Various - Harvard Psychological Studies, Volume 1

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[15] Wundt., W., 'Physiolog. Psych.,' 4te Aufl., Leipzig, 1893,
Bd. II., S. 144.

[16] v. Helmholtz, H., 'Handbuch d. Physiol. Optik,' 2te Aufl.,
Hamburg u. Leipzig, 1896, S. 705.

[17] Wundt, W., _op. citat._, S. 139.

Satisfactorily as the movement hypothesis explains this and other
optical illusions, it yet falls short of furnishing an entirely
adequate explanation. It seems to me certain that several causes exist
to produce this illusion, and also the illusion that is often
associated with it, the well-known Mueller-Lyer illusion. But in what
degree each is present has not yet been determined by any of the
quantitative studies in this particular illusion. I made a number of
tests of the optical illusion, with these results: that the illusion
is strongest when the attention is fixed at about the middle of the
open space, that there is scarcely any illusion left when the
attention is fixed on the middle of the filled space. It is stronger
when the outer end-point of the open space is fixated than when the
outer end of the filled space is fixated. For the moving eye, I find
the illusion to be much stronger when the eye passes over the filled
space first, and then over the open space, than when the process is
reversed.

Now, the movement hypothesis does not, it seems to me, sufficiently
explain all the fluctuations in the illusion. My experiments with the
tactual illusion justify the belief that the movement theory is even
less adequate to explain all of the variations there, unless the
movement hypothesis is given a wider and richer interpretation than is
ordinarily given to it. In the explanation of the tactual illusion
which I have here been studying two other important factors must be
taken into consideration. These I shall call, for the sake of
convenience, the aesthetic factor and the time factor. These factors
should not, however, be regarded as independent of the factor of
movement. That term should be made wide enough to include these within
its meaning. The importance of the time factor in the illusion for
passive touch I have already briefly mentioned. I have also, in
several places in the course of my experiments, called attention to
the importance of the aesthetic element in our space judgments. I wish
now to consider these two factors more in detail.

The foregoing discussion has pointed to the view that the
space-perceiving and the localizing functions of the skin have a
deep-lying common origin in the motor sensations. My experiments show
that, even in the highly differentiated form in which we find them in
their ordinary functioning, they plainly reveal their common origin. A
formula, then, for expressing the judgments of distance by means of
the resting skin might be put in this way. Let _P_ and _P'_ represent
any two points on the skin, and let _L_ and _L'_ represent the local
signs of these points, and _M_ and _M'_ the muscle sensations which
give rise to these local signs. Then _M-M'_ will represent the
distance between _P_ and _P'_, whether that distance be judged
directly in terms of the localizing function of the skin or in terms
of its space-perceiving function. This would be the formula for a
normal judgment. In an illusory judgment, the temporal and aesthetic
factors enter as disturbing elements. Now, the point which I insist on
here is that the judgments of the extent of the voluntary movements,
represented in the formula by _M_ and _M'_, do not depend alone on the
sensations from the moving parts or other sensations of objective
origin, as Dresslar would say, nor alone on the intention or impulse
or innervation as Loeb and others claim, but on the sum of all the
sensory elements that enter, both those of external and those of
internal origin. And, furthermore, these sensations of external origin
are important in judgments of space, only in so far as they are
referred to sensations of internal origin. Delabarre says, "Movements
are judged equal when their sensory elements are judged equal. These
sensory elements need not all have their source in the moving parts.
All sensations which are added from other parts of the body and which
are not recognized as coming from these distant sources, are mingled
with the elements from the moving member, and influence the
judgment."[18] The importance of these sensations of inner origin was
shown in many of the experiments in sections VI. to VIII. In the
instance where the finger-tip was drawn over an open and a filled
space, in the filled half the sensations were largely of external
origin, while in the open half they were of internal origin. The
result was that the spaces filled with sensations of internal origin
were always overestimated.

The failure to recognize the importance of these inwardly initiated
sensations is the chief defect in Dresslar's reasoning. He has
endeavored to make our judgments in the illusion in question depend
entirely on the sensations of external origin. He insists also that
the illusion varies according to the variations in quantity of these
external sensations. Now my experiments have shown, I think, very
clearly that it is not the numerical or quantitative extent of the
objective sensations which disturbs the judgment of distance, but the
sensation of inner origin which we set over against these outer
sensations. The piece of plush, because of the disagreeable sensations
which it gives, is judged shorter than the space filled with closely
crowded tacks. Dresslar seems to have overlooked entirely the fact
that the feelings and emotions can be sources of illusions in the
amount of movement, and hence in our judgments of space. The
importance of this element has been pointed out by Muensterberg[19] in
his studies of movement.

[18] Delabarre, E.B., 'Ueber Bewegungsempfindungen,' Inaug.
Dissert., Freiburg, 1891.

[19] Muensterberg, H., 'Beitraege zur Experimentellen Psychol.,'
Freiburg i. B., 1892, Heft 4.

Dresslar says again, "The explanations heretofore given, wholly based
on the differences in the time the eye uses in passing over the two
spaces, must stop short of the real truth." My experiments, however,
as I have already indicated, go to prove quite the contrary. In short,
I do not think we have any means of distinguishing our tactual
judgments of time from our similar judgments of space. When the
subject is asked to measure off equal spaces, he certainly uses time
as means, because when he is asked to measure off equal times he
registers precisely the same illusion that he makes in his judgments
of spatial distances. The fact that objectively equal times were used
by Dresslar in his experiments is no reason for supposing that the
subject also regarded these times as equal. What I have here asserted
of active touch is true also of the resting skin. When a stylus is
drawn over the skin, the subject's answer to the question, How long is
the distance? is subject to precisely the same illusion as his answer
to the question, How long is the time?

I can by a simple illustration show more plainly what I mean by the
statement that the blending of the inner and outer sensations is
necessary for the perception of space. I shall use the sense of sight
for the illustration, although precisely the same reasoning would
apply to the sense of touch. Suppose that I sat in an entirely passive
position and gazed at a spot on an otherwise blank piece of paper
before me. I am perfectly passive so far as motion on my part is
concerned. I may be engaged in any manner of speculation or be in the
midst of the so-called active attention to the spot; but I must be and
for the present remain motionless. Now, while I am in this condition
of passivity, suppose the spot be made to move slowly to one side by
some force external to myself. I am immovable all the while, and yet
am conscious of this movement of the spot from the first position,
which I call _A_, to the new position, _A'_, where it stops. The
sensation which I now have is qualitatively different from the
sensation which I had from the spot in its original position. My world
of experience thus far has been a purely qualitative one. I might go
on to eternity having experiences of the same kind, and never dream of
space, or geometry, nor should I have the unique experience of a
geometrical illusion, either optical or tactual. Now suppose I set up
the bodily movements of the eyes or the head, or of the whole body,
which are necessary to follow the path of that point, until I overtake
it and once more restore the quality of the original sensation. This
circle, completed by the two processes of external activity and
restoration by internal activity, forms a group of sensations which
constitutes the ultimate atom in our spatial experience. I have my
first spatial experience when I have the thrill of satisfaction that
comes from overtaking again, by means of my own inner activity, a
sensation that has escaped me through an activity not my own. A being
incapable of motion, in a world of flux, would not have the spatial
experience that we have. A being incapable of motion could not make
the distinction between an outer change that can be corrected by an
internal change, and an outer change that cannot so be restored. Such
an external change incapable of restoration by internal activity we
should have if the spot on the paper changed by a chemical process
from black to red.

Now such a space theory is plainly not to be confused with the theory
that makes the reversibility of the spatial series its primary
property. It is evident that we can have a series of sensations which
may be reversed and yet not give the notion of space. But we should
always have space-perception if one half of the circular process above
described comes from an outer activity, and the other half from an
inner activity. This way of describing the reversibility of the
spatial series makes it less possible to urge against it the
objections that Stumpf[20] has formulated against Bain's genetic
space-theory. Stumpf's famous criticism applies not only to Bain, but
also to the other English empiricists and to Wundt. Bain says: "When
with the hand we grasp something moving and move with it, we have a
sensation of one unchanged contact and pressure, and the sensation is
imbedded in a movement. This is one experience. When we move the hand
over a fixed surface, we have with the feelings of movement a
succession of feelings of touch; if the surface is a variable one,
the sensations are constantly changing, so that we can be under no
mistake as to our passing through a series of tactual impressions.
This is another experience, and differs from the first not in the
sense of power, but in the tactile accompaniment. The difference,
however, is of vital importance. In the one case, we have an object
moving and measuring time and continuous, in the other case we have
coexistence in space. The coexistence is still further made apparent
by our reversing the movement, and thereby meeting the tactile series
in the inverse order. Moreover, the serial order is unchanged by the
rapidity of our movements."[21]

[20] Stumpf, K., 'Ueber d. psycholog. Ursprung d.
Raumvorstellung,' Leipzig, 1873, S. 54.

[21] Bain, A., 'The Senses and the Intellect,' 3d ed., New
York, 1886, p. 183.

Stumpf maintained in his exhaustive criticism of this theory, first,
that there are cases where all of the elements which Bain requires for
the perception of space are present, and yet we have no presentation
of space. Secondly, there are cases where not all of these elements
are present, and where we have nevertheless space presentation. It is
the first objection that concerns me here. Stumpf gives as an example,
under his first objection, the singing of a series of tones, C, G, E,
F. We have here the muscle sensations from the larynx, and the series
of the tone-sensations which are, Stumpf claims, reversed when the
muscle-sensations are reversed, etc. According to Stumpf, these are
all the elements that are required by Bain, and yet we have no
perception of space thereby. Henri[22] has pointed out two objections
to Stumpf's criticism of Bain's theory. He says that Bain assumes,
what Stumpf does not recognize, that the muscle sensations must
contain three elements--resistance, time, and velocity--before they
can lead to space perceptions. These three elements are not to be
found in the muscle sensations of the larynx as we find them in the
sensations that come from the eye or arm muscles. In addition to this,
Henri claims that Bain's theory demands a still further condition. If
we wish to touch two objects, _A_ and _B_, with the same member, we
can get a spatial experience from the process only if we insert
between the touching of _A_ and the touching of _B_ a continual
series of tactual sensations. In Stumpf's instance of the singing of
tones, this has been overlooked. We can go from the tone C to the tone
F without inserting between the two a continuous series of musical
sensations.

[22] Henri, V., 'Ueber d. Raumwahrnehmungen d. Tastsinnes,'
Berlin, 1898, S. 190.

I think that all such objections to the genetic space theories are
avoided by formulating a theory in the manner in which I have just
stated. When one says that there must be an outer activity producing a
displacement of sensation, and then an inner activity retaining that
sensation, it is plain that the singing of a series of tones ascending
and then descending would not be a case in point.

* * * * *

TACTUAL TIME ESTIMATION.

BY KNIGHT DUNLAP.

I. GENERAL NATURE OF THE WORK.

The experiments comprised in this investigation were made during the
year 1900-1901 and the early part of the year 1901-1902. They were
planned as the beginning of an attempt at the analysis of the
estimation of time intervals defined by tactual stimulations. The only
published work in this quarter of the field so far is that of
Vierordt,[1] who investigated only the constant error of time
judgment, using both auditory and tactual stimulations, and that of
Meumann,[2] who in his last published contribution to the literature
of the time sense gives the results of his experiments with 'filled'
and 'empty' tactual intervals. The stimuli employed by Meumann were,
however, not purely tactual, but electrical.

[1] Vierordt: 'Der Zeitsinn,' Tuebingen, 1868.

[2] Meumann, E.: 'Beitraege zur Psychologie des
Zeitbewusstseins,' III., _Phil. Studien,_ XII., S. 195-204.

The limitation of time intervals by tactual stimulations offers,
however, a rich field of variations, which promise assistance in the
analytical problem of the psychology of time. The variations may be
those of locality, area, intensity, rigidity, form, consecutiveness,
and so on, in addition to the old comparisons of filled and empty
intervals, intervals of varying length, and intervals separated by a
pause and those not so separated.

To begin with, we have selected the conditions which are mechanically
the simplest, namely, the comparison of two empty time intervals, both
given objectively with no pause between them. We have employed the
most easily accessible dermal areas, namely, that of the fingers of
one or both hands, and introduced the mechanically simplest
variations, namely, in locality stimulated and intensity of
stimulation.

It was known from the results of nearly all who have studied the time
sense experimentally, that there is in general a constant error of
over- or underestimation of time intervals of moderate length, and
from the results of Meumann,[3] that variations in intensity of
limiting stimulation influenced the estimation decidedly, but
apparently according to no exact law. The problem first at hand was
then to see if variations introduced in tactual stimulations produce
any regularity of effect, and if they throw any new light on the
phenomena of the constant error.

[3] Meumaun, E.: 'Beitraege zur Psychologie des Zeitsinns,' II.,
_Phil. Studien_, IX., S. 264.

The stimulations employed were light blows from the cork tip of a
hammer actuated by an electric current. These instruments, of which
there were two, exactly alike in construction, were similar in
principle to the acoustical hammers employed by Estel and Mehner. Each
consisted essentially of a lever about ten inches in length, pivoted
near one extremity, and having fastened to it near the pivot an
armature so acted upon by an electromagnet as to depress the lever
during the passage of an electric current. The lever was returned to
its original position by a spring as soon as the current through the
electromagnet ceased. A clamp at the farther extremity held a small
wooden rod with a cork tip, at right angles to the pivot, and the
depression of the lever brought this tip into contact with the dermal
surface in proximity with which it had been placed. The rod was easily
removable, so that one bearing a different tip could be substituted
when desired. The whole instrument was mounted on a compact base
attached to a short rod, by which it could be fastened in any desired
position in an ordinary laboratory clamp.

During the course of most of the experiments the current was
controlled by a pendulum beating half seconds and making a mercury
contact at the lowest point of its arc. A condenser in parallel with
the contact obviated the spark and consequent noise of the current
interruption. A key, inserted in the circuit through the mercury cup
and tapping instrument, allowed it to be opened or closed as desired,
so that an interval of any number of half seconds could be interposed
between successive stimulations.

In the first work, a modification of the method of right and wrong
cases was followed, and found satisfactory. A series of intervals,
ranging from one which was on the whole distinctly perceptible as
longer than the standard to one on the whole distinctly shorter, was
represented by a series of cards. Two such series were shuffled
together, and the intervals given in the order so determined. Thus,
when the pile of cards had been gone through, two complete series had
been given, but in an order which the subject was confident was
perfectly irregular. As he also knew that in a given series there were
more than one occurrence of each compared interval (he was not
informed that there were exactly two of each), every possible
influence favored the formation each time of a perfectly fresh
judgment without reference to preceding judgments. The only fear was
lest certain sequences of compared intervals (_e.g._, a long compared
interval in one test followed by a short one in the next), might
produce unreliable results; but careful examination of the data, in
which the order of the interval was always noted, fails to show any
influence of such a factor.

To be more explicit with regard to the conditions of judgment; two
intervals were presented to the subject in immediate succession. That
is, the second stimulation marked the end of the first interval and
the beginning of the second. The first interval was always the
standard, while the second, or compared interval, varied in length, as
determined by the series of cards, and the subject was requested to
judge whether it was equal to, or longer or shorter than the standard
interval.

In all of the work under Group 1, and the first work under Group 2,
the standard interval employed was 5.0 seconds. This interval was
selected because the minimum variation possible with the pendulum
apparatus (1/2 sec.) was too great for the satisfactory operation of a
shorter standard, and it was not deemed advisable to keep the
subject's attention on the strain for a longer interval, since 5.0
sec. satisfied all the requirements of the experiment.

In all work here reported, the cork tip on the tapping instrument was
circular in form, and 1 mm. in diameter. In all, except one experiment
of the second group, the areas stimulated were on the backs of the
fingers, just above the nails. In the one exception a spot on the
forearm was used in conjunction with the middle finger.

In Groups 1 and 2 the intensity of stroke used was just sufficient to
give a sharp and distinct stimulation. The intensity of the
stimulation was not of a high degree of constancy from day to day, on
account of variations in the electric contacts, but within each test
of three stimulations the intensity was constant enough.

In experiments under Group 3 two intensities of strokes were employed,
one somewhat stronger than the stroke employed in the other
experiments, and one somewhat weaker--just strong enough to be
perceived easily. The introduction of the two into the same test was
effected by the use of an auxiliary loop in the circuit, containing a
rheostat, so that the depression of the first key completed the
circuit as usual, or the second key completed it through the rheostat.

At each test the subject was warned to prepare for the first
stimulation by a signal preceding it at an exact interval. In
experiments with the pendulum apparatus the signal was the spoken word
'now,' and the preparatory interval one second. Later, experiments
were undertaken with preparatory intervals of one second and 1-4/5
seconds, to find if the estimation differed perceptibly in one case
from that in the other. No difference was found, and in work
thereafter each subject was allowed the preparatory interval which
made the conditions subjectively most satisfactory to him.

Ample time for rest was allowed the subject after each test in a
series, two (sometimes three) series of twenty to twenty-four tests
being all that were usually taken in the course of the hour. Attention
to the interval was not especially fatiguing and was sustained without
difficulty after a few trials.

Further details will be treated as they come up in the consideration
of the work by groups, into which the experiment naturally falls.

II. EXPERIMENTAL RESULTS.

1. The first group of experiments was undertaken to find the direction
of the constant error for the 5.0 sec. standard, the extent to which
different subjects agree and the effects of practice. The tests were
therefore made with three taps of equal intensity on a single dermal
area. The subject sat in a comfortable position before a table upon
which his arm rested. His hand lay palm down on a felt cushion and the
tapping instrument was adjusted immediately over it, in position to
stimulate a spot on the back of the finger, just above the nail. A few
tests were given on the first finger and a few on the second
alternately throughout the experiments, in order to avoid the numbing
effect of continual tapping on one spot. The records for each of the
two fingers were however kept separately and showed no disagreement.

The detailed results for one subject (_Mr_,) are given in Table I. The
first column, under _CT_, gives the values of the different compared
intervals employed. The next three columns, under _S_, _E_ and _L_,
give the number of judgments of _shorter_, _equal_ and _longer_,
respectively. The fifth column, under _W_, gives the number of errors
for each compared interval, the judgments of _equal_ being divided
equally between the categories of _longer_ and _shorter_.

In all the succeeding discussion the standard interval will be
represented by _ST_, the compared interval by _CT_. _ET_ is that _CT_
which the subject judges equal to _ST_.

TABLE I.

_ST_=5.0 SEC. SUBJECT _Mr._ 60 SERIES.

_CT_ _S_ _E_ _L_ _W_
4. 58 1 1 1.5
4.5 45 11 4 9.5
5. 32 13 15 21.5
5.5 19 16 25 27
6. 5 4 51 7
6.5 1 2 57 2

We can calculate the value of the average _ET_ if we assume that the
distribution of wrong judgments is in general in accordance with the
law of error curve. We see by inspection of the first three columns
that this value lies between 5.0 and 5.5, and hence the 32 cases of
_S_ for _CT_ 5.0 must be considered correct, or the principle of the
error curve will not apply.

The method of computation may be derived in the following way: If we
take the origin so that the maximum of the error curve falls on the
_Y_ axis, the equation of the curve becomes

y = ke^{-[gamma] squaredx squared}

and, assuming two points (x_{1} y_{1}) and (x_{2} y_{2}) on the
curve, we deduce the formula

____________
+-D \/ log k/y_{1}
x_{1} = ---------------------------------
____________ ____________
\/ log k/y_{1} +- \/ log k/y_{2}

where D = x_{1} +- x_{2}, and k = value of y when x = 0.

x_{1} and x_{2} must, however, not be great, since the condition
that the curve with which we are dealing shall approximate the form
denoted by the equation is more nearly fulfilled by those portions of
the curve lying nearest to the _Y_ axis.