Various - Harvard Psychological Studies, Volume 1

V >> Various >> Harvard Psychological Studies, Volume 1

Pages:
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55

Now since for any ordinates, y_{1} and y_{2} which we may select
from the table, we know the value of x_{1} +- x_{2}, we can compute
the value of x_{1}, which conversely gives us the amount to be added
to or subtracted from a given term in the series of _CT_'s to produce
the value of the average _ET_. This latter value, we find, by
computing by the formula given above, using the four terms whose
values lie nearest to the _Y_ axis, is 5.25 secs.

In Table II are given similar computations for each of the nine
subjects employed, and from this it will be seen that in every case
the standard is overestimated.

TABLE II. _ST_= 5.0 SECS.

Subject. Average ET. No. of Series.
_A_. 5.75 50
_B_. 5.13 40
_Hs_. 5.26 100
_P_. 5.77 38
_Mn_. 6.19 50
_Mr_. 5.25 60
_R_. 5.63 24
_Sh_. 5.34 100
_Sn_. 5.57 50

This overestimation of the 5.0 sec. standard agrees with the results
of some of the experimenters on auditory time and apparently conflicts
with the results of others. Mach[4] found no constant error. Hoering[5]
found that intervals over 0.5 sec. were overestimated. Vierordt,[6]
Kollert,[7] Estel[8] and Glass,[9] found small intervals overestimated
and long ones underestimated, the indifference point being placed at
about 3.0 by Vierordt, 0.7 by Kollert and Estel and 0.8 by Glass.
Mehner[10] found underestimation from 0.7 to 5.0 and overestimation
above 5.0. Schumann[11] found in one set of experiments overestimation
from 0.64 to 2.75 and from 3.5 to 5.0, and underestimation from 2.75
to 3.5. Stevens[12] found underestimation of small intervals and
overestimation of longer ones, placing the indifference point between
0.53 and 0.87.

[4] Mach, E.: 'Untersuchungen ueber den Zeitsinn des Ohres,'
_Sitzungsber. d. Wiener Akad._, Math.-Nat. Kl., Bd. 51, Abth.
2.

[5] Hoering: 'Versuche ueber das Unterscheidungsvermoegen des
Hoersinnes fuer Zeitgroessen,' Tuebingen, 1864.

[6] Vierordt: _op. cit._

[7] Kollert, J.: 'Untersuchungen ueber den Zeitsinn,' _Phil.
Studien_, I., S. 79.

[8] Estel, V.: 'Neue Versuche ueber den Zeitsinn,' _Phil.
Studien_, II., S. 39.

[9] Glass R.: 'Kritisches und Experimentelles ueber den
Zeitsinn,' _Phil. Studien_, IV., S. 423.

[10] Mehner, Max: 'Zum Lehre vom Zeitsinn,' _Phil. Studien_,
II., S. 546.

[11] Schumann, F.: 'Ueber die Schaetzung kleiner Zeitgroessen,'
_Zeitsch. f. Psych._, IV., S. 48.

[12] Stevens, L.T.: 'On the Time Sense,' _Mind_, XI., p. 393.

The overestimation, however, is of no great significance, for data
will be introduced a little later which show definitely that the
underestimation or overestimation of a given standard is determined,
among other factors, by the intensity of the stimulation employed. The
apparently anomalous results obtained in the early investigations are
in part probably explicable on this basis.

As regards the results of _practice_, the data obtained from the two
subjects on whom the greatest number of tests was made (_Hs_ and _Sh_)
is sufficiently explicit. The errors for each successive group of 25
series for these two subjects are given in Table III.

TABLE III.

_ST_ = 5.0 SECONDS.

SUBJECT _Hs_. SUBJECT _Sh_.
CT (1) (2) (3) (4) (1) (2) (3) (4)
4. 2.5 2.5 1.5 2.5 0. .5 0. .5
4.5 6.0 3.0 3.5 7.0 5.0 3.5 2.0 .5
5. 14.0 11.0 11.0 11.0 8.5 11.5 4.0 7.0
5.5 11.5 11.5 6.0 12.5 11.0 16.0 14.0 15.0
6. 12.0 9.0 6.5 6.0 3.5 2.0 1.5 1.0
6.5 4.0 3.5 4.0 3.5 4.0 .5 0. 0.

No influence arising from practice is discoverable from this table,
and we may safely conclude that this hypothetical factor may be
disregarded, although among the experimenters on auditory time
Mehner[13] thought results gotten without a maximum of practice are
worthless, while Meumann[14] thinks that unpracticed and hence
unsophisticated subjects are most apt to give unbiased results, as
with more experience they tend to fall into ruts and exaggerate their
mistakes. The only stipulation we feel it necessary to make in this
connection is that the subject be given enough preliminary tests to
make him thoroughly familiar with the conditions of the experiment.

[13] _op. cit._, S. 558, S. 595.

[14] _op. cit._ (II.), S. 284.

2. The second group of experiments introduced the factor of a
difference between the stimulation marking the end of an interval and
that marking the beginning, in the form of a change in locality
stimulated, from one finger to the other, either on the same hand or
on the other hand. Two classes of series were given, in one of which
the change was introduced in the standard interval, and in the other
class in the compared interval.

In the first of these experiments, which are typical of the whole
group, both of the subject's hands were employed, and a tapping
instrument was arranged above the middle finger of each, as above the
one hand in the preceding experiment, the distance between middle
fingers being fifteen inches. The taps were given either two on the
right hand and the third on the left, or one on the right and the
second and third on the left, the two orders being designated as _RRL_
and _RLL_ respectively. The subject was always informed of the order
in which the stimulations were to be given, so that any element of
surprise which might arise from it was eliminated. Occasionally,
however, through a lapse of memory, the subject expected the wrong
order, in which case the disturbance caused by surprise was usually so
great as to prevent any estimation.

The two types of series were taken under as similar conditions as
possible, four (or in some cases five) tests being taken from each
series alternately. Other conditions were the same as in the preceding
work. The results for the six subjects employed are given in Table IV.

TABLE IV.

_ST_= 5.0 SECS. TWO HANDS. 15 INCHES.

Subject. Average RT. No. of Series.
RRL. RLL.* (Table II.)
_Hs._ 4.92 6.55 (5.26) 50
_Sh._ 5.29 5.28 (5.34) 50
_Mr._ 5.02 6.23 (5.25) 60
_Mn._ 5.71 6.71 (6.19) 24
_A._ 5.34 5.89 (5.75) 28
_Sn._ 5.62 6.43 (5.47) 60

*Transcriber's Note: Original "RRL"

From Table IV. it is apparent at a glance that the new condition
involved introduces a marked change in the time judgment. Comparison
with Table II. shows that in the cases of all except _Sh_ and _Sn_ the
variation _RRL_ shortens the standard subjectively, and that _RLL_
lengthens it; that is, a local change tends to lengthen the interval
in which it occurs. In the case of _Sh_ neither introduces any change
of consequence, while in the case of _Sn_ both values are higher than
we might expect, although the difference between them is in conformity
with the rest of the results shown in the table.

Another set of experiments was made on subject _Mr_, using taps on the
middle finger of the left hand and a spot on the forearm fifteen
inches from it; giving in one case two taps on the finger and the
third on the arm, and in the other one tap on the finger and the
second and third on the arm; designating the orders as _FFA_ and _FAA_
respectively. Sixty series were taken, and the values found for the
average _ET_ were 4.52 secs, for _FFA_ and 6.24 secs, for _FAA_, _ST_
being 5.0 secs. This shows 0.5 sec. more difference than the
experiment with two hands.

Next, experiments were made on two subjects, with conditions the same
as in the work corresponding to Table IV., except that the distance
between the fingers stimulated was only five inches. The results of
this work are given in Table V.

TABLE V.

_ST_= 5.0 SECS. TWO HANDS. 5 INCHES.

Subject RRL. RLL. No. of Series.
_Sh._ 5.32 5.32 60
_Hs._ 4.40 6.80 60

It will be noticed that _Hs_ shows a slightly wider divergence than
before, while _Sh_ pursues the even tenor of his way as usual.

Series were next obtained by employing the first and second fingers on
one hand in exactly the same way as the middle fingers of the two
hands were previously employed, the orders of stimulation being 1, 1,
2, and 1, 2, 2. The results of sixty series on Subject _Hs_ give the
values of average _ET_ as 4.8 secs. for 1, 1, 2, and 6.23 sees, for 1,
2, 2, _ST_ being 5.0 secs., showing less divergence than in the
preceding work.

These experiments were all made during the first year's work. They
show that in most cases a change in the locality stimulated influences
the estimation of the time interval, but since the details of that
influence do not appear so definitely as might be desired, the ground
was gone over again in a little different way at the beginning of the
present year.

A somewhat more serviceable instrument for time measurements was
employed, consisting of a disc provided with four rows of sockets in
which pegs were inserted at appropriate angular intervals, so that
their contact with fixed levers during the revolution of the disc
closed an electric circuit at predetermined time intervals. The disc
was rotated at a uniform speed by an electric motor.

Experiments were made by stimulation of the following localities: (1)
First and third fingers of right hand; (2) first and second fingers of
right hand; (3) first fingers of both hands, close together, but just
escaping contact; (4) first fingers of both hands, fifteen inches
apart; (5) first fingers of both hands, thirty inches apart; (6) two
positions on middle finger of right hand, on same transverse line.

A standard of two seconds was adopted as being easier for the subject
and more expeditious, and since qualitative and not quantitative
results were desired, only one _CT_ was used in each case, thus
permitting the investigation to cover in a number of weeks ground
which would otherwise have required a much longer period. The subjects
were, however, only informed that the objective variations were very
small, and not that they were in most cases zero. Tests of the two
types complementary to each other (_e.g._, _RRL_ and _RRL_) were in
each case taken alternately in groups of five, as in previous work.

TABLE VI.

_ST_= 2.0 SECS.

_Subject W._

(1) CT=2.0 (3) CT=2.2 (5) CT=2.0
113 133 RRL RLL RRL RLL
S 3 3 9 20 5 21
E 18 19 25 16 18 14
L 24 28 16 14 17 15

_Subject P._

(1) CT=2.0 (3)CT={1.6 (5) CT={1.6
{2.4 {2.4
113 133 RRL(1.6) RLL(2.4) RRL(1.6) RLL(2.4)
S 2 16 12 16 15 10
E 38 32 32 21 26 19
L 10 2 6 15 14 21

_Subject B._

(1) CT=2.0 (2) CT=2.0 (6) CT=2.0
113 133 112 122 aab abb
S 4 21 5 20 7 6
E 23 19 22 24 40 38
L 23 10 23 6 3 6

_Subject Hy._

(1) CT=2.0 (2) CT=2.4 (1a) CT=2.0
113 133 112 122 113 133
S 12 46 17 40 17 31
E 9 2 14 8 9 7
L 29 2 19 2 14 2

In the series designated as (1a) the conditions were the same
as in (1), except that the subject abstracted as much as
possible from the tactual nature of the stimulations and the
position of the fingers. This was undertaken upon the
suggestion of the subject that it would be possible to perform
the abstraction, and was not repeated on any other subject.

The results are given in Table VI., where the numerals in the
headings indicate the localities and changes of stimulation, in
accordance with the preceding scheme, and _'S'_, _'E'_ and _'L'_
designate the number of judgments of _shorter_, _equal_ and _longer_
respectively.

It will be observed that in several cases a _CT_ was introduced in one
class which was different from the _CT_ used in the other classes with
the same subject. This was not entirely arbitrary. It was found with
subject _W_, for example, that the use of _CT_ = 2.0 in (3) produced
judgments of shorter almost entirely in both types. Therefore a _CT_
was found, by trial, which produced a diversity of judgments. The
comparison of the different classes is not so obvious under these
conditions as it otherwise would be, but is still possible.

The comparison gives results which at first appear quite irregular.
These are shown in Table VII. below, where the headings (1)--(3),
etc., indicate the classes compared, and in the lines beneath them
'+' indicates that the interval under consideration is estimated as
relatively greater (more overestimated or less underestimated) in the
second of the two classes than in the first,--indicating the opposite
effect. Results for the first interval are given in the line denoted
'first,' and for the second interval in the line denoted 'second.'
Thus, the plus sign under (1)--(3) in the first line for subject _P_
indicates that the variation _RLL_ caused the first interval to be
overestimated to a greater extent than did the variation 133.

TABLE VII.

SUBJECT _P._ SUBJECT _W._ SUBJECT _B._ SUBJECT _Hy._
(1)--(3) (3)--(4) (1)--(3) (3)--(5) (2)--(1) (6)--(2) (2)--(1)
First. + - + - - + -
Sec. + + - + + + +

The comparisons of (6) and (2), and (1) and (3) confirm the
provisional deduction from Table IV., that the introduction of a
_local change_ in an interval _lengthens_ it subjectively, but the
comparisons of (3) and (5), (3) and (4), and (2) and (1) show
apparently that while the _amount_ of the local change influences the
lengthening of the interval, it does not vary directly with this
latter in all cases, but inversely in the first interval and directly
in the second. This is in itself sufficient to demonstrate that the
chief factors of the influence of locality-change upon the time
interval are connected with the spatial localization of the areas
stimulated, but a further consideration strengthens the conclusion and
disposes of the apparent anomaly. It will be noticed that in general
the decrease in the comparative length of the first interval produced
by increasing the spatial change is less than the increase in the
comparative length of the second interval produced by a corresponding
change. In other words, the disparity between the results for the two
types of test is greater, the greater the spatial distance introduced.

The results seem to point to the existence of two distinct factors in
the so-called 'constant error' in these cases: first, what we may call
the _bare constant error_, or simply the constant error, which appears
when the conditions of stimulation are objectively the same as regards
both intervals, and which we must suppose to be present in all other
cases; and second, the particular lengthening effect which a change in
locality produces upon the interval in which it occurs. These two
factors may work in conjunction or in opposition, according to
conditions. The bare constant error does not remain exactly the same
at all times for any individual and is probably less regular in
tactual time than in auditory or in optical time, according to the
irregularity actually found and for reasons which will be assigned
later.

3. The third group of experiments introduced the factor of variation
in intensity of stimulation. By the introduction of a loop in the
circuit, containing a rheostat, two strengths of current and
consequently of stimulus intensity were obtained, either of which
could be employed as desired. One intensity, designated as _W_, was
just strong enough to be perceived distinctly. The other intensity,
designated as _S_, was somewhat stronger than the intensity used in
the preceding work.

In the first instance, sixty series were taken from Subject _B_, with
the conditions the same as in the experiments of Group 1, except that
two types of series were taken; the first two stimulations being
strong and the third one weak in the first type (_SSW_), and the order
being reversed in the second type (_WSS_). The results gave values of
_ET_ of 5.27 secs. for _SSW_ and 5.9 secs. for _WSS_.

In order to get comprehensive qualitative results as rapidly as
possible, a three-second standard was adopted in the succeeding work
and only one compared interval, also three seconds, was given,
although the subject was ignorant of that fact--the method being thus
similar to that adopted later for the final experiments of Group 2,
described above. Six types of tests were given, the order of
stimulation in the different types being _SSS, WWW, SSW, WWS, SWW_ and
_WSS_, the subject always knowing which order to expect. For each of
the six types one hundred tests were made on one subject and one
hundred and five on another, in sets of five tests of each type, the
sets being taken in varied order, so that possible contrast effect
should be avoided. The results were practically the same, however, in
whatever order the sets were taken, no contrast effect being
discernible.

The total number of judgments of _CT_, longer, equal, and shorter, is
given in Table VIII. The experiments on each subject consumed a number
of experiment hours, scattered through several weeks, but the relative
proportions of judgments on different days was in both cases similar
to the total proportions.

TABLE VIII.

_ST=CT=_ 3.0 SECS.

Subject _R_, 100. Subject _P_, 105.
L E S d L E S d
SSS 32 56 12 + 20 SSS 16 67 22 - 9
WWW 11 53 36 - 25 WWW 19 72 14 + 5
SSW 6 27 67 - 61 SSW 17 56 32 - 15
WWS 57 36 7 + 50 WWS 37 61 7 + 30
WSS 10 45 45 - 35 WSS 9 69 27 - 18
SWW 3 31 66 - 63 SWW 3 64 33 - 25

By the above table the absolute intensity of the stimulus is clearly
shown to be an important factor in determining the constant error of
judgment, since in both cases the change from _SSS_ to _WWW_ changed
the sign of the constant error, although in opposite directions. But
the effect of the relative intensity is more obscure. To discover more
readily whether the introduction of a stronger or weaker stimulation
promises a definite effect upon the estimation of the interval which
precedes or follows it, the results are so arranged in Table IX. that
reading downward in any pair shows the effect of a decrease in the
intensity of (1) the first, (2) the second, (3) the third, and (4) all
three stimulations.

TABLE IX.

Subject _R._ Subject _P._

(1) _SSS_ + 20 - 6
_WSS_ - 35 - 55 - 18 - 12

_SWW_ - 63 - 25
_WWW_ - 25 - 38 + 5 + 30

(2) _SSW_ - 61 - 15
_SWW_ - 63 - 2 - 25 + 10

_WSS_ - 35 - 18
_WWS_ + 50 + 85 + 30 - 48

(3) _SSS_ + 20 - 6
_SSW_ - 61 - 81 - 15 - 7

_WWS_ + 50 + 30
_WWW_ - 25 - 75 + 5 - 25

(4) _SSS_ + 20 - 6
_WWW_ - 15 - 35 + 5 + 11

There seems at first sight to be no uniformity about these results.
Decreasing the first stimulation in the first case increases, in the
second case diminishes, the comparative length of the first interval.
We get a similar result in the decreasing of the second stimulation.
In the case of the third stimulation only does the decrease produce a
uniform result. If, however, we neglect the first pair of (3), we
observe that in the other cases the effect of a _difference_ between
the two stimulations is to lengthen the interval which they limit. The
fact that both subjects make the same exception is, however, striking
and suggestive of doubt. These results were obtained in the first
year's work, and to test their validity the experiment was repeated at
the beginning of the present year on three subjects, fifty series
being taken from each, with the results given in Table X.

TABLE X.

_ST_ = 3.0 secs. = _CT_.

Subject _Mm._ Subject _A._ Subject _D._

S E L d S E L d S E L d
SSS 24 13 13 - 11 7 30 13 + 6 10 31 9 - 1
WSS 33 9 8 - 25 20 24 6 - 14 17 27 6 - 11
SSW 19 15 16 - 3 23 16 11 - 12 10 31 9* - 1
WWW 19 12 19 0 13 26 11 - 2 1 40 9 + 8
SWW 18 30 2 - 16 23 21 6* - 17 7 38 5 - 2
WWS 13 16 21 + 8 12 30 8 - 4 15 25 10 - 5

*Transcriber's Note: Original "16" changed to "6", "19" to "9".

Analysis of this table shows that in every case a difference between
the intensities of the first and second taps lengthens the first
interval in comparative estimation. In the case of subject _Mm_ a
difference in the intensities of the second and third taps lengthens
the second interval subjectively. But in the cases of the other two
subjects the difference shortens the interval in varying degrees.

The intensity difference established for the purposes of these
experiments was not great, being less than that established for the
work on the first two subjects, and therefore the fact that these
results are less decided than those of the first work was not
unexpected. The results are, however, very clear, and show that the
lengthening effect of a difference in intensity of the stimulations
limiting an interval has its general application only to the first
interval, being sometimes reversed in the second. From the combined
results we find, further, that a uniform change in the intensity of
three stimulations is capable of reversing the direction of the
constant error, an intensity change in a given direction changing the
error from positive to negative for some subjects, and from negative
to positive for others.

III. INTERPRETATION OF RESULTS.

We may say provisionally that the _change_ from a tactual stimulation
of one kind to a tactual stimulation of another kind tends to lengthen
subjectively the interval which the two limit. If we apply the same
generalization to the other sensorial realms, we discover that it
agrees with the general results obtained by Meumann[15] in
investigating the effects of intensity changes upon auditory time, and
also with the results obtained by Schumann[16] in investigations with
stimulations addressed alternately to one ear and to the other.
Meumann reports also that the change from stimulation of one sense to
stimulation of another subjectively lengthens the corresponding
interval.

[15] _op. cit._ (II.), S. 289-297.

[16] _op. cit._, S. 67.

What, then, are the factors, introduced by the change, which produce
this lengthening effect? The results of introspection on the part of
some of the subjects of our experiments furnish the clue which may
enable us to construct a working hypothesis.

Many of the subjects visualize a time line in the form of a curve. In
each case of this kind the introduction of a change, either in
intensity or location, if large enough to produce an effect on the
time estimation, produced a distortion on the part of the curve
corresponding to the interval affected. All of the subjects employed
in the experiments of Group 2 were distinctly conscious of the change
in attention from one point to another, as the two were stimulated
successively, and three of them, _Hy_, _Hs_ and _P_, thought of
something passing from one point to the other, the representation
being described as partly muscular and partly visual. Subjects _Mr_
and _B_ visualized the two hands, and consciously transferred the
attention from one part of the visual image to the other. Subject _Mr_
had a constant tendency to make eye movements in the direction of the
change. Subject _P_ detected these eye movements a few times, but
subject _B_ was never conscious of anything of the kind.