Various - Harvard Psychological Studies, Volume 1

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The inclined position of the screen was of course observed by every
reactor, but of the changes in the enclosing walls no subject was
informed, and none discerned them on any occasion. Each observer was
questioned as to alterations in the experimental conditions after the
use of each arrangement, and at the close of the whole series inquiry
was made of each as to the planes of the upper boundaries of the
walls. On various occasions, but not customarily, the observer was
aware of a change of some kind in the whole set of conditions, but the
particular feature altered was not suspected. The results for all
three arrangements are given in the following table; of the sections
of this table the third is incomplete, full results having been
reached in the cases of only three observers:

TABLE XV.

Ascending Planes. Descending Planes.
Observer Const. Err. Av. Dev. M. Var. Const. Err. Av. Dev. M. V.
_C_ (50) - 8.02 11.82 9.47 - 48.14 48.14 9.52
_F_ (50) + 78.88 78.88 2.89 + 25.54 25.54 1.98
_G_ (50) - 22.56 24.64 6.58 -101.20 101.20 7.39
_H_ (50) - 83.84 83.84 11.78 -230.20 230.20 11.88
_J_ (50) +315.64 315.64 18.16 +120.12 120.12 9.01
Average: + 55.96 102.96 9.78 -44.98 104.84 7.96

Horizontal Planes.
Observer. Const. Err. Av. Dev. Mean Var.
_C_ (50) - 27.86 27.86 9.58
_G_ (50) - 73.84 73.84 7.59
_J_ (50) +243.72 243.72 18.52

For every individual observer, the position of the disc on the screen
has been affected by each change in the direction of these visible
lines. In every case, also, its location when these boundaries lay in
a horizontal plane was intermediate between the other two. The
importance of such relations in the objects of the visual field as
factors in our ordinary determination of the subjective horizon is
made evident by these experimental results. They become construction
lines having assumed permanence in the world of visual-motor
experience. The conception of unchanging spatial relations in the
fundamental lines of perspective vision receives constant
reinforcement from the facts of daily experience. The influence of the
above-described changes in experimental conditions is mediated through
their effect upon the location of the focus of the limiting and
perspective lines of vision. As the plane of the upper boundaries of
the enclosing walls was elevated and depressed the intersection of the
two systems of lines was correspondingly raised and lowered, and in
dependence upon the location of this imaginary point the determination
of the position of the white disc was made, and the plane of
perspective positively or negatively rotated.

Why such perspective lines should enter into the process of judgment
it is not difficult to infer. The plane of perspective for human
beings is characteristically horizontal, in consequence of the
distribution of important objects within the field of visual
perception. Roughly, the belt of the earth's horizon contains the loci
of all human perspective planes. Both natural and artificial
arrangements of lines converge there. The systems of visual objects on
the earth and in the sky are there broken sharply off in virtue of
their practically vast differences in quality and significance for the
observer. The latter perspective probably never extends downward
illusorily to points on the earth's surface; and the former system of
objects is carried continuously upward to skyey points only on
relatively rare occasions, as when one mistakes clouds for mountains
or the upper edge of a fog-belt on the horizon for the rim of sea and
sky. The point of convergence of the fundamental lines of perspective
thus becomes assimilated with the idea of the visual horizon, as that
concept has fused with the notion of a subjective horizon. There can
be little doubt that the disposition of such lines enters constantly
into our bodily orientation in space along with sensations arising
from the general body position and from those organs more specially
concerned with the static sense.

Upon the misinterpretation of such objective planes depends the
illusion of underestimation of the height or incline of a hill one is
breasting, and of the converse overestimation of one seen across a
descending slope or intervening valley. The latter illusion is
especially striking, and in driving over forest roads (in which case
the correction of a wider range of view is excluded) the stretch of
level ground at the foot of a hill one is descending is constantly
mistaken for an opposing rise. This illusion is put into picturesque
words by Stevenson when he describes the world, seen from the summit
of a mountain upon which one stands, as rising about him on every side
as toward the rim of a great cup. The fitness of the image may be
proved by climbing the nearest hill. In all such cases a
reconstruction of the sensory data of judgment takes place, in which
the most significant factor is the plane determined by the positions
of the observing eye and the perspective focus. In these judgments of
spatial relationship, as they follow one another from moment to
moment, this plane becomes a temporary subjective horizon, and
according as it is positively or negatively rotated do corresponding
illusions of perception appear.

* * * * *

THE ILLUSION OF RESOLUTION-STRIPES ON THE COLOR-WHEEL.

BY EDWIN B. HOLT.

If a small rod is passed slowly before a rotating disc composed of two
differently colored sectors, the rod appears to leave behind it on the
disc a number of parallel bands of about the width of the rod and of
about the colors, alternately arranged, of the two sectors. These
appear not to move, but gradually to fade away.

This phenomenon was first observed by Muensterberg, and by him shown to
Jastrow,[1] who, with Moorehouse, has printed a study, without,
however, offering an adequate explanation of it.

[1] Jastrow, J., and Moorehouse, G.W.: 'A Novel Optical
Illusion,' _Amer. Jour. of Psychology_, 1891, IV., p. 201.

I. APPARATUS FOR PRODUCING THE ILLUSION.

Any form of color-wheel may be used, but preferably one which is
driven by electricity or clock-work, so that a fairly constant speed
is assured. Several pairs of paper discs are needed, of the ordinary
interpenetrating kind which permit a ready readjustment of the ratios
between the two sectors, as follows: one pair consisting of a white
and a black disc, one of a light-and a dark-colored disc (light green
and dark red have been found admirably suited to the purpose), and a
pair of discs distinctly different in color, but equal in luminosity.

The rod should be black and not more than a quarter of an inch broad.
It may be passed before the rotating disc by hand. For the sake of
more careful study, however, the rod should be moved at a constant
rate by some mechanical device, such as the pendulum and works of a
Maelzel metronome removed from their case. The pendulum is fixed just
in front of the color-disc. A further commendable simplification of
the conditions consists in arranging the pendulum and disc to move
concentrically, and attaching to the pendulum an isosceles-triangular
shield, so cut that it forms a true radial sector of the disc behind
it. All the colored bands of the illusion then appear as radial
sectors. The radial shields should be made in several sizes (from 3 to
50 degrees of arc) in black, but the smallest size should also be
prepared in colors matching the several discs. Such a disposition,
then, presents a disc of fused color, rotating at a uniform rate, and
in front of this a radial sector oscillating from side to side
concentrically with the disc, and likewise at a uniform rate. Several
variations of this apparatus will be described as the need and purpose
of them become clear.

II. PREVIOUS DISCUSSION OF THE ILLUSION.

Although Jastrow and Moorehouse (_op. cit._) have published a somewhat
detailed study of these illusion-bands, and cleared up certain points,
they have not explained them. Indeed, no explanation of the bands has
as yet been given. The authors mentioned (_ibid._, p. 204) write of
producing the illusion by another method. "This consists in sliding
two half discs of the same color over one another leaving an open
sector of any desired size up to 180 degrees and rotating this against
a background of a markedly different color, in other words we
substitute for the disc composed of a large amount of one color, which
for brevity we may call the 'majority color,' and a small amount of
another, the 'minority color,' one in which the second color is in the
background and is viewed through an opening in the first. With such an
arrangement we find that we get the series of bands both when the wire
is passed in front of the disc and when passed in back between disc
and background; and further experimentation shows that the time
relations of the two are the same. (There is, of course, no essential
difference between the two methods when the wire is passed in front of
the disc.)" That is true, but it is to be borne in mind that there is
a difference when the wire is passed behind the disc, as these authors
themselves state (_loc. cit._, note):--"The time-relations in the two
cases are the same, but the _color-phenomena_ considerably
_different_." However, "these facts enable us to formulate our first
generalization, viz., that for all purposes here relevant [_i.e._, to
a study of the _time-relations_] the seeing of a wire now against one
background and then immediately against another is the same as its now
appearing and then disappearing; a rapid succession of changed
appearances is equivalent to a rapid alternation of appearance and
disappearance. Why this is so we are unable to say," etc. These
authors now take the first step toward explaining the illusion. In
their words (_op. cit._, p. 205), "the suggestion is natural that we
are dealing with the phenomena of after-images.... If this is the true
explanation of the fact that several rods are seen, then we should,
with different rotation rates of disc and rod, see as many rods as
multiplied by the time of one rotation of the disc would yield a
constant, _i.e._, the time of an after image of the kind under
consideration." For two subjects, J.J. and G.M., the following
tabulation was made.

J.J. G.M.
Av. time of rot. of disc when 2 images of rod were seen .0812 sec. .0750 sec.
" " " " 3 " " " " .0571 " .0505 "
" " " " 4 " " " " .0450 " .0357 "
" " " " 5 " " " " .0350 " .0293 "
" " " " 6 " " " " .0302 " .0262 "

"Multiplying the number of rods by the rotation rate we get for J.J.
an average time of after image of .1740 sec. (a little over 1/6 sec.)
with an average deviation of .0057 (3.2%); for G.M. .1492 (a little
over 1/7 sec.) with an average deviation of .0036 (2.6%). An
independent test of the time of after-image of J.J. and G.M. by
observing when a black dot on a rotating white disc just failed to
form a ring resulted in showing in every instance a longer time for
the former than for the latter." That this constant product of the
number of 'rods' seen by the time of one rotation of the disc equals
the duration of after-image of the rod is established, then, only by
inference. More indubitable, since directly measured on two subjects,
is the statement that that person will see more 'rods' whose
after-image persists longer. This result the present writer fully
confirms. What relation the 'constant product' bears to the duration
of after-image will be spoken of later. But aside from all
measurement, a little consideration of the conditions obtaining when
the rod is passed _behind_ the disc will convince any observer that
the bands are indeed after-images somehow dependent on the rod. We may
account it established that _the bands are after-images_.

From this beginning one might have expected to find in the paper of
Jastrow and Moorehouse a complete explanation of the illusion. On
other points, however, these authors are less explicit. The changes in
width of the bands corresponding to different sizes of the sectors and
different rates of movement for the rod and disc, are not explained,
nor yet, what is more important, the color-phenomena. In particular
the fact needs to be explained, that the moving rod analyzes the
apparently homogeneous color of the disc; or, as Jastrow and
Moorehouse state it (_op. cit._, p. 202): "If two rotating discs were
presented to us, the one pure white in color, and the other of ideally
perfect spectral colors in proper proportion, so as to give a
precisely similar white, we could not distinguish between the two; but
by simply passing a rod in front of them and observing in the one case
but not in the other the parallel rows of colored bands, we could at
once pronounce the former to be composite, and the latter simple. In
the indefinitely brief moment during which the rod interrupts the
vision of the disc, the eye obtains an impression sufficient to
analyze to some extent into its elements this rapid mixture of
stimuli." The very question is as to _how_ the eye obtains the
'impression sufficient to analyze' the mixture.

It may be shown at this point that the mistake of these authors lies
in their recognition of but one set of bands, namely (_ibid._, p.
201), 'bands of a color similar to that present in greater proportion'
on the disc. But, on the other hand, it is to be emphasized that those
bands are separated from one another, not by the fused color of the
disc, as one should infer from the article, but by _other bands_,
which are, for their part, of a color similar to that present in
_lesser_ proportion. Thus, bands of the two colors alternate; and
either color of band is with equal ease to be distinguished from the
fused color of the main portion of the disc.

Why our authors make this mistake is also clear. They first studied
the illusion with the smaller sector of the disc open, and the rod
moving behind it; and since in this case the bands are separated by
strips not of the minority but of the fused color, and are of about
the width of the rod itself, these authors came to recognize bands of
but one sort, and to call these 'images of the rod.' But now, with the
rod moving in front of the disc, there appear bands of two colors
alternately disposed, and neither of these colors is the fused color
of the disc. Rather are these two colors approximately the majority
and minority colors of the disc as seen at rest. Thus, the recognition
of but one set of bands and the conclusion (_ibid._, p. 208) that 'the
bands originate during the vision of the minority color,' are wholly
erroneous. The bands originate as well during the vision of the
majority color, and, as will later be shown, the process is
continuous.

Again, it is incorrect, even in the case of those bands seen behind
the open sector, to call the bands 'images of the rod,' for images of
the rod would be of the color of the rod, whereas, as our authors
themselves say (_ibid._, p. 201), the bands 'are of a color similar to
that present in greater proportion' on the disc. Moreover the 'images
of the rod' are of the most diverse widths. In fact, we shall find
that the width of the rod is but one of several factors which
determine the width of its 'images,' the bands.

Prejudiced by the same error is the following statement (_ibid._, p.
208): "With the majority color darker than the minority color the
bands are darker than the resulting mixture, and lighter when the
majority color is the lighter." If this is to be true, one must read
for 'the bands,' 'the narrower bands.'

Another observation found in this article must be criticised. It is
asserted that difference of shade between the two sectors of the disc,
as well as difference of color, is essential to the illusion. To
support this, four cases are given: two in which the sectors were so
similar in luminosity as to bring out the illusion but faintly; two in
which like luminosities yielded no illusion at all. The present writer
agrees that if the two sectors are closely similar in luminosity, the
illusion is fainter. He also selected a red and a green so near each
other in brightness that when a rod 4 mm. broad (which is the largest
rod that Jastrow and Moorehouse mention having used) was passed by
hand before the disc, no trace of a band could be seen. The pendulum,
however, bearing a shield considerably wider than 4 mm. (say of 15
degrees) and moving before the very same red and green shades, mixed
in the same proportions, yielded the illusion with the utmost
clearness. Colors of like luminosities yield the illusion less
strikingly, nevertheless they yield it.

Again (_op. cit._, p. 205), these authors say: "It has been already
observed that the distance between the bands diminishes as the
rotation rate and the rate of movement of the rod increases." But what
had been said before is (_ibid._, p. 203) that 'the bands are
separated by smaller and smaller spaces as the rate of movement of the
rod becomes slower and slower'; and this is equivalent to saying that
the distance between the bands diminishes as the rate of movement of
the rod decreases. The statements are contradictory. But there is no
doubt as to which is the wrong one--it is the first. What these
authors have called 'distance between the bands' has here been shown
to be itself a band. Now, no point about this illusion can be more
readily observed than that the widths of both kinds of band vary
directly with the speed of the rod, inversely, however (as Jastrow and
Moorehouse have noted), with the speed of the disc.

Perhaps least satisfactory of all is their statement (_ibid._, p. 206)
that "A brief acquaintance with the illusion sufficed to convince us
that its appearance was due to contrast of some form, though the
precise nature of this contrast is the most difficult point of all."
The present discussion undertakes to explain with considerable
minuteness every factor of the illusion, yet the writer does not see
how in any essential sense contrast could be said to be involved.

With the other observations of these authors, as that the general
effect of an increase in the width of the interrupting rod was to
render the illusion less distinct and the bands wider, etc., the
observations of the present writer fully coincide. These will
systematically be given later, and we may now drop the discussion of
this paper.

The only other mention to be found of these resolution-bands is one by
Sanford,[2] who says, apparently merely reiterating the results of
Jastrow and Moorehouse, that the illusion is probably produced by the
sudden appearance, by contrast, of the rod as the lighter sector
passes behind it, and by its relative disappearance as the dark sector
comes behind. He thus compares the appearance of several rods to the
appearance of several dots in intermittent illumination of the strobic
wheel. If this were the correct explanation, the bands could not be
seen when both sectors were equal in luminosity; for if both were
dark, the rod could never appear, and if both were light, it could
never disappear. The bands can, however, be seen, as was stated above,
when both the sectors are light or both are dark. Furthermore, this
explanation would make the bands to be of the same color as the rod.
But they are of other colors. Therefore Sanford's explanation cannot
be admitted.

[2] Sanford, E.C.: 'A Course in Experimental Psychology,'
Boston, 1898, Part I., p. 167.

And finally, the suggestions toward explanation, whether of Sanford,
or of Jastrow and Moorehouse, are once for all disproved by the
observation that if the moving rod is fairly broad (say three quarters
of an inch) and moves _slowly_, the bands are seen nowhere so well as
_on the rod itself_. One sees the rod vaguely through the bands, as
could scarcely happen if the bands were images of the rod, or
contrast-effects of the rod against the sectors.

The case when the rod is broad and moves slowly is to be accounted a
special case. The following observations, up to No. 8, were made with
a narrow rod about five degrees in width (narrower will do), moved by
a metronome at less than sixty beats per minute.

III. OUTLINE OF THE FACTS OBSERVED.

A careful study of the illusion yields the following points:

1. If the two sectors of the disc are unequal in arc, the bands are
unequal in width, and the narrower bands correspond in color to the
larger sector. Equal sectors give equally broad bands.

2. The faster the rod moves, the broader become the bands, but not in
like proportions; broad bands widen relatively more than narrow ones;
equal bands widen equally. As the bands widen out it necessarily
follows that the alternate bands come to be farther apart.

3. The width of the bands increases if the speed of the revolving disc
decreases, but varies directly, as was before noted, with the speed of
the pendulating rod.

4. Adjacent bands are not sharply separated from each other, the
transition from one color to the other being gradual. The sharpest
definition is obtained when the rod is very narrow. It is appropriate
to name the regions where one band shades over into the next
'transition-bands.' These transition-bands, then, partake of the
colors of both the sectors on the disc. It is extremely difficult to
distinguish in observation between vagueness of the illusion due to
feebleness in the after-image depending on faint illumination,
dark-colored discs or lack of the desirable difference in luminosity
between the sectors (cf. p. 171) and the indefiniteness which is due
to broad transition-bands existing between the (relatively) pure-color
bands. Thus much, however, seems certain (Jastrow and Moorehouse have
reported the same, _op. cit._, p. 203): the wider the rod, the wider
the transition-bands. It is to be noticed, moreover, that, for rather
swift movements of the rod, the bands are more sharply defined if this
movement is contrary to that of the disc than if it is in like
direction with that of the disc. That is, the transition-bands are
broader when rod and disc move in the same, than when in opposite
directions.

5. The total number of bands seen (the two colors being alternately
arranged and with transition-bands between) at any one time is
approximately constant, howsoever the widths of the sectors and the
width and rate of the rod may vary. But the number of bands is
inversely proportional, as Jastrow and Moorehouse have shown (see
above, p. 169), to the time of rotation of the disc; that is, the
faster the disc, the more bands. Wherefore, if the bands are broad
(No. 2), they extend over a large part of the disc; but if narrow,
they cover only a small strip lying immediately behind the rod.

6. The colors of the bands approximate those of the two sectors; the
transition-bands present the adjacent 'pure colors' merging into each
other. But _all_ the bands are modified in favor of the color of the
moving rod. If, now, the rod is itself the same in color as one of the
sectors, the bands which should have been of the _other_ color are not
to be distinguished from the fused color of the disc when no rod moves
before it.

7. The bands are more strikingly visible when the two sectors differ
considerably in luminosity. But Jastrow's observation, that a
difference in luminosity is _necessary_, could not be confirmed.
Rather, on the contrary, sectors of the closest obtainable luminosity
still yielded the illusion, although faintly.

8. A _broad_ but slowly moving rod shows the bands overlying itself.
Other bands can be seen left behind it on the disc.

9. But a case of a rod which is broad, or slowly-moving, or both, is a
special complication which involves several other and _seemingly_
quite contradictory phenomena to those already noted. Since these
suffice to show the principles by which the illusion is to be
explained, enumeration of the special variations is deferred.

IV. THE GEOMETRICAL RELATIONS BETWEEN THE ROD AND THE SECTORS OF THE
DISC.

It should seem that any attempt to explain the illusion-bands ought to
begin with a consideration of the purely geometrical relations holding
between the slowly-moving rod and the swiftly-revolving disc. First of
all, then, it is evident that the rod lies in front of each sector
successively.

Let Fig. 1 represent the upper portion of a color-wheel, with center
at _O_, and with equal sectors _A_ and _B_, in front of which a rod
_P_ oscillates to right and left on the same axis as that of the
wheel. Let the disc rotate clockwise, and let _P_ be observed in its
rightward oscillation. Since the disc moves faster than the rod, the
front of the sector _A_ will at some point come up to and pass behind
the rod _P_, say at _p^{A}. P_ now hides a part of _A_ and both are
moving in the same direction. Since the disc still moves the faster,
the front of _A_ will presently emerge from behind _P_, then more and
more of _A_ will emerge, until finally no part of it is hidden by _P_.
If, now, _P_ were merely a line (having no width) and were not
moving, the last of _A_ would emerge just where its front edge had
gone behind _P_, namely at _p^{A}_. But _P_ has a certain width and a
certain rate of motion, so that _A_ will wholly emerge from behind _P_
at some point to the right, say _p^{B}_. How far to the right this
will be depends on the speed and width of _A_, and on the speed and
width of _P_.