Various - Harvard Psychological Studies, Volume 1

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That we do associate a sensation with whatever idea we have previously
connected it with, even though that idea be that of the number of
objects producing it, is clearly shown by some experiments which I
performed in the laboratory of Columbia University. I took three
little round pieces of wood and set them in the form of a triangle. I
asked the subject to pass his right hand through a screen and told him
I wanted to train him to perceive one, two, three and four contacts at
a time on the back of his hand, and that I would tell him always how
many I gave him until he learned to do it. When it came to three I
gave him two points near the knuckles and one toward the wrist and
told him that was three. Then I turned the instrument around and gave
him one point near the knuckles and two toward the wrist and told him
that was four. As soon as he was sure he distinguished all of the
points I stopped telling him and asked him to answer the number. I had
four subjects, and each one learned very soon to recognize the four
contacts when three were given in the manner mentioned above. I then
repeated the same thing on the left hand, except that I did not tell
him anything, but merely asked him to answer the number of contacts he
felt. In every case the idea of four was so firmly associated with
that particular kind of a sensation that it was still called four when
given on the hand which had not been trained. I gave each subject a
diagram of his hand and asked him to indicate the position of the
points when three were given and when four were given. This was done
without difficulty. Two subjects said they perceived the four contacts
more distinctly than the three, and two said they perceived the three
more distinctly than the four.

It seems very evident that the sensation produced by three contacts is
no more complex when interpreted as four than when interpreted as
three. If that is true, then it must also be evident that the
sensation produced by one contact is no more complex when interpreted
as two than when interpreted as one. The converse should also be true,
that the sensation produced by two contacts is no less complex when
interpreted as one than when interpreted as two. Difference in number
does not indicate difference in complexity. The sensation of four is
not made up of four sensations of one. It is a unit as much as the
sensation of one is.

There remains but one point to be elaborated. If number is not a
quality of objects, but is merely a matter of attitude of the subject,
we should not expect to find a very clear-cut line of demarcation
between the different numbers except with regard to those things which
we constantly consider in terms of number. Some of our associations
are so firmly established and so uniform that we are likely to regard
them as necessary. It is not so with our associations of number and
touch sensations. We have there only a vague, general notion of what
the sensation of one or two is, because usually it does not make much
difference to us, yet some sensations are so well established in our
minds that we call them one, two or four as the case may be without
hesitation. Other sensations are not so, and it is difficult to tell
to which class they belong. Just so it is easy to tell a pure yellow
color from a pure orange, yet they shade into each other, so that it
is impossible to tell where one leaves off and the other begins. If we
could speak of a one-two sensation as we speak of a yellow-orange
color we might be better able to describe our sensations. It would,
indeed, be convenient if we could call a sensation which seems like
one with a suggestion of two about it a two-one sensation, and one
that seems nearly like two but yet suggests one a one-two sensation.
Since we cannot do this, we must do the best we can and describe a
sensation in terms of the number it most strongly suggests. Subjects
very often, as has been mentioned before, describe a sensation as
'more than one but less than two,' but when pressed for an answer will
say whichever number it most resembles. A person would do the same
thing if he were shown spectral colors from orange to yellow and told
to name each one either orange or yellow. At one end he would be sure
to say orange and at the other yellow, but in the middle of the series
his answers would likely depend upon the order in which the colors
were shown, just as in determining the threshold for the perception of
two points by the method of minimal changes the answers in the
ascending series are not the same as those in the descending series.
The experiments have shown that the sensation produced by two points,
even when they are called one, is not the same as that produced by
only one point, but the difference is not great enough to suggest a
different number.

If the difference between one and two were determined by the distance,
then the substitution of lines for knobs of the aesthesiometer ought to
make no difference. And if the sensations produced by two objects fuse
when near together, then the sensations produced by lines ought to
fuse as easily as those produced by knobs.

In regard to the higher numbers difficulties will arise unless we take
the same point of view and say that number is an inference from a
sensation which is in itself a unit. It has been shown that four
points across the ends of the fingers will be called four or less, and
that four points, one on the end of each alternate finger and one at
the base of each of the others, will be called four or more--usually
more. In either case each contact is on a separate finger, and it is
hardly reasonable to suppose there is no diffusion when they are in a
straight row, but that when they are in irregular shape there is
diffusion. It is more probable that the subject regards the sensation
produced by the irregular arrangement as a novelty, and tries to
separate it into parts. He finds both proximal and distal ends of his
fingers concerned. He may discover that the area covered extends from
his index to his little finger. He naturally infers, judging from past
experience, that it would take a good many points to do that, and
hence he overestimates the number. When a novel arrangement was given,
such as moving some of the weights back on the wrist and scattering
others over the fingers, very little idea of number could be gotten,
yet they were certainly far enough apart to be felt one by one if a
person could ever feel them that way, and the number was not so great
as to be entirely unrecognizable.

* * * * *

THE SUBJECTIVE HORIZON.

BY ROBERT MACDOUGALL.

I.

The general nature of the factors which enter into the orientation of
the main axes of our bodies, under normal and abnormal conditions, has
been of much interest to the psychologist in connection with the
problem of the development of space and movement perception. The
special points of attack in this general investigation have comprised,
firstly, the separation of resident, or organic, from transient, or
objective, factors; secondly, the determination of the special organic
factors which enter into the mechanism of judgment and their several
values; and thirdly, within this latter field, the resolution of the
problem of a special mechanism of spatial orientation, the organ of
the static sense.

The special problem with which we are here concerned relates to the
group of factors upon which depends one's judgment that any specified
object within the visual field lies within the horizontal plane of the
eyes, or above or below that plane, and the several functions and
values of these components. The method of procedure has been suggested
by the results of preceding investigations in this general field.

The first aim of the experiments was to separate the factors of
resident and transient sensation, and to determine the part played by
the presence of a diversified visual field. To do so it was necessary
to ascertain, for each member of the experimental group, the location
of the subjective visual horizon, and the range of uncertainty in the
observer's location of points within that plane. Twelve observers in
all took part in the investigation. In the first set of experiments no
attempt was made to change the ordinary surroundings of the observer,
except in a single point, namely, the provision that there should be
no extended object within range of the subject's vision having
horizontal lines on a level with his eyes.

The arrangements for experimentation were as follows: A black wooden
screen, six inches wide and seven feet high, was mounted between two
vertical standards at right angles to the axis of vision of the
observer. Vertically along the center of this screen and over pulleys
at its top and bottom passed a silk cord carrying a disc of white
cardboard, 1 cm. in diameter, which rested against the black surface
of the screen. From the double pulley at the bottom of the frame the
two ends of the cord passed outward to the observer, who, by pulling
one or the other, could adjust the disc to any desired position. On
the opposite side of the screen from the observer was mounted a
vertical scale graduated in millimeters, over which passed a light
index-point attached to the silk cord, by means of which the position
of the cardboard disc in front was read off. The observer was seated
in an adjustable chair with chin and head rests, and a lateral
sighting-tube by which the position of the eyeball could be vertically
and horizontally aligned. The distance from the center of the eyeball
to the surface of the screen opposite was so arranged that, neglecting
the radial deflection, a displacement of 1 mm. in either direction was
equal to a departure of one minute of arc from the plane of the eyes'
horizon.

The observer sat with the light at his back, and by manipulation of
the cords adjusted the position of the white disc freely up and down
the screen until its center was judged to be on a level with the eye.
Its position was then read off the vertical scale by the conductor
(who sat hidden by an interposed screen), and the error of judgment
was recorded in degrees and fractions as a positive (upward) or
negative (downward) displacement. The disc was then displaced
alternately upward and downward, and the judgment repeated. From the
time of signalling that the point had been located until this
displacement the observer sat with closed eyes. These determinations
were made in series of ten, and the individual averages are in general
based upon five such series, which included regularly the results of
sittings on different days. In some cases twice this number of
judgments were taken, and on a few occasions less. The number of
judgments is attached to each series of figures in the tables. In that
which follows the individual values and their general averages are
given as minutes of arc for (_a_) the constant error or position of
the subjective horizon, (_b_) the average deviation from the objective
horizon, and (_c_) the mean variation of the series of judgments.

TABLE I.

Observer. Constant Error. Average Deviation. Mean Variation.
_A_ (100) -19.74 38.78 10.67
_C_ (90) -18.18 23.89 10.82
_D_ (100) -19.84 33.98 7.95
_E_ (50) - 4.28 72.84 6.90
_F_ (100) +46.29 46.29 2.05
_G_ (50) +14.96 35.40 8.40
_H_ (50) -27.22 27.46 5.78
_I_ (50) + 6.62 53.34 7.45
_K_ (50) + 1.08 30.26 6.59
_L_ (20) -56.70 56.70 10.39

Average: -7.70 41.89 7.69

The average subjective horizon shows a negative displacement, the
exceptional minority being large. No special facts could be connected
with this characteristic, either in method of judgment or in the past
habits of the reactor. The average constant error is less than an
eighth of a degree, and in neither direction does the extreme reach
the magnitude of a single degree of arc. Since the mean variation is
likewise relatively small, there is indicated in one's ordinary
judgments of this kind a highly refined sense of bodily orientation in
space.

II.

In order to separate the resident organic factors from those presented
by the fixed relations of the external world, an adaptation of the
mechanism was made for the purpose of carrying on the observations in
a darkened room. For the cardboard disc was substituted a light
carriage, riding upon rigid parallel vertical wires and bearing a
miniature ground-glass bulb enclosing an incandescent electric light
of 0.5 c.p. This was encased in a chamber with blackened surfaces,
having at its center an aperture one centimeter in diameter, which was
covered with white tissue paper. The subdued illumination of this
disc presented as nearly as possible the appearance of that used in
the preceding series of experiments. No other object than this spot of
moving light was visible to the observer. Adjustment and record were
made as before. The results for the same set of observers as in the
preceding case are given in the following table:

TABLE II.

Subject. Constant Error. Average Deviation. Mean Variation.
_A_ (50) - 52.76 55.16 30.08
_C_ (30) - 7.40 42.00 35.31
_D_ (50) - 14.24 38.60 30.98
_E_ (50) - 43.12 86.44 30.19
_F_ (100) - 2.01 72.33 20.27
_G_ (100) - 21.89 47.47 32.83
_H_ (50) - 1.62 59.10 29.95
_I_ (50) - 32.76 41.60 24.40
_K_ (50) - 61.70 100.02 52.44
_L_ (40) -128.70 128.90 27.83

Average: - 36.62 67.16 31.43

Changes in two directions may be looked for in the results as the
experimental conditions are thus varied. The first is a decrease in
the certainty of judgment due to the simple elimination of certain
factors upon which the judgment depends. The second is the appearance
of definite types of error due to the withdrawal of certain
correctives of organic tendencies which distort the judgment in
specific directions. The loss in accuracy is great; the mean variation
increases from 7.69 to 31.43, or more than 400 per cent. This large
increase must not, however, be understood as indicating a simple
reduction in the observer's capacity to locate points in the
horizontal plane of the eyes. The two series are not directly
comparable; for in the case of the lighted room, since the whole
visual background remained unchanged, each determination must be
conceived to influence the succeeding judgment, which becomes really a
correction of the preceding. To make the two series strictly parallel
the scenery should have been completely changed after each act of
judgment. Nevertheless, a very large increase of uncertainty may
fairly be granted in passing from a field of visual objects to a
single illuminated point in an otherwise dark field. It is probable
that this change is largely due to the elimination of those elements
of sensation depending upon the relation of the sagittal axis to the
plane against which the object is viewed.

The change presented by the constant error can here be interpreted
only speculatively. I believe it is a frequently noted fact that the
lights in a distant house or other familiar illuminated object on
land, and especially the signal lights on a vessel at sea appear
higher than their respective positions by day, to the degree at times
of creating the illusion that they hang suspended above the earth or
water. This falls in with the experimental results set forth in the
preceding table. It cannot be attributed to an uncomplicated tendency
of the eyes of a person seated in such a position to seek a lower
direction than the objective horizon, when freed from the corrective
restraint of a visual field, as will be seen when the results of
judgments made in complete darkness are cited, in which case the
direction of displacement is reversed. The single illuminated spot
which appears in the surrounding region of darkness, and upon which
the eye of the observer is directed as he makes his judgment, in the
former case restricts unconscious wanderings of the eye, and sets up a
process of continuous and effortful fixation which accompanies each
act of determination. I attribute the depression of the eyes to this
process of binocular adjustment. The experience of strain in the act
of fixation increases and decreases with the distance of the object
regarded. In a condition of rest the axes of vision of the eyes tend
to become parallel; and from this point onward the intensity of the
effort accompanying the process of fixation increases until, when the
object has passed the near-point of vision, binocular adjustment is no
longer possible. In the general distribution of objects in the visual
field the nearer, for the human being, is characteristically the
lower, the more distant the higher, as one looks in succession from
the things at his feet to the horizon and _vice versa_. We should,
therefore, expect to find, when the eyes are free to move in
independence of a determinate visual field, that increased convergence
is accompanied by a depression of the line of sight, decreased
convergence by an elevation of it. Here such freedom was permitted,
and though the fixed distance of the point of regard eliminated all
large fluctuations in convergence, yet all the secondary
characteristics of intense convergence were present. Those concerned
in the experiment report that the whole process of visual adjustment
had increased in difficulty, and that the sense of effort was
distinctly greater. To this sharp rise in the general sense of strain,
in cooeperation with the absence of a corrective field of objects, I
attribute the large negative displacement of the subjective horizon in
this series of experiments.

III.

In the next set of experiments the room was made completely dark. The
method of experimentation was adapted to these new conditions by
substituting for the wooden screen one of black-surfaced cardboard,
which was perforated at vertical distances of five millimeters by
narrow horizontal slits and circular holes alternately, making a scale
which was distinctly readable at the distance of the observer.
Opposite the end of one of these slits an additional hole was punched,
constituting a fixed point from which distances were reckoned on the
scale. As the whole screen was movable vertically and the observer
knew that displacements were made from time to time, the succession of
judgments afforded no objective criterion of the range of variation in
the series of determinations, nor of the relation of any individual
reaction to the preceding. The method of experimentation was as
follows: The observer sat as before facing the screen, the direction
of which was given at the beginning of each series by a momentary
illumination of the scale. In the darkness which followed the observer
brought the direction of sight, with open eyes, as satisfactorily as
might be into the plane of the horizontal, when, upon a simple signal,
the perforated scale was instantly and noiselessly illuminated by the
pressure of an electrical button, and the location of the point of
regard was read off the vertical scale by the observer himself, in
terms of its distance from the fixed point of origin described above.
The individual and general averages for this set of experiments are
given in the following table:

TABLE III.

Observer. Constant Error. Average Deviation. Mean Variation.
_A_ (50) + 7.75 20.07 19.45
_C_ " + 14.41 25.05 2.94
_D_ " + 14.42 34.54 29.16
_E_ " +108.97 108.97 23.13
_F_ " - 5.12 23.00 2.02
_G_ " + 20.72 34.80 10.23
_H_ " + 35.07 53.60 33.95
_I_ " + 25.52 30.68 22.49
_K_ " - 8.50 40.65 21.07

Average: + 23.69 41.26 17.16

The point at which the eyes rest when seeking the plane of the horizon
in total darkness is above its actual position, the positive
displacement involved being of relatively large amount.

In addition to the removal of the whole diversified visual field there
has now been eliminated the final point of regard toward which, in the
preceding set of experiments, the sight was strained; and the factor
of refined visual adjustment ceases longer to play a part in the
phenomenon. The result of this release is manifested in a tendency of
the eyes to turn unconsciously upward. This is their natural position
when closed in sleep. But this upward roll is not an uncomplicated
movement. There takes place at the same time a relaxation of binocular
convergence, which in sleep may be replaced by a slight divergence.
This tendency of the axes of vision to diverge as the eyes are raised
is undoubtedly connected biologically with the distribution of
distances in the higher and lower parts of the field of vision, of
which mention has already been made. Its persistence is taken
advantage of in the artificial device of assisting the process of
stereoscopic vision without instruments by holding the figures to be
viewed slightly above the primary position, so that the eyes must be
raised in order to look at them and their convergence thereby
decreased. It is by the concomitance of these two variables that the
phenomena of both this and the preceding series of experiments are to
be explained. In the present case the elimination of a fixed point of
regard is followed by a release of the mechanism of convergence, with
a consequent approximation to parallelism in the axes of vision and
its concomitant elevation of the line of sight.

The second fact to be noted is the reduction in amount of the mean
variation. The series of values under the three sets of experimental
conditions hitherto described is as follows: I. 7'.69; II. 31'.42;
III. 17'.16. This increase of regularity I take to be due, as in the
case of the lighted room, to the presence of a factor of constancy
which is not strictly an element in the judgment of horizontality.
This is a system of sensory data, which in the former case were
transient--the vision of familiar objects; and in the latter
resident--the recognition of specific experiences of strain in the
mechanism of the eye. The latter sensations exist under all three sets
of conditions, but they are of secondary importance in those cases
which include the presence of an objective point of regard, while in
the case of judgments made in total darkness the observer depends
solely upon resident experiences. Attention is thus directed
specifically toward these immediate sensational elements of judgment,
and there arises a tendency to reproduce the preceding set of
eye-strains, instead of determining the horizon plane afresh at each
act of judgment upon more general data of body position.

If the act of judgment be based chiefly upon sensory data connected
with the reinstatement of the preceding set of strains, progressions
should appear in these series of judgments, provided a constant factor
of error be incorporated in the process. This deflection should be
most marked under conditions of complete darkness, least in the midst
of full illumination. Such a progression would be shown at once by the
distribution of positive and negative values of the individual
judgments about the indifference point of constant error. As instances
of its occurrence all cases have been counted in which the first half
of the series of ten judgments was uniformly of one sign (four to six
being counted as half) and the second half of the opposite sign. The
percentages of cases in which the series presented such a progression
are as follows: In diffused light, 7.6%; in darkness, point of regard
illuminated, 18.3%; in complete darkness, 26.1%. The element of
constant error upon which such progressions depend is the tendency of
the eye to come to rest under determinate mechanical conditions of
equilibrium of muscular strain.

The relation of the successive judgments of a series to the
reinstatement of specific eye-strains and to the presence of an error
of constant tendency becomes clearer when the distribution of those
series which show progression is analyzed simultaneously with
reference to conditions of light and darkness and to binocular and
monocular vision respectively. Their quantitative relations are
presented in the following table: