best introduce this particular research.

"The perception of things, or objects, involves certain
Operations on the part of the perceiver. Among them are the
maintenance of thing-identity, thing-continuity, and thing-
stability. The tendency to maintain stability or uniformity

is commonly spoken of as constancy." Thus Bartley (1)
defines the general phenomenon of constancy. Implicit in
this definition is the basic premise that the perceiving
organism.is an active participant in all situations where
constancy results. To what extent this participation is
active, to what extent the contributions of the organism
will be explicit, is dependent, among other things, upon

the visual field involved in a given visual perception. In
general it might be stated (hereinafter referred to as

Case I) that the greater the perceiving organism's famili-
arity with the perceived object, the greater the relatedness
of that object to its surrounds, and the more eptimal the
general conditions for visual perception, the greater the
extent to which these variables of visual perception
approach the ultimate, the less will the perceiving organism
be involved, consciously, in the solution of the particular
visual problem involved.

For essentially, visual perception is a problem-solving
process, a process of making meaningful the bare essentials
of visual perception, that is, the geometrical stimulus
pattern on the retina superimposed upon that portion of
past experience which is drawn upon to lend significance to
the retinal pattern. The implicit judgments of a visual

perception at this level tend to become reflexive in nature.

 

(l) Bartley, S. Howard, "Beginning Experimental Psy-
cholggy', 1950, McGraw-Hill Book Company, Inc., New York,
Del-7e

While this statement is creditable, it would be erron-
eous to assume the converse of it (to be referred to as
Case II). That is, it is not necessarily true that-the
less familiar the perceiving organism is with the primary
features of a visual field and the more ambiguous the
stimulus pattern on the retina, the more the perceiver will
be involved in a problem solving way at the conscious,
conceptual and/or rational level.

One unique feature of visual perception rests in.the
fact that for certain types of situations in the visual
field, the givens, Operative in the field, do not demand
any one response to the exclusion of all others. In such
cases as those represented by the first statement above
(Case I) the consistancy with which that type of visual
field will be resolved in the same way time after time
approaches certainty. If, however, the component variables
comprising the visual field are of the nature of those
illustrated in Case II (1.6., ambiguous, unidentifiable,
etc.) the variations in type and degree of resolution
will be so diverse as to deny any systematic appraisal of
responses. That is to say, the final resolution of the
problem presented by any visual field may take any one of
as many forms as combinations of past experience, learning,
and Operating givens in the visual field allow. Under con-
ditions of this sort the judgment of the organism is rendered
less pOsitive as the degree of impoverishment or ambiguity

increases. The less the stimulus value and cue value in
the environment, the less precise will be any evaluation
of that environment and consequently any judgments arising
out of it.

In this connection an explanation of the terminology
used here is called for. Traditionally, the terms "cue"
and "stimulus" and ”stimulus value" have been employed so
loosely as to have lost the refinements which at first set
them apart one from the other. For purposes of this paper,
however, a stimulus will be thought of as a pattern Of
physical energies impinging upon the sense receptors of the
organism at some level at or above threshold for that type
of receptor; by stimulus value is meant the prOperty or
”prOperties residual in the stimulus itself which are poten-
‘tially capable of being utilized by the organism in the
'evaluation or formulation of judgments about the stimulus;
a cue, then, is the actual utilization of a stimulus situation.

The point of this differentiation is the fact that a
given stimulus situation may abound in stimulus value on a
given dimension (i.e., vision) and yet be impossible of
resolution or evaluation solely by virtue of the ambiguity
of the situation and the impossibility of interpreting and
utilizing the stimulus value present. If past learning
and/or experience offer no background on which the stimulus
values may be cast, they may never achieve cue rank, that

is, be meaningful. On the other hand, a stimulus config-

uration, easily recognizable in surrounds habitually assoc-
iated with the stimulus in the past, may lose its identity
when presented in a strange environment or in any environ-
ment bereft of those features traditionally associated with
the stimulus. This is one of the fundamental principles
underlying the Operation of constancy of the sort in which
we are interested here.

This very principle denies the implication, found in
some literature concerned with constancy, that constancy
involving visual mechanisms is a matter of identical retinal
image formation from moment to moment. Rather, constancy
is, in a large part at least, a function of the incorpor-
ating of available stimulus value into the matrix of past
experience and learning, and the conceptualizing of the
resulting cues into a system of judgment and evaluation
adequate to the stimulus situation involved.

The difficulty in dealing with constancy and in attain-
ing any degree of specificity regarding its Operation stems
from the fact that many researchers put the cart before
the horse, as it were. That is, they seek the answer to
the question "Why do things look as they do?" in the
Object world rather than in the visual world (using the
terminology employed by Gibson (2)). In terms of the

definitions set down here, this course will be unavailing.

 

(2) Gibson, James J., "The Perception of the Visual
World", 1950, Houghton Mifflin 00., Boston.

The Object world is no more nor less than a set of givens
(physical energy values), and is important only insofar as
an organism chooses to attend to certain configurations of
this infinite set of physical energies. How the organism
‘will evaluate and conceptualize and respond to this config-
uration is a truer statement of the problem to be faced in
dealing with this phenomenon of constancy. As Miller (3)
points out, "Each different set of visual conditions
results in a different shape and/or intensity pattern on
the retina, and it is these retinal images rather than
'objects' that form the stimulus material for perception."
Perhaps a more precise statement of the problem facing
experimenters in this area is a necessity for quantification
of the degree to which constancy will be maintained through-
out any series of retinal image formations produced by any
one object presented in a number of different orientations.
Several experimenters have attempted measurement of
this sort and also investigation Of various manipulations
in the visual field which act in quantifiable ways to deter-
mine the degree Of stability or maintenance of constancy.

Thouless (h), in order to quantify constancy introduced the

 

(3) Miller, James Woodell, "The Effect of Magnification
on the Perception of Elipses", unpublished Masters thesis,
Michigan State College, East Lansing, Mich., 19h9.

((4.) ThOflBSS, Re He, Brite JO Of PBYO, 1931, VOle 21,
339‘359e

concepts of the real object (R), the stimulus Object (S),
and the phenomenal Object (P). R is the object in the
visual world, S is the retinal image of R in a given
orientation with respect to the observer, and P is the
experience of the physical object in any specific instance.
As a result of his eXperimentation.Thouless discovered that
the P value, the experience of the object represented by
the subject, corresponded to neither the geometric value
of the real object nor to its stimulus value projected on
the retina. Rather, the P value fell somewhere between
the R value and the S value. This discrepancy between
what there is for the observer to perceive and his actual
perception of the target Thouless termed regression.
Definitively stated, regression (Rg) is the degree of
which the value Of the phenomenal object differs from the
stimulus value in the direction of the real object. This
relationship Thouless verbalized in this way:
"When a stimulus which by itself would give
rise to a certain phenomenal character is pre-
‘ sented together with perceptual cues which indi-

cate a real character of the object, the result-

ing phenomenal character is neither that indi-

cated by the stimulus alone nor that indicated

by these perceptual cues, but is a compromise

between them."
This relationship he called the "Law of Phenomenal Re-

gression", and devised an index of regression which is

expressed as P-S/R-S.

Later58tavrianOs (5) investigated the relationShips
which were thought to exist between judgments Of inclination
and shape perception. As an indication that such relation-
ships did exist, she cited a corollary of Thouless which
indicates that any decrease in perceptual cues regarding
the nature of the real object reduces the regression of
the phenomenal object in the direction of the real object.

The work of Eissler and.Klimpfinger (6) also lent
itself in support of a hypothesis of this sort. They con-
cluded on the basis of their experimentation.that shape
and perception of object orientation were related. Stav-
rianos also mentions that Koffka (7) states in his theoret-
ical treatment of this subject matter that ”a certain
combination Of shape and orientation is invarient for a
given retinal image".

With these studies as background Stavrianos executed
three experiments using circles and rectangles as targets.
Although her hypothesis was unconfirmed, the experimen-
tation did show that 1) while shape judgments of tilted
figures were accurate and showed little variation as a

function of presented angle or other environmental con-

 

(5) Stavrianos, B. K., "The Relation of Shape Per-
ception to Explicit Judgments of Inclination", Arch.,
Psychol., N.Y., 19h5, No. 296.

(6) Klimpfinger, S., "Uber den Einfluss von intone
tionaler Einstellung und Ubung auf die Gestaltkonstanz",
Arch. ges. Psychol., 1933. 88, 551-598.

(7) Koffka, K., Principles of Gestalt Psychology,
New York: Harcourt, Brace, 1935.

ditions, the values for tilt varied greatly under different
types of experimental conditions: 2) accuracy of tilt judg-
ment decreased as a result of cue reduction (by means of
monocular vision and/or reduction tube) even though there
was no decrease in accuracy of shape judgment (no loss of
constancy): and 3) correlation of paired shape and tilt
judgment revealed no relation.

It is to be remembered that Stavrianos in the course
of these three experiments presented her targets under a
whole gamut of conditions and situations and combinations
of then. And of the number of conditions and situations
which have direct bearing on the degree of constancy which
will be maintained in a given visual field, such as level
of illumination, interposition, collateral cues of various
kinds, observer acquaintance with the nature of the per-
ceived object, etc., we single out in the present investi-
gation still another factor, instrumental magnification.

Instrumental magnification.will alter a visual per-
ception in either one of two ways, either by increasing
the size of the perceived Object in accordance with the
Optics of the instrumentation (i.e., twice as large in the
case Of two power Opera glasses) or by decreasing the per-
ceived distance from the Object to the observer by a like
amount (one-half the distance under two power magnification).
Whether an object will be affected by instrumental magni-

fication in terms of size or of distance depends in turn

10

upon the degree of constancy maintained in the situation.
Generally, it may be said that the greater the degree of
constancy, the greater the tendency for instrumental
magnification to alter the visual field in terms of distance.

Instrumental magnification, regardless of the physical
dimension.altered, does cause some change in the relation
of the seen Object to the stimulus pattern. One such
change occurs in the angular values of surfaces with
respect to each other, or a reduction in the third dimen-
sion. This decrease of depth value of three dimensional
objects is referred to as flattening effect.

Referring to the diagrams in Figures Ia, Ib, and lo,
this flattening effect can perhaps be explained in terms
of the geometry involved. Figure la represents the stim-
ulus pattern on the retina produced by the two-dimensional
object KY, tilted on its axis at h5° away from the observer.
The extension of this tOp edge away, into depth, intro-
duces the third dimension, producing a three-dimensional
object. Figure Ic demonstrates what occurs with the intro-
duction Of a two-power lens into the situation. Assuming
that in this case magnification serves to increase size
rather than to decrease distance, we see XY double its
size, XlYl. However, instrumental magnification can Operate
in only two dimensions, height and width. Thus, whereas
the height (h) of XY has doubled, its depth (third dimen.

sion), d1, has remained constant. In order that the doubled

Figure I. Geometry involved in unaided and
aided perception of a tilted
plane surface.

 

11

 

Fig. I a.

 

Fig. I e.

 

 

 

 

 

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12

image be accommodated in the depth dimension d it must

1.
change its angular orientation from its original position
at h5° from the line of regard to something significantly
less. There has been a reduction of the third dimension.
Perhaps, however, the situation is such that the
degree of constancy is sufficient to cause perception of
the object XY not as XlYl, twice as large as XY, but as
XZYZ, twice as near as XY. The geometry of this situation
is demonstrated in Figure Ib. In.this case the manner in
whichx2Y2 is perceived is geometrically determined by X111
as regards the third dimension. That is, whether the pore
ceived Object resulting from instrumental magnification is
seen as an Object twice as large or as one twice as near,
the original object, KY, and its Object-prOperties have
been lost to the situation. Therefore, if the original
object, XY, is perceived as XZYZ, it will suffer the same

loss of third dimension as did x1311.

II. STATEMENT OF THE PROBLEM

It has been pointed out that one of a number of factors
which creates conditions either in the visual world or in
the visual field which may introduce changes in the shape
and even the identity, and consequently the degree Of con-
stancy, of an Object is instrumental magnification. Instru-
mental magnification alters the perceived shape of an
object. Yet, under conditions of magnification all objects
are not altered in the same way. Cubical Objects contain-
ing little or no detail are distorted and flattened in a
manner characteristically referred to as Chinese perspective.
Cubical objects such as steeples, bell towers, buildings
of classical Greek design, etc., do not suffer this type
of distortion but shift in shape in a way which gives rise
to Chinese perspective, due primarily to the wealth of
detail inherent in the perception of them. Two dimensional
figures, on the other hand, are much more liable to the
distortions occurring under conditions of instrumental
magnification.

As was pointed out previously, Thouless, Koffka,
Stavrianos, and Miller all dealt with two dimensional
objects with plane surfaces, and found what Thouless called
regression in the direction of the real Object when the,

two dimensional targets were tilted in respect to the

11;

observer's line of regard. Phenomenologically, this tilt-
ing produces a third-dimensional character in an object
actually possessing but two dimensions and lying in a single
plane. The very act Of displacing on its axis any portion
of an object, a circle or elipse in this case, away from
the Observer, I'awayness" being a correlative of depth,
provides a third dimension. With the addition of the third
dimension we might, all other conditions being the same, as,
for example, those found in Thouless' experimental situation,
expect to find a decrease in this third dimension with the
introduction of instrumental magnification.

It is to be remembered that the experimental situations
of Thouless, Stavrianos, and Miller provided a large amount
of collateral cues in addition to those inherent in the
target themselves. What the organism would do in a situation
affording no collateral cues at all, how his perception Of
a two-dimensional Object given three-dimensional prOperties
by virtue of orientation (tilting) would be altered given
only the object and the stimulus values native to its
geometry, was the problem posed for this experiment.

By way of comparing Miller's experimental environment,
for instance, with the one presented here, it might be said
that the degree of active participation on the part of the
two different sets of subjects was quite different. Whereas
for Miller's subjects a certain degree of internal manipu-

lation (conceptualization) of the retinal image was possible,

15

this same sort of juggling necessarily was limited in scOpe
if not in degree by the total absence of collateral cue

in the present experimental situation. The retinal images
of Miller's (and Thouless', and Stavrianos') subjects were
composed of the target circumscribed by a given amount of
collateral cues. Subtle as those cues might have been,

one can be sure that in a visual field lacking the normal
amount of cue prOperty, the organism will certainly seize
hold of whatever cue value remains. It would seem, there-
fore, quite difficult to attribute to target or environment
their respective roles in producing the conceptual outcome
in terms of an ambiguous situation.

Removing all cues from the field, except those residing
in the target itself, can be expected to introduce a great
deal more ambiguity into the situation than any reported
in the literature to date. Without the possibility of
environmental reference, the observer is left to make
judgments on the basis of object (target) prOperties alone.
Whether or not, or to what extent the organism could do
this, and to what extent his judgments would correspond
in any way, such as by phenomenal regression, with those
indicated by the results Of Thouless and.Miller, is the

real nature of this problem.

III. EXPERIMENTAL PROCEDURE
Subjects

Twenty-one subjects were used in the experiment,
twelve of which were female, and all were undergraduates
at Michigan State College. All twenty-one subjects par-
ticipated in the complete eXperiment, under both aided
and unaided conditions. All subjects reported 20/20
vision uncorrected. No subject evidenced, either verbally,
or in terms of performance, any awareness of the nature
or purpose of the experiment, and all were naive regarding

the experimental variables and their manipulation.
Apparatus

The experiment was performed in two adjoining light
proof rooms. An aperture fourteen by twenty-eight inches
was cut into the wall between the two rooms and located at
eye-level to the subjects who were seated at a table thir-
teen feet six inches from this aperture. Attached to the
center wall and immediately around the aperture was a
large plywood box referred to as the stage and which
measured forty-six inches long, thirty inches wide, and
thirty-five inches high. The rear panel of the stage con-
tained an Opening seven inches square into which the tar-

gets were placed for presentation. Thus the distance from

17

target to observer became seventeen feet four inches.
Located above the front aperture and inside the stage was
the light source, a General Electric CH-h ultraviolet lamp
and its accessory parts, which included its screw base
socket, transformer and special filter which eliminated

the small component of white light emitted by the source.
The lamp was of Spotlight construction and was beamed
directly on the target area. All surfaces except those of
the target prOper were painted flat black to absorb not
only the small amounts of white light which might still
have been present in the emission from the source but also
to absorb the traces of white light reflection caused by
any foreign matter present in the commercial fluorescent
paint used to coat the targets themselves. Between presen-
tations, all target changing activity was hidden from the
Observer by means of a pair of monk's cloth curtains sus-
pended from a traverse rod which was Operated from the rear
of the stage by the experimenter. The curtains provided
complete occlusion of the stage interior during target
changing.

There were twelve targets fabricated from twelve gauge
wire. The targets are described in terms of the size of
their majordminor axis ratios. Three different sized tar-
gets were used: a) 5x5 (a minor axis of five inches and a
major axis of five inches), b) hx5, and c) 3x5. Four of

each size target were constructed, one each for the four

18

different degrees at which they were mounted for presen-
tation, 6° (upright), 22.5o (away from the Observer), ESQ,
and 67.50. These twelve figures were mounted on seven inch
squares, constructed to afford a light-tight fit when placed
in the Opening at the rear of the stage for presentation.

A reduction screen with an aperture two and one-quarter
inches high and three and one-quarter inches wide was placed
thirty inches from the subject to restrict the field of
vision during the part of the experiment in which the bi-
noculars did not serve this purpose. The aperture in the
reduction screen was, of course, moveable to compensate
for variations in sitting height of the twenty-one subjects.

To enable the subjects to represent the plane in which
they perceived the targets to lie (phenomenal tilt), a tilt-
board, ten and one-half by seven inches covered with white
matte material, was affixed coaxially with the shaft of a
one hundred and twenty vOlt Variac. Changing the position
of the tilt-board thus changed readings on a voltemeter
connected in series with the Variac. These voltage read-
ings, having previously been calibrated in terms of angular
degrees of tilt, were tranSposed into the angle at which the
subject had positioned the tilt-board for any one presentation.

Instructions to Subjects

A literal transcription of instructions given the

subjects follows: "You are to be presented visually a

19

series of forms or figures some of which are mounted in
positions other than upright. YOur task is to duplicate
the plane in which the various figures lie by manipulating
the tilt-board in front of you until the plane at which you
set the tilt-board best approximates the plane in which you

perceive the object to be oriented."
Method

The subjects were introduced into the experimental
situation under normal illumination and allowed to look
about while the experimenter made preliminary preparations.
The only things visible to the subject were the tilt-board
arrangement, the reduction screen, the table and chair he
was to use, the dimensions Of the room, and the aperture
through the wall.

After the subject had seated himself, normal illumin-
ation was removed and replaced by illumination afforded by
a red bulb of twenty-five watts. The subject was partially
dark adapted in this environment for three minutes, during
which time he was given his instructions, allowed to man-
ipulate the tilt-board, and Operate the buzzer system which
informed the experimenter in the other room of completion of
evaluation of one target and.readiness for the next. -After
the three minute period of dark adaptation the experimenter
indicated to the subject that the experiment was about to

begin.

20

After placing in position the first of the twelve
targets of the series (the order of appearance of which
had been determined by reference to tables of random order),
the experimenter drew Open the curtains, exposing the target
to the view of the Observer who evaluated the target. When
the subject had satisfied himself as to the orientation of
the target he positioned the tilt-board to represent the
plane of the target's orientation. Having done this he
pressed the buzzer to indicate his completion of the task,
and the experimenter recorded the judgment as represented
on the voltmeter, closed the curtains and replaced the
target with the next. This cycle was repeated through the
series of twelve targets. The complete series was repeated
ten times without pause under these conditions.

The second half of the experiment consisted of the same
task performed under the same conditions except for the
introduction of instrumental magnification into the situation.
The twenty-one subjects all performed in the unaided situ-
ation, but were divided into two groups as regards the aided
situation, twelve using two power (2X) Opera glasses, and
nine using seven power (7X) military glasses. In both the
aided and unaided situations, techniques of presentation by
eXperimenter and representation by the subject were the
same. This half of the experiment was performed two days
after the first part.

After the complete set of readings was taken, the

21

voltage readings were transposed into degrees of tilt,

the means for the ten trials per target were derived and

an analysis of variance applied to the compiled data. The
analysis of variance technique was chosen in preference to
t-score methods because the data was of a continuous rather

than a discontinuous nature.

IV. RESULTS AND INTERPRETATION

Figure II represents a graphical representation of
the gross trend of the experimental results yielded by sub-
jects using two-power glasses while Figure III represents
the trend of results for subjects using seven-power glasses.
InSpection of Figure II shows the type of response curve
which seems to be typical for behavior in problems and
environments of the type found in this experiment. Nelson
(8), for instance, established a nearly identical curve
attained from the plotting of minor-major axis ratios of
the drawings by his subjects of the same targets used here.
The curve Of best fit, in the case of both Figure II and
Figure III is an approximation and is not mathematically
refined. However, it appears as obvious that in the case
of judgments of tilt Of targets having stimulus values in
the middle ranges (between .35 and .65) where no instrumental
magnification is employed, these judgments are consistently
and significantly overestimations of actual tilt values.
In the situation utilizing instrumental magnification of
two power, however, a more nearly straight-line function
results, one which indicates an increasingly great under-

estimation of actual angular orientation as stimulus values

 

(8) Nelson, Thomas M., "The Perception of a Form in an
Undifferentiated Field as Indicated by the Observer's Draw-
ings", unpublished Masters thesis, Michigan State College,
19 3.

23

decrease from 1.0 (a circle to .00 (a straight line).

Although this reaponse curve seems to indicate re-
gression, as do those of Thouless and Miller, the results
obtained with the seven-power glasses, as represented in
Figure III, differ. For in this case, where instrumental
magnification was considerably greater, the type of responses
were not at all as one might expect. Whereas the reSponse
curves for the unaided eye are very similar in both Figure
II and Figure III, the response pattern Of the aided Obser-
vations is quite dissimilar. It is quite probable that
mathematically derived curves established for the data of
each of the two conditions in Figure III would very nearly
coincide. This is in contrast to the Obvious and signifi-
cant difference of the two curves in Figure II. It will
be noted, also, that for the range of stimulus values used,
the pOpulations of the data for the two viewing conditions
intermingle. Since the function of instrumental magnifi-
cation is of primary importance in this experiment, the
eXplanation of this phenomenon becomes crucial and will be
attempted later.

The analysis of variance technique, which was employed
in the treatment of these data, indicates some of the
relationships which exist between the several variables
Operating in this experimentation. The number of variables
actually dealt with here was kept to a minimum by the experi-

mental design. Nelson's similar and concurrent study found

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25

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26

such variables as age of subjects, time per response, and
order of presentation (aided or unaided condition first or
last) to Operate at levels statistically insignificant.
The sex variable, not taken into account here, was found by
Nelson to be significant beyond the one percent level of
confidence. However, that variable would account for but
one degree of freedom and would reduce the error term by
E62 units.

The results of the analysis of variance of the means
of the trials is presented in Table IV. Bartletts' test
of homogeneity was applied to each of the sub-groups and
the resulting value Of X2 (chi square) was not significant,
indicating homogeneity and insuring the validity of the
application of the analysis of variance technique.

InSpection of Table IV will show that the variable
dealing with the influence of the various subjects was
significant beyond the one percent level of confidence.
This, of course, was to be expected in view of the necessity
for the subject to contribute to the situation some scheme
or conceptualization which would aid him in solving the
perceptual problem. In the experimental situation, im-
poverished as it was with regard to available stimulus
value, the Observer was compelled to utilize his own system
of evaluation and judgment of the targets in lieu of the
kind of cues customarily utilized in making judgments of the

sort required here. That the various subjects did tend to

27

evaluate each target in much the same way seems to indicate
that judgments of tilt were made either in terms of a common
scheme, or by employment of individual approaches which
resulted in like judgments for any one target.

The introduction of instrumental magnification was a
variable which was significant beyond the one percent level
of confidence. The significant difference existing between
aided and unaided conditions, when analyzed in terms of
Figures II and III, must be attributed to the two-power
glasses. For it is obvious from inSpection of these graphs
that the estimations of tilt under seven-power magnifica-
tions closely approximated estimations made under unaided
conditions. 0n the other hand, Figure II demonstrates the
significant difference between estimations of tilt under'
unaided and two-power magnification.

The interaction of subjects and aided vs. unaided
conditions was significant. The fact of similar evaluations
of tilt for a given from Observer to observer was mentioned
above as being attributable to either.one of two possibil-
ities, that the observers reSponded in terms of a common
conceptual system or that the several Observers utilized
individual schemes. The significant character of the inter-
action term indicates that the second alternative is, in
fact, the valid one. That is, there were significant differ-
ences between observers with respect to the influence of

. aided and unaided conditions. Whereas the introduction of

28

magnification into the environment served to increase the
estimate Of tilt for one observer, the responses of another
observer indicated greater estimates of tilt under unaided
conditions. It is to be remembered in this connection that
the values plotted in Figures II and III represent aggregate
measures and mask the unique behavior of individual Observers
represented by the raw data.

The figures or targets were broken down in the analysis
into their two structural components, the target itself,
having physical dimensions and its angular orientation
or tilt, both of which factors are also significant at the
one percent level. The three targets are each signifi-
cantly different from each other in terms of their physical
dimensions. Figure Iva: demonstrates the fact that the
three targets tend to order themselves in terms of esti-
mation of magnitude of tilt with the 5x5 figure evidencing
the smallest estimations and the 3x5 target showing the
largest estimation. This ranking of the estimation of the
magnitude of tilt may be a function of similarity or dis-
similarity between the target in question and a circle. The
experimentation gives no verification of this, however,
although this type of evaluating process may well have been
the most pOpular scheme utilized by the various subjects
in making their judgments.

The experimental results seem to indicate that esti-

mations of tilt coincided with actual physical orientation.

29

The analysis tends to support this statement in that it
indicates that, while the estimate of the magnitude of
tilt at 67.50 is not significantly different than that at
90°, the estimates of magnitude of tilt at 90° and 67.50
are significantly different from those estimates at both
h5° and 22.5°, the estimates of which are, in turn,
significantly different from each other. This relationship
is demonstrated in Figure IVb.

These particular results seem to be explainable in
terms of our previous assumption that all targets are
judged as being circles at different angular orientations.
This assumption, however, allows only for the Operation of
Objective stimulus conditions and ignores any other con-
tribution the individual observer may make. More will be
said about this in a succeeding section.

Tables II and III are designed to discover the _
significant differences in extimates of magnitude of tilt
under the three conditions, unaided eye, two-power magni-

fication, and seven-power magnification.

ACTUAL TILT

E STIMATE 0F TILT

30

07.? ’

es)- 6

 

 

z e . C
y "5 *5 I85 I35 '50
ESTIMATE OF TILT

Figure IV 8e

Relation Of actual tilt of targets to estimation of
tilt (phenomenal tilt).

..I '

 

 

10¢: ' '
00 -
O
a L.— 11
3° O an mm
FIG URE

Figure IV b.

Relation of geometric figures to estimation of tilt
(phenomenal tilt).

V. DISCUSSION

In the history of sense psychology as well as in other
fields, much has been done in attempting to establish the
relationships which exist between a real object in a real
world, the nature of its associated retinal image, and its
sensation or phenomenology. Some generalizations have been
made, one of which has to do with geometry, that is, with
the relation of size of the real object (its visual angle)
to the size of the retinal image. However, such a fixed
relationship does not obtain between the shape, size and
orientation of a plane figure, and the size and shape of
its associated retinal image. Two plane surfaces will
function in exactly the same way, visually, given only
identical visual angles. The fixed relations existing
between a plane surface's shape, size, distance, and
orientation, and the size and shape of the retinal image,
then, offer nothing with which to differentiate that sur-
face Or configuration from any other subtending the iden-
tical visual angle. This fact was illustrated by Ames (9)
in experiments conducted at the Dartmouth Eye Institute in
which he demonstrated the equivalence of three-dimensional

objects by presenting to the Observer through objectively

 

(9) See Bartley, S. Howard, "Beginning EXperimental
Psycfiglogy", 1950, McGraw-Hill Book Company, Inc., New York,
13.]. Q i

32

different physical constellations ("targets") which give
rise to identical retinal images and are therefore perceived
as the same object in space.

The perception of Objects, including plane surfaces,
' involves not only their known size, perceived size, and
shape, but also the orientation of them in regard to the
observer and to themselves. For normally, the perception
of an object of any kind in space is more than the perception
of space relationships to other Objects and to the observer.
One of the axioms of Space perception is that what an
object is seen to be and where it is seen to lie are mutually
dependent and form a reciprocal relationship.

In this present research, however, not all these
necessary elements of space perception were available to
the observer in his judgments concerning the nature Of the
visual field. Not only were there no spatial relations
between the target and any other object or surface in the
field, but the exact nature of the targets and their geometry
were unknown to him. The more knowledge that he was
working with a series of circles and ellipses afforded the
observer little with which he could discriminate between
an ellipse of a certain major-minor axis ratio.and a circle
tilted at such a degree as to effect a stimulus value.
(visual angle) nearly identical to that of the ellipse
oriented in a plane perpendicular to the line of regard.

It is significant that the observers were able to

33

discriminate at all in the situation, and indicate the
Operation of some principle other than those customarily
considered as functioning in a visual task involving the
types of mechanisms at work here. The principles to which
we refer are necessarily a contribution of the Observer
himself and are not abstracted as such from the visual
field. They amount to the Observer's conceptualizations
about his perceptions. It is just this type of thing
which was referred to earlier in this paper.

The diversity Of the kinds of conceptual schemes
which any group of observer's might utilize are a function
of the total visual field depending on the complexity of
the retinal image. In this present study, it is relatively
safe to assume that the undifferentiated nature of the
field and the simplicity of the target configurations
limited the scOpe of conceptual activity. The fact of
inter-observer similarity as regards judgments bears out
this assumption, since any diversity of conceptual schemes
would produce a marked lack of correspondence of judgments
from observer to observer.

In this connection, however, it should be pointed out
that one subject, whose judgments were made under unaided
and seven-power conditions, made reSponses of a sort which
deviated to a degree which invalidated them. While his
judgments made during the unaided portion of the experiment

deviated no more than one standard deviation from other

3h

observers' responses, this subject's responses under seven-
power magnification were completely inconsistent in terms
of the other observers' judgments. For this subject merely
set the tilt-board at the vertical position on the first
response for the aided trials and left it in that position
for the succeeding 119 trials. Whether this subject was
trying to outguess the experimenter, whether he suSpected
he was being fooled, or whether he gave up any attempt to
solve the perceptual problem is not known.

It was suggested earlier that it would be quite possible
for an observer to make reSponses in terms of figures of
different major-minor axis ratios all oriented in the
vertical plane. However, introspective reports by this
particular subject, subsequent to his performance, gave no
indication of this type of resOlution of the problem. It
can only be concluded that his behavior was a function
either of his lack of understanding concerning the nature
of his task, or of some other factor of which the experi-
menter is unaware. In either case it was considered
advisable to discard the response data of this subject.

Another subject, whose responses were made under
unaided and two-power magnification occasionally adjusted
the tilt-board to represent the target as lying in the
quadrant away from the target. Although there appeared
to be no consistent pattern to these reaponses either in

terms of targets or angular orientation, they appeared

35

frequently enough to merit attention. Since no intrOSpec-
tive report of the subject was available, it can only be
assumed that his estimations in that quadrant were of such
I a magnitude with respect to the vertical as to preclude
the possibility of the responses resulting from a faulty
estimation of the vertical.

Keeping in mind the nature of the field and the total
absence of collateral cue, it would be impossible to assume
that for a retinal pattern produced by a given target there
can be any 'right' orientation. That is, with no depth cues
or interposition in the visual field, it would be virtually
impossible to determine which edge is the nearer one, and
consequently to make adequate judgments in terms of orien-
tation with respect to quadrant.

For this reason Figure II bears two curves depicting
the responses under two-power magnification. The solid
line represents the means of scores including this subject's
uncorrected scores. The broken line represents the means
of scores which include this subject's corrected scores,
that is, his scores corrected by adding to each response
a value which results in an equivalent setting in the
quadrant used by all other subjects.

This leads to a consideration of general performance
under seven-power magnification as demonstrated by Figure 111.
It was remarked earlier that, whereas the results Obtained\

in the unaided situations and the one employing two-power

36

magnification fell in with expectations, the responses
resulting from judgments of the targets under seven-power
magnification seem to fall outside any traditional
rationale. However, a consideration of events evoked by
another situation involving only slightly different primary
features may serve to explain the discrepancy between
anticipated results and actual reaponses.

It was explained in a preceding section that the
introduction Of instrumental magnification incurs a certain
degree of distortion in the retinal image, distortion
which involves the third dimension. The amount of dis-
tortion thus produced is a function of the degree of
magnification produced by the Optics of the instrumentation
employed. A similar type of distortion of the retinal
image occurs with the monocular use of size lenses, the
amount of distortion in this case depending upon the amount
of meridional magnification of the lens. Experiments with
size lenses (10) seem to indicate that distortions produced
by magnifications of two or three percent are reconcilable
by the subject, while distortions produced by greater
magnifications act in quite another way. Individuals
whose behavior is mediated through size lenses Of this
latter type appear to suppress the character of the retinal

image produced by the size lenses and behave as if monocular,

 

(10) Ogle, K. N., "Researches in Visual Perception",
1950, W. B. Saunders Company, Philadelphia and London.

37

that is, as if the eye whose retinal image was distorted
by the size lens was inOperative.

The distortions of the retinal image in both cases is
of much the same kind. In this experiment the observers
had adequate Opportunity to become acquainted with the
targets under Operationally normal conditions, due in part
to what learning theorists refer to as "practice effect"
in the unaided portion of the experiment, and in part to
their own conceptualizations concerning the nature of the
targets.

In view of these factors it can be assumed that the
Observers, while judging targets under seven-power magni-
fication, reSponded in the same way as subjects behaving
under the influence of retinal bmages distorted to the
degree produced by size lenses ground at five or more
degrees away from the vertical axis of the lens. That is,
the observer suppressed the character of the retinal image
produced by instrumental magnification and responded in
terms of the 'known' size, shape, and orientation of the
target as these variables were conceived to be during the
unaided portion Of the experiment. Such an explanation
would account for the correSpondent nature of the two curves
in Figure III.

The major finding of this experiment deals with the
role of magnification as it effects the perception of plane
surfaces in a field totally undifferentiated. The results

38

of the experimentation indicate that in a situation.impover-
ished with regard to collateral cues, more regression is
evidenced in the case of magnification (specifically two-
power magnification) than is the case under unaided conditions.

This fact is contrary to the findings of Miller (11)
who found that in every case more regression resulted under
unaided than aided conditions. This difference, however,
can'be attributed to differences in the two experimental
situations. The visual field for Miller's subjects con-
tained certain amounts of collateral cue which could only
be decreased with the introduction of binoculars and the
constriction of the visual field incident to their use. In
‘the visual field incorporated in this research, however,
with its total lack of cues other than those residual in
the targets themselves, the addition of instrumental magni-
fication could delete nothing from the retinal stimulus
pattern, but would tend,:rather, to enhance those cues
which were available, that is, those native to the geo-
metry Of the target.

Figures II and III demonstrate still another phenomp
enon, found but not discussed by either Thouless or Bruns-
wick (12), who established regression ratios Of much the
same kind as those Of Thouless. It will be noted that the

 

(11) Miller, J. W., "The Effect of Magnification on the
Perception of Elipses", unpublished Masters thesis, Michigan
State College, East Lansing, Michigan, l9h9.

(12) Koffka, K., "Principles Of Gestalt Psychology",
Harcourt and Brace, New York, 1935.

39

curves denoting unaided responses in both Figures II and III
show a significant increment in judgments of tilt in the
middle stimulus range (.035 - .065). That is, the esti-
mation of magnitude of tilt of figures whose stimulus
values (minordmajor axis ratios) lie approximately between
.035 and .065 was larger than the actual value, while at

the lower end actual values and estimated values are nearly
equal, and at the upper end the phenomenon of regression

is visible.

The question concerning just how to deal with reSponses
of this kind is posed at this juncture. If Thouless' "Law
of Phenomenal Regression" deals with underestimations of
tilted figures, would it be prOper to structure a "Law of
Phenomenal Progression"? Actually, the question should be
one concerned with the validity of any law of this type.

For in Thouless' "Law of Phenomenal Regression" there is

the implicit assumption that the organizing factors attribut-
able to the formation of regression to the real object (Rg)
are inherent in the target and in the visual field which
constitutes its surrounds. This assumption asserts the
Operation of objective stimulus conditions to the exclusion
of the active role of the perceiving organism. Such con-
cepts as this can never hOpe to adequately explain the
traditional query "Why do things look as they do?" However,
measures of this sort do fulfill a function which Koffka (l3)

 

(13) Ibid.

to

accurately verbalizes:

"These measures were so useful because, by
referring each result to a well-defined range
(.00-1.00 in the case of Rg), they yielded
comparable figures for very diverse constell-
ations, each having its own range defined in
some way."

Error does arise, however, when the specified value of these
measures are misused and made to answer the whole question.

Although this research did answer the questions asked
of it, then, it in turn posed other questions which can be
adequately answered only by further research and investi-
gation.

One such question arises with regard to the type of
behavior evoked under high powers of magnification (seven-
power). The step between the two different powers of
magnification was so large as to have passed by what might
be the definite point at which the type of reSponse
represented in Figure III begins to occur. Therefore,
an experiment employing a series of powers of magnification
between two-power and ten-power is advised in the hOpe
that this point or range might be established.

Also, this research might well have offered more of
an explicit nature about the conceptualizations utilized
by the several observers if adequate intrOSpective reports
had been required of the subjects. ‘

It is felt that the incorporation of these two

techniques in one further experiment would answer the

further questions suggested by this research.

VI. SUMMARY

The chief concern of this research was twofold: the
determination of the effect of an undifferentiated field
upon the perception of certain Specified types of objects,
and also the determination of the effect Of instrwnental
magnification upon the perception of the same Objects in
the same type of field.

Twenty-one subjects were used, all undergraduates of
Michigan State College, and all of which were naive as to
the nature of the experimentation and the experimental
variables involved.

The apparatus was constructed in such a manner as to
eliminate all extra-retinal cues which the subjects would
ordinarily utilize in making the type Of judgments demanded
here. The target objects, themselves being the only visible
feature in the total visual field, were coated with a
fluorescent paint and presented under ultra-violet light
from which all traces of visible, white lighthere removed,
thus insuring a perfectly undifferentiated field.

The twelve targets, all differing from each other
either in physical dimensions or angular orientation, were
each presented in random order ten times under unaided
conditions, and ten times under aided conditions two days

later. Under both conditions the subjects represented

their judgments by manipulating a tilt-board which gave
electrical readings which in turn were recorded by the
experimenter and later transposed into direct angular
readings.

The resulting data were subjected to an analysis of
variance and the significance of the various factors was
determined as well as the significance of the various
interactions between them. All these variables and their
interaction terms were found to be significant beyond the
one percent level of confidence.

In order that any verbalization concerning the experi-
ment might be most explicit, three terms which were pri-
marily involved in the research were Operationally defined.
They were the terms "cue", "stimulus", and "stimulus value".

In keeping with the purpose of the experimentation, it
was determined that, regardless of just how the targets
were adjudged to be oriented in the undifferentiated field
in.which they were exposed, the judgments were made in terms
of a conceptual pattern contributed by the observer himself
in lieu of any possibility of evaluations based on relation-
ships existing either between the target object and any
other objects in the visual field or between the target
object and any other feature of the environment which would
otherwise have provided collateral stimulus value,

Too, it was shown that, under the influence of instru-

mental magnification, judgments of angular orientation of

1&3

plane surfaces in an undifferentiated field evidenced less
size constancy, that is, suffered more regression (Thouless'
Rg) than did objects of the same kind whose angular
orientations were evaluated in an Operationally normal
manner.

A significant corollary of this fact indicated that
with the introduction of a high degree of instrumental
magnification the observer evidently suppresses the retinal
pattern produced in this way and makes judgments of angular
orientation more in keeping with what he knows to be the
true physical dimensions of the stimulus object.

The approach used in this research was one which
emphasized the active role of the perceiving organism.

The point was maintained throughout the execution of this
experiment that in perceptual situations of all kinds, the
responses made by the observer are a function of more than
the bare features of the visual field. And what other than
these features are utilized in perception is a contribution
of the perceiver.

By way of further clarifying the problems remaining in
the area of size and shape constancy (considered here to be
invariants of each other), the experimenter suggested further
research involving critical intrOSpective reports from
observers in an effort to gain insight into the nature of
rationalizations and conceptualizations employed by observers
in their judgments made of objects in an undifferentiated
field.

To further delineate that point at which a conceptual
scheme does break down under higher powers of magnification,
it was also suggested that experimentation using approxi-
mately the same primary features be carried out using
successively higher powers of magnification extending from

perhaps two-power to ten-power magnification.

1.
2.

3.

h.

5.

6.

7.

8.

9.
10.

11.

VII. BIBLIOGRAPHY

Bartley, S. Howard. Beginning Experimental Ps cholo .
McGraw-Hill Book Company, Inc.,‘New York: I9EU.

Gibson, James J. The Perception 23 the Visual World.
Houghton Mifflin Company, Boston: I930.

Klimpfinger, S. Uber den Einfluss von intentionaler
Einstellung und Ubung auf die Gestaltkonstanz.

Arch. 533. Psychol. 1933.

Koffka, K. Principles of Gestalt Psychology. Har-
court, Brace, New YorE? I935. _

Miller, James Woodell. The Effect of Magnification
23 the Perception.2£ EII-ses. Unpublished Masters
TheEIE, Michigan State CoIIege, East Lansing,
Michigan: l9h9.

Nelson, Thomas M. The Perception 23.2 Form in 25
Undifferentiated FieldIgg In cated b the Observer's
Drawin . UnpublishedIMasters ThesistMIEHigan State
CoIIege, East Lansing, Michigan: 1953.

 

Ogle, K. N. Researches in Visual Perce tion. W. B.
Saunders Company, PEIlEdeIpEIa and London: 1950.

Stavrianos, B. K. The Relation of Shape Perception
to Explicit Judgments of Inclination. Arch. Ps -
ohol., New Yerk: l9hS.

Thouless, R. H. Phenomenal Regression to the Real'
Object. I. Brit. g. Psychol., 1931, 21, 339-359.

Thouless, R. H. Phenomenal Regression to the Real
Object. II. Brit.'£. Psychol., 1931, 22, 1-30.

Thouless, R. H. Individual Differences in Phenomenal
Regression. Brit. J. Psychol., 1932, 22, 216-2ul.

VIII. APPENDIX I

RAW SCORE TABULATIONS OF TARGET OBSERVATIONS

UNDER NAKED AND AIDED EYE CONDITIONS

#7

 

OBJECT sun or sun or
nuns 5091 1109 I D N ID D F RENCE
1 5x5 0 45° 22.777 25,555 576
2 4x5 6 45° 21,605 22,557 952
5 5x5 6 67§° 16,401 16,914 515
4 5x5 6 225° 24.141 25,252 1091
5 6x5 0 225° 24,615 25,547 554
6 5x5 0 45° 20,592 21,152 760
7 4x5 6 575° 19,762 20,216 454
8 5x5 6 90° 16,196 16,755 559
9 5x5 6 67§° 21,256 22,597 1159
10 4x5 0 90° 19,557 20,102 565
11 4x5 0 224° 24,166 24,957 791
12 5x5 0 90° 20.565 21,579 795
.24“
29 22.2 .22 2212 291622
13x6) - 795 , 1159 576 1091 5621
(4x5) - 565 454 952 791 2722
(m; - 9.22. .912 122 92.: 2.92.9.
TOTALS 1699 2106 2266 2416 8689

TABLE I

ANALYSIS OF VARIANCE OF ROW DEGREES OF FREEDOM FOR

DIFFERENCE BETWEEN 2XI 7Xn AND UNAIDED VISION

§ggagz 2,9, sums 09 sgyARES MEAN SQUARES F

 

 

 

JL.......
ROWE 41 26,986,626 —--—.-. -.. ..-
2X x 7X x
UNAIDED 2 13,676,699 6,787,860 19.0 .06
WITHIN 69 13,410,827 646,867 -- ——-
TABLE II

COMPARISON OF PERFORMANCE OF AIDED AND UNAIDED SUBJECTS

ON JUDGMENT OF TILT'

 

 

 

 

I MEAN SIGNIFIOAIII

DIFEERENCE or DIFFERENCE 0.9. t a
UNAIDED vs. 2x 1055-799 61.22 594 5.65 .01
UNAIDED vs. 7x 1265-1055 67.57 556 5.44 .01
2x vs. 7x 1265-799 74.65 250 6.25 .01

 

ITABLE 111

#9

ANALYSIS OF VARIANCE 0F THE‘MEANS 0F TEN TRIALS
FOR TILT DATA

SOURCES OF ' SUMS OF F

 

 

 

_!ABIA!Q£2 £534 EQHASEQ VAL!E§,- 922
TOTAL 505 ...-.. ...... ....--
suBJECTs 20 25,760,155 142.00 .01
AIDED vs.

UNAIDED 1 149,654 17.67 .01
INTERACTION

SUBJECTS AND

AID. vs. UNAID.20 5,056,759 16.25 .01
FIGURES 11 6,059,617 ------ --..--
OBJECTS 2 1,096,172 65.56 .01
TILTS 5 5,457,045 216.57 .01
INTERACTION
TILT vs. . _
OBJECTS 6 1,604,602 50.00 .01
ERROR 451 5,775,669 ---- ------

 

TABLE IV

IX . APPENDIX II

 

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