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

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