Harvard Psychological Studies Part 16

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

BY EDWIN B. HOLT.

If a small rod is pa.s.sed 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 Munsterberg, 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 a.s.sured. 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 pa.s.sed 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 subst.i.tute 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 pa.s.sed in front of the disc and when pa.s.sed 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 pa.s.sed 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 pa.s.sed 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 pa.s.sed _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 a.n.a.lyzes the apparently h.o.m.ogeneous 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 pa.s.sing 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 p.r.o.nounce 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 a.n.a.lyze 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 a.n.a.lyze' 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 a.s.serted 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 pa.s.sed 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 s.p.a.ces 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 pa.s.ses 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.