Sixteen Experimental Investigations from the Harvard Psychological Laboratory - Hugo Münsterberg (best life changing books txt) 📗
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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.
Now, similarly, at p^{B} the sector B has come around and begins
to pass behind P. It in turn will emerge at some point to the right,
say p^{C}. And so the process will continue. From p^{A} to p^{B}
the pendulum covers some part of the sector A; from p^{B} to
p^{C} some part of sector B; from p^{C} to P^{D} some part of
A again, and so on.
[Illustration: Fig. 1.]
If, now, the eye which watches this process is kept from moving, these
relations will be reproduced on the retina. For the retinal area
corresponding to the triangle p^{A}Op^{B}, there will be less
stimulation from the sector A than there would have been if the
pendulum had not partly hidden it. That is, the triangle in question
will not be seen of the fused color of A and B, but will lose a
part of its A-component. In the same way the triangle p^{B}OpC
will lose a part of its B-component; and so on alternately. And by
as much as either component is lost, by so much will the color of the
intercepting pendulum (in this case, black) be present to make up the
deficiency.
We see, then, that the purely geometrical relations of disc and
pendulum necessarily involve for vision a certain banded appearance of
the area which is swept by the pendulum, if the eye is held at rest.
We have now to ask, Are these the bands which we set out to study?
Clearly enough these geometrically inevitable bands can be exactly
calculated, and their necessary changes formulated for any given
change in the speed or width of A, B, or P. If it can be shown
that they must always vary just as the bands we set out to study are
observed to vary, it will be certain that the bands of the illusion
have no other cause than the interception of retinal stimulation by
the sectors of the disc, due to the purely geometrical relations
between the sectors and the pendulum which hides them.
And exactly this will be found to be the case. The widths of the bands
of the illusion depend on the speed and widths of the sectors and of
the pendulum used; the colors and intensities of the bands depend on
the colors and intensities of the sectors (and of the pendulum); while
the total number of bands seen at one time depends on all these
factors.
V. GEOMETRICAL DEDUCTION OF THE BANDS.
In the first place, it is to be noted that if the pendulum proceeds
from left to right, for instance, before the disc, that portion of the
latter which lies in front of the advancing rod will as yet not have
been hidden by it, and will therefore be seen of the unmodified, fused
color. Only behind the pendulum, where rotating sectors have been
hidden, can the bands appear. And this accords with the first
observation (p. 167), that “The rod appears to leave behind it on the
disc a number of parallel bands.” It is as if the rod, as it passes,
painted them on the disc.
Clearly the bands are not formed simultaneously, but one after another
as the pendulum passes through successive positions. And of course the
newest bands are those which lie immediately behind the pendulum. It
must now be asked, Why, if these bands are produced successively, are
they seen simultaneously? To this, Jastrow and Moorehouse have given
the
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