Various - Harvard Psychological Studies, Volume 1

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Approximately half of the time two were called equal to one, and if
there had been no difference in the sensations half of the remaining
judgments should have been that two was smaller than one, but two were
called larger than one more than twice as many times as one was called
larger than two. There was such uniformity in the reports of the
different subjects that no one varied much from this average ratio.

This experiment seems to indicate a very slight power of
discrimination of stimulations within the threshold. In striking
contrast to this is the power to perceive variations of distance
between two points outside the threshold. To test this the
aesthesiometer was spread enough to bring the points outside the
threshold. The back of the hand was then stimulated with the two
points and then the distance varied slightly, the hand touched and the
subject asked to tell which time the points were farther apart. A
difference of 2 mm. was usually noticed, and one of from 3 to 5 mm.
was noticed always very clearly.

I wondered then what would be the result if small cards set parallel
to each other were used in place of the knobs of the aesthesiometer. I
made an aesthesiometer with cards 4 mm. long in place of knobs. These
cards could be set at any angle to each other. I set them at first 10
mm. apart and parallel to each other and asked the subjects to compare
the contact made by them with a contact by one card of the same size.
The point touched by the one card was always between the points
touched by the two cards, and the one card was put down so that its
edge would run in the same direction as the edges of the other cards.
The result of this was that:

Two were called less, 14 per cent.
" " " equal, 36 " "
" " " greater, 50 " "

I then increased the distance of the two cards to 15 mm., the other
conditions remaining the same, and found that:

Two were called less, 11 per cent.
" " " equal, 50 " "
" " " greater, 39 " "

It will be noticed that the ratio in this last series is not
materially different from the ratio found when the two knobs of the
aesthesiometer were compared with one knob. The ratio found when the
distance was 10 mm., however, is somewhat different. At that distance
two were called greater half of the time, while at 15 mm. two were
called equal to one half of the time. The explanation of the
difference, I think, is found in the comments of one of my subjects. I
did not ask them to tell in what way one object was larger than the
other--whether longer or larger all around or what--but simply to
answer 'equal,' 'greater,' or 'less.' One subject, however, frequently
added more to his answers. He would often say 'larger crosswise' or
'larger lengthwise' of his hand. And a good deal of the time he
reported two larger than one, not in the direction in which it really
was larger, but the other way. It seems to me that when the two cards
were only 10 mm. apart the effect was somewhat as it would be if a
solid object 4 mm. wide and 10 mm. long had been placed on the hand.
Such an object would be recognized as having greater mass than a line
4 mm. long. But when the distance is 15 mm. the impression is less
like that of a solid body but still not ordinarily like two objects.

In connection with the subject of diffusion the _Vexirfehler_ is of
interest. An attempt was made to develop the _Vexirfehler_ with the
aesthesiometer. Various methods were tried, but the following was most
successful. I would tell the subject that I was going to use the
aesthesiometer and ask him to close his eyes and answer simply 'one' or
'two.' He would naturally expect that he would be given part of the
time one, and part of the time two. I carefully avoided any suggestion
other than that which could be given by the aesthesiometer itself. I
would begin on the back of the hand near the wrist with the points as
near the threshold as they could be and still be felt as two. At each
successive putting down of the instrument I would bring the points a
little nearer together and a little lower down on the hand. By the
time a dozen or more stimulations had been given I would be working
down near the knuckles, and the points would be right together. From
that on I would use only one point. It might be necessary to repeat
this a few times before the illusion would persist. A great deal seems
to depend on the skill of the operator. It would be noticed that the
first impression was of two points, and that each stimulation was so
nearly like the one immediately preceding that no difference could be
noticed. The subject has been led to call a thing two which ordinarily
he would call one, and apparently he loses the distinction between the
sensation of one and the sensation of two. After going through the
procedure just mentioned I put one knob of the aesthesiometer down one
hundred times in succession, and one subject (Mr. Meakin) called it
two seventy-seven times and called it one twenty-three times. Four of
the times that he called it one he expressed doubt about his answer
and said it might be two, but as he was not certain he called it one.
Another subject (Mr. George) called it two sixty-two times and one
thirty-eight times. A third subject (Dr. Hylan) called it two
seventy-seven times and one twenty-three times. At the end of the
series he was told what had been done and he said that most of his
sensations of two were perfectly distinct and he believed that he was
more likely to call what seemed somewhat like two one, than to call
what seemed somewhat like one two. With the fourth subject (Mr.
Dunlap) I was unable to do what I had done with the others. I could
get him to call one two for four or five times, but the idea of two
would not persist through a series of any length. He would call it two
when two points very close together were used. I could bring the knobs
within two or three millimeters of each other and he would report two,
but when only one point was used he would find out after a very few
stimulations were given that it was only one. After I had given up the
attempt I told him what I had been trying to do and he gave what seems
to me a very satisfactory explanation of his own case. He says the
early sensations keep coming up in his mind, and when he feels like
calling a sensation two he remembers how the first sensation felt and
sees that this one is not like that, and hence he calls it one. I pass
now to a brief discussion of what these experiments suggest.

It has long been known that two points near together on the skin are
often perceived as one. It has been held that in order to be felt as
two they must be far enough apart to have a spatial character, and
hence the distance necessary for two points to be perceived has been
called the 'space-threshold.' This threshold is usually determined
either by the method of minimal changes or by the method of right and
wrong cases.

If, in determining a threshold by the method of minimal changes--on
the back of the hand, for example, we assume that we can begin the
ascending series and find that two are perceived as one always until
the distance of twenty millimeters is reached, and that in the
descending series two are perceived as two until the distance of ten
millimeters is reached, we might then say that the threshold is
somewhere between ten and twenty millimeters. But if the results were
always the same and always as simple as this, still we could not say
that there is any probability in regard to the answer which would be
received if two contacts 12, 15, or 18 millimeters apart were given by
themselves. All we should know is that if they form part of an
ascending series the answer will be 'one,' if part of a descending
series 'two.'

The method of right and wrong cases is also subject to serious
objections. There is no lower limit, for no matter how close together
two points are they are often called two. If there is any upper limit
at all, it is so great that it is entirely useless. It might be argued
that by this method a distance could be found at which a given
percentage of answers would be correct. This is quite true, but of
what value is it? It enables one to obtain what one arbitrarily calls
a threshold, but it can go no further than that. When the experiment
changes the conditions change. The space may remain the same, but it
is only one of the elements which assist in forming the judgment, and
its importance is very much overestimated when it is made the basis
for determining the threshold.

Different observers have found that subjects sometimes describe a
sensation as 'more than one, but less than two.' I had a subject who
habitually described this feeling as 'one and a half.' This does not
mean that he has one and a half sensations. That is obviously
impossible. It must mean that the sensation seems just as much like
two as it does like one, and he therefore describes it as half way
between. If we could discover any law governing this feeling of
half-way-between-ness, that might well indicate the threshold. But
such feelings are not common. Sensations which seem between one and
two usually call forth the answer 'doubtful,' and have a negative
rather than a positive character. This negative character cannot be
due to the stimulus; it must be due to the fluctuating attitudes of
the subject. However, if the doubtful cases could be classed with the
'more than one but less than two' cases and a law be found governing
them, we might have a threshold mark. But such a law has not been
formulated, and if it had been an analysis of the 'doubtful' cases
would invalidate it. For, since we cannot have half of a sensation or
half of a place as we might have half of an area, the subject regards
each stimulation as produced by one or by two points as the case may
be. Occasionally he is stimulated in such a way that he can regard the
object as two or as one with equal ease. In order to describe this
feeling he is likely to use one or the other of the methods just
mentioned.

We might say that when the sum of conditions is such that the subject
perceives two points, the points are above the threshold, and when the
subject perceives one point when two are given they are below the
threshold. This might answer the purpose very well if it were not for
the _Vexirfehler_. According to this definition, when the
_Vexirfehler_ appears we should have to say that one point is above
the threshold for twoness, which is a queer contradiction, to say the
least. It follows that all of the elaborate and painstaking
experiments to determine a threshold are useless. That is, the
threshold determinations do not lead us beyond the determinations
themselves.

In order to explain the fact that a person sometimes fails to
distinguish between one point and two points near together, it has
been suggested that the sensations fuse. This, I suppose, means either
that the peripheral processes coalesce and go to the center as a
single neural process, or that the process produced by each stimulus
goes separately to the brain and there the two set up a single
activity. Somewhat definite 'sensory circles,' even, were once
believed in.

If the only fact we had to explain was that two points are often
thought to be one when they are near together, 'fusion' might be a
good hypothesis, but we have other facts to consider. If this one is
explained by fusion, then the mistaking of one point for two must be
due to diffusion of sensations. Even that might be admissible if the
_Vexirfehler_ were the only phenomenon of this class which we met. But
it is also true that several contacts are often judged to be more than
they actually are, and that hypothesis will not explain why certain
arrangements of the stimulating objects are more likely to bring about
that result than others. Still more conclusive evidence against
fusion, it seems to me, is found in the fact that two points, one on
each hand, may be perceived as one when the hands are brought
together. Another argument against fusion is the fact that two points
pressed lightly may be perceived as one, and when the pressure is
increased they are perceived as two. Strong pressures should fuse
better than weak ones, and therefore fusion would imply the opposite
results. Brueckner[1] has found that two sensations, each too weak to
be perceived by itself, may be perceived when the two are given
simultaneously and sufficiently near together. This reenforcement of
sensations he attributes to fusion. But we have a similar phenomenon
in vision when a group of small dots is perceived, though each dot by
itself is imperceptible. No one, I think, would say this is due to
fusion. It does not seem to me that we need to regard reenforcement as
an indication of fusion.

[1] Brueckner, A.: 'Die Raumschwelle bei Simultanreizung,'
_Zeitschrift fuer Psychologie_, 1901, Bd. 26, S. 33.

My contention is that the effects sometimes attributed to fusion and
diffusion of sensations are not two different kinds of phenomena, but
are identical in character and are to be explained in the same way.

Turning now to the explanation of the special experiments, we may
begin with the _Vexirfehler_.[2] It seems to me that the _Vexirfehler_
is a very simple phenomenon. When a person is stimulated with two
objects near together he attends first to one and then to the other
and calls it two; then when he is stimulated with one object he
attends to it, and expecting another one near by he hunts for it and
hits upon the same one he felt before but fails to remember that it is
the same one, and hence thinks it is another and says he has felt two
objects. Observers agree that the expectation of two tends to bring
out the _Vexirfehler_. This is quite natural. A person who expects two
and receives one immediately looks about for the other without waiting
to fixate the first, and therefore when he finds it again he is less
likely to recognize it and more likely to think it another point and
to call it two. Some observers[3] have found that the apparent
distance of the two points when the _Vexirfehler_ appears never much
exceeds the threshold distance. Furthermore, there being no distinct
line of demarcation between one and two, there must be many sensations
which are just about as much like one as they are like two, and hence
they must be lumped off with one or the other group. To the
mathematician one and two are far apart in the series because he has
fractions in between, but we perceive only in terms of whole numbers;
hence all sensations which might more accurately be represented by
fractions must be classed with the nearest whole number. A sensation
is due to a combination of factors. In case of the _Vexirfehler_ one
of these factors, viz., the stimulating object, is such as to suggest
one, but some of the other conditions--expectation, preceding
sensation, perhaps blood pressure, etc.--suggest two, so that the
sensation as a whole suggests _one-plus_, if we may describe it that
way, and hence the inference that the sensation was produced by two
objects.

[2] Tawney, Guy A.: 'Ueber die Wahrnehmung zweier Punkte
mittelst des Tastsinnes mit Ruecksicht auf die Frage der Uebung
und die Entstehung der Vexirfehler,' _Philos. Stud._, 1897, Bd.
XIII., S. 163.

[3] See Nichols: 'Number and Space,' p. 161. Henri, V., and
Tawney, G.: _Philos. Stud._, Bd. XI., S. 400.

This, it seems to me, may account for the appearance of the
_Vexirfehler_, but why should not the subject discover his error by
studying the sensation more carefully? He cannot attend to two things
at once, nor can he attend to one thing continuously, even for a few
seconds. What we may call continuous attention is only a succession of
attentive impulses. If he could attend to the one object continuously
and at the same time hunt for the other, I see no reason why he should
not discover that there is only one. But if he can have only one
sensation at a time, then all he can do is to associate that
particular sensation with some idea. In the case before us he
associates it with the idea of the number two. He cannot conceive of
two objects unless he conceives them as located in two different
places. Sometimes a person does find that the two objects of his
perception are both in the same place, and when he does so he
concludes at once that there is but one object. At other times he
cannot locate them so accurately, and he has no way of finding out the
difference, and since he has associated the sensation with the idea of
two he still continues to call it two. If he is asked to locate the
points on paper he fills out the figure just as he fills out the
blind-spot, and he can draw them in just the same way that he can draw
lines which he thinks he _sees_ with the blind-spot, but which really
he only _infers_.

Any sensation, whether produced by one or by many objects, is one, but
there may be a difference in the quality of a sensation produced by
one object and that of a sensation produced by more than one object.
If this difference is clear and distinct, the person assigns to each
sensation the number he has associated with it. He gives it the name
two when it has the quality he has associated with that idea. But the
qualities of a sensation from which the number of objects producing it
is inferred are not always clear and distinct. The quality of the
sensation must not be confused with any quality of the object. If we
had to depend entirely on the sense of touch and always remained
passive and received sensations only when we were touched by
something, there is no reason why we should not associate the idea of
one with the sensation produced by two objects and the idea of two
with that produced by one object--assuming that we could have any idea
of number under such circumstances. The quality of a sensation from
which number is inferred depends on several factors. The number itself
is determined by the attitude of the subject, but the attitude is
determined largely by association. A number of facts show this. When a
person is being experimented on, it is very easy to confuse him and
make him forget how two feel and how one feels. I have often had a
subject tell me that he had forgotten and ask me to give him two
distinctly that he might see how it felt. In other words, he had
forgotten how to associate his ideas and sensations. In developing the
_Vexirfehler_ I found it much better, after sufficient training had
been given, not to give two at all, for it only helped the subject to
perceive the difference between two and one by contrast. But when one
was given continually he had no such means of contrast, and having
associated the idea of two with a sensation he continued to do so. The
one subject with whom I did not succeed in developing the
_Vexirfehler_ to any great extent perceived the difference by
comparing the sensation with one he had had some time before. I could
get him, for a few times, to answer two when only one was given, but
he would soon discover the difference, and he said he did it by
comparing it with a sensation which he had had some time before and
which he knew was two. By this means he was able to make correct
associations when otherwise he would not have done so. It has been
discovered that when a subject is being touched part of the time with
two and part of the time with one, and the time it takes him to make
his judgments is being recorded, he will recognize two more quickly
than he will one if there is a larger number of twos in the series
than there is of ones. I do not see how this could be if the sensation
of two is any more complex than that of one. But if both sensations
are units and all the subject needs to do is to associate the
sensation with an idea, then we should expect that the association he
had made most frequently would be made the most quickly.

If the feeling of twoness or of oneness is anything but an inference,
why is it that a person can perceive two objects on two fingers which
are some distance apart, but perceives the same two objects as one
when the fingers are brought near together and touched in the same
way? It is difficult to see how bringing the fingers together could
make a sensation any less complex, but it would naturally lead a
person to infer one object, because of his previous associations. He
has learned to call that _one_ which seems to occupy one place. If two
contacts are made in succession he will perceive them as two because
they are separated for him by the time interval and he can perceive
that they occupy different places.

When two exactly similar contacts are given and are perceived as one,
we cannot be sure whether the subject feels only one of the contacts
and does not feel the other at all, or feels both contacts and thinks
they are in the same place, which is only another way of saying he
feels both as one. It is true that when asked to locate the point he
often locates it between the two points actually touched, but even
this he might do if he felt but one of the points. To test the matter
of errors of localization I have made a few experiments in the
Columbia University laboratory. In order to be sure that the subject
felt both contacts I took two brass rods about four inches long,
sharpened one end and rounded off the other. The subject sat with the
palm of his right hand on the back of his left and his fingers
interlaced. I stimulated the back of his fingers on the second
phalanges with the sharp end of one rod and the blunt end of the other
and asked him to tell whether the sharp point was to the right or to
the left of the other. I will not give the results in detail here, but
only wish to mention a few things for the purpose of illustrating the
point in question. Many of the answers were wrong. Frequently the
subject would say both were on the same finger, when really they were
on fingers of opposite hands, which, however, in this position were
adjacent fingers. Sometimes when this happened I would ask him which
finger they were on, and after he had answered I would leave the point
on the finger on which he said both points were and move the other
point over to the same finger, then move it back to its original
position, then again over to the finger on which the other point was
resting, and so on, several times. The subject would tell me that I
was raising one point and putting it down again in the same place all
of the time. Often a subject would tell me he felt both points on the
same finger, but that he could not tell to which hand the finger
belonged. When two or more fingers intervened between the fingers
touched no subject ever had any difficulty in telling which was the
sharp and which the blunt point, but when adjacent fingers were
touched it was very common for the subject to say he could not tell
which was which. This cannot be because there is more difference in
the quality of the contacts in one case than in the other. If they
were on the same finger it might be said that they were stimulating
the same general area, but since one is on one hand and one on the
other this is impossible. The subject does not think the two points
are in the same place, because he feels two qualities and hence he
infers two things, and he knows two things cannot be in the same place
at the same time. If the two contacts were of the same quality
probably they would be perceived as one on account of the absence of
difference, for the absence of difference is precisely the quality of
oneness.

These facts, together with those mentioned before, seem to me to
indicate that errors of localization are largely responsible for
judgments which seem to be due to fusion or diffusion of sensations.
But they are responsible only in this way, they prevent the correction
of the first impression. I do not mean that a person never changes his
judgment after having once made it, but a change of judgment is not
necessarily a correction. Often it is just the contrary. But where a
wrong judgment is made and cannot be corrected inability to localize
is a prominent factor. This, however, is only a secondary factor in
the perception of number. The cardinal point seems to me the
following:

Any touch sensation, no matter by how many objects it is produced, is
one, and number is an inference based on a temporal series of
sensations. It may be that we can learn by association to infer number
immediately from the quality of a sensation, but that means only that
we recognize the sensation as one we have had before and have found it
convenient to separate into parts and regard one part after the other,
and we remember into how many parts we separated it. This separating
into parts is a time process. What we shall regard as _one_ is a mere
matter of convenience. Continuity sometimes affords a convenient basis
for unity and sometimes it does not. There is no standard of oneness
in the objective world. We separate things as far as convenience or
time permits and then stop and call that _one_ which our own attitude
has determined shall be one.