Sixteen Experimental Investigations from the Harvard Psychological Laboratory, Hugo Münsterberg [top fiction books of all time TXT] 📗

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.

 

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