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

the bands 1-2, 2-3, etc., are less intense

than the bands x-9, 9-10, etc., because there the recent or weighted

unit-effects are black, while here they are the respective colors.

Also the bands grow dimmer from x-9 to 15-16, that is, as they

become older, for the small increment of one color which would give

band 15-16 is almost wholly overridden by the larger and fresher mass

of stimulation which makes for mere fusion. This last is true of the

bands always, whatever the rate or width of the rod.

 

10. In general, equal sectors give equal bands, but if one sector is

considerably more intense than the other, the bands of the brighter

color will, for a broad and swiftly-moving rod, be the broader. The

brighter sector, though equal in width to the other, contributes more

toward determining the fusion-color; and this fact is represented by

an intrusion of the stronger color into the transition-bands, at the

expense of the weaker. For in these, even the decreased amount of the

stronger color, on the side next a strong-color band, is yet more

potent than the increased amount of the feebler color. In order to

observe this fact one must have the rod broad, so as to give a broad

transition-band on which the encroachment of the stronger color may be

evident. The process is the same with a narrow rod and narrow

transition-bands, but, being more limited in extent, it is less easily

observed. The rod must also move rapidly, for otherwise the bands

overlap and become obscure, as will be seen in the next paragraph.

 

11. If the disc consists of a broad and narrow sector, and if the rod

is broad and moves at first rapidly but more slowly with each new

stroke, there are seen at first broad, faint bands of the

minority-color, and narrow bands of the majority-color. The former

grow continuously more intense as the rod moves more slowly, and grow

narrower in width down to zero; whereupon the other bands seem to

overlap, the overlapped part being doubly deep in color, while the

non-overlapped part has come to be more nearly the color of the minor

sector. The overlapped portion grows in width. As the rate of the rod

now further decreases, a confused state ensues which cannot be

described. When, finally, the rod is moving very slowly, the phenomena

described above in paragraph 9 occur.

 

The successive changes in appearance as the rod moves more and more

slowly, are due to the factors previously mentioned, and to one other

which follows necessarily from the given conditions but has not yet

been considered. This is the last new principle in the illusion which

we shall have to take up. Just as the transition-bands are regions

where two pure-color bands overlap, so, when the rod is broad and

moves slowly, other overlappings occur to produce more complicated

arrangements.

 

These can be more compactly shown by diagram than by words. Fig. 10,

a, b and c (Plate VI.), show successively slower speeds of the

rod, while all the other factors are the same. In practice the

tendency is to perceive the transition-bands as parts of the broad

faint band of the minor color, which lies between them. It can be

seen, then, how the narrow major-color bands grow only slightly wider

(Fig. 10, a, b) until they overlap (c); how the broad

minor-color bands grow very narrow and more intense in color, there

being always more of the major color deducted (in b they are reduced

exactly to zero, z, z, z). In c the major-color bands overlap

(o, o, o) to give a narrow but doubly intense major-color band

since, although with one major, two minor locus-bands are deducted.

The other bands also overlap to give complicated combinations between

the o-bands. These mixed bands will be, in part at least,

minor-color bands (q, q, q), since, although a minor locus-band

is here deducted, yet nearly two major locus-bands are also taken,

leaving the minor color to predominate. This corresponds with the

observation above, that, ‘… the non-overlapped part has come to be

more nearly the color of the minor sector.’

 

A slightly slower speed of the rod would give an irreducible confusion

of bands, since the order in which they overlap becomes very

complicated. Finally, when the rod comes to move very slowly, as in

Fig. 9, the appearance suffers no further change, except for a gradual

narrowing of all the bands, up to the moment when the rod comes to

rest.

 

It is clear that this last principle adduced, of the multiple

overlapping of bands when the rod is broad and moves slowly, can give

for varying speeds of the rod the greatest variety of combinations of

the bands. Among these is to be included that of no bands at all, as

will be understood from Fig. 11 (Plate VII). And in fact, a little

practice will enable the observer so to adjust the rate of the (broad)

rod to that of the disc that no bands are observable. But care must be

taken here that the eye is rigidly fixated and not attracted into

movement by the rod, since of course if the eye moves with the rod, no

bands can be seen, whatever the rate of movement may be.

 

Thus, all the phenomena of these illusion-bands have been explained as

the result solely of the hiding by the rod of successive sectors of

the disc. The only physiological principles involved are those (1) of

the duration of after-images, and (2) of their summation into a

characteristic effect. It may have seemed to the reader tedious and

unnecessary so minutely to study the bands, especially the details

last mentioned; yet it was necessary to show how all the possible

observable phenomena arise from the purely geometrical fact that

sectors are successively hidden. Otherwise the assertions of previous

students of the illusion, that more intricate physiological processes

are involved, could not have been refuted. The present writer does not

assert that no processes like contrast, induction, etc., come into

play to modify somewhat the saturation, etc., of the colors in the

bands. It must be here as in every other case of vision. But it is now

demonstrated that these remoter physiological processes contribute

nothing essential to the illusion. For these could be dispensed with

and the illusion would still remain.

 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VI.

Fig. 10.]

 

If any reader still suspects that more is involved than the

persistence of after-images, and their summation into a characteristic

effect, he will find it interesting to study the illusion with a

camera. The ‘physiological’ functions referred to belong as well to

the dry-plate as to the retina, while the former exhibits, presumably,

neither contrast nor induction. The illusion-bands can be easily

photographed in a strong light, if white and black sectors are used in

place of colored ones. It is best to arrange the other variable

factors so as to make the transition-bands as narrow as possible (p.

174, No. 4). The writer has two negatives which show the bands very

well, although so delicately that it is not feasible to try to

reproduce them.

 

VIII. SOME CONVENIENT DEVICES FOR EXHIBITING THE ILLUSION.

 

The influence of the width of sector is prettily shown by a special

disc like that shown in Fig. 12 (Plate VII.), where the colors are

dark-red and light-green, the shaded being the darker sector. A narrow

rod passed before such a disc by hand at a moderate rate will give

over the outer ring equally wide green and red bands; but on the inner

rings the red bands grow narrower, the green broader.

 

The fact that the bands are not ‘images of the rod’ can be shown by

another disc (Fig. 13, Plate VII.). In all three rings the lighter

(green) sector is 60° wide, but disposed on the disc as shown. The

bands are broken into zigzags. The parts over the outer ring lag

behind those over the middle, and these behind those over the inner

ring—‘behind,’ that is, farther behind the rod.

 

Another effective variation is to use rods alike in color with one or

the other of the sectors. Here it is clear that when the rod hides the

oppositely-colored sector, the deduction of that color is replaced

(not by black, as happens if the rod is black) but by the very color

which is already characteristic of that band. But when the rod hides

the sector of its own color, the deduction is replaced by the very

same color. Thus, bands like colored with the rod gain in depth of

tone, while the other pure-color bands present simply the

fusion-color.

 

IX. A STROBOSCOPE WHICH DEPENDS ON THE SAME PRINCIPLE.

 

If one produce the illusion by using for rod, not the pendulum of a

metronome, but a black cardboard sector on a second color-mixer placed

in front of the first and rotating concentrically with it, that is,

with the color-disc, one will observe with the higher speeds of the

rod which are now obtainable several further phenomena, all of which

follow simply from the geometrical relations of disc and rod (now a

rotating sector), as discussed above. The color-mixer in front, which

bears the sector (let it still be called a ‘rod’), should rotate by

hand and independently of the disc behind, whose two sectors are to

give the bands. The sectors of the disc should now be equal, and the

rod needs to be broader than before, say 50° or 60°, since it is to

revolve very rapidly.

 

First, let the rod and disc rotate in the same direction, the disc at

its former rate, while the rod begins slowly and moves faster and

faster. At first there is a confused appearance of vague, radial

shadows shuffling to and fro. This is because the rod is broad and

moves slowly (cf. p. 196, paragraph II).

 

As the velocity of the rod increases, a moment will come when the

confusing shadows will resolve themselves into four (sometimes five)

radial bands of one color with four of the other color and the

appropriate transition-bands between them. The bands of either color

are symmetrically disposed over the disc, that is, they lie at right

angles to one another (if there are five bands they lie at angles of

72°, etc.). But this entire system of bands, instead of lying

motionless over the disc as did the systems hitherto described, itself

rotates rapidly in the opposite direction from disc to rod. As the rod

rotates forward yet faster, no change is seen except that the system

of bands moves backward more and more slowly. Thus, if one rotate the

rod with one’s own hand, one has the feeling that the backward

movement of the bands is an inverse function of the increase in

velocity of the rod. And, indeed, as this velocity still increases,

the bands gradually come to rest, although both the disc and the rod

are rotating rapidly.

 

But the system of bands is at rest for only a particular rate of the

rod. As the latter rotates yet faster, the system of bands now

commences to rotate slowly forward (with the disc and rod), then more

and more rapidly (the velocity of the rod still increasing), until it

finally disintegrates and the bands vanish into the confused flicker

of shadows with which the phenomenon commenced.

 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VII.

Fig. 11.

Fig. 12. Fig. 13.]

 

This cycle now plays itself off in the reverse order if the speed of

the rod is allowed gradually to decrease. The bands appear first

moving forward, then more slowly till they come