Curiosities of Light and Sight

CHAPTER IV.

SOME OPTICAL ILLUSIONS.

Optical illusions generally result from the mind’s faulty interpretation of phenomena presented to it through the medium of the visual organs. They are of many different kinds, but a large class, which at first sight may seem to have little or nothing in common, arise, I believe, from a single cause, namely, the inability of the mind to form and adhere to a definite scale or standard of measurement.

In specifying quantities and qualities by physical methods, the standards of reference that we employ are invariable. We may, for example, measure a length by reference to a rule, an interval of time by a clock, a mass or weight by comparison with standardised lumps of metal, and in all such cases—provided that our instruments are good ones and skilfully used—we have every confidence in the constancy and uniformity of our results.

But two lengths, which when tested with the same foot rule are found to be exactly equal, are not necessarily equal in the estimate formed of them by the mind. Look, for instance, at the two lines in Fig. 25. According to the foot rule each of them is just one inch in length, but the mind unhesitatingly pronounces the upright one to be considerably longer than the other; the standard which it applies is not, like a physical one, identical in the two cases. Many other examples might be cited illustrative of the general uncertainty of mental estimates.

Fig. 25.—Illusion of Length.

The variation of the vague mental standard which we unconsciously employ seems to be governed by a law of very wide if not universal application. Though this law is in itself simple and intelligible enough, it cannot easily be formulated in terms of adequate generality. The best result of my efforts is the following unwieldy statement:—The mental standard which is applied in the estimation of a quality or a condition tends to assimilate itself, as regards the quality or condition in question, to the object or other entity under comparison of which the same (quality or condition) is an attribute.

In plainer but less precise language, there is a disposition to minimise extremes of whatever kind; to underestimate any deviation from a mean or average state of things, and consequently to vary our conception of the mean or standard condition in such a manner that the deviation from it which is presented to our notice in any particular instance may seem to be small rather than large.

Thus, when we look at a thing which impresses us as being long or tall, the mental standard of length is at once increased. It is as if, in making a physical measurement, our foot rule were automatically to add some inches to its length, while still supposed to represent a standard foot: clearly anything measured by means of the augmented rule would seem to contain a fewer number of feet, and, therefore, to be shorter than if the rule had not undergone a change.

It is not an uncommon thing for people visiting Switzerland for the first time to express disappointment at the apparently small height of the mountains. A mountain of 10,000 feet certainly does not seem to be twenty times as lofty as a hill of 500. The fact is that a different scale of measurement is applied in the two cases; though the observer is unaware of it, the mountain is estimated in terms of a larger unit than the hill.

Fig. 26.—Illusion of Length.

If we mentally compare two adjacent things of unequal length, such as the two straight lines in Fig. 26, there is a tendency to regard the shorter one as longer than it would appear if seen alone, and the longer one as shorter. The lower of the two lines in the figure is just twice as long as the other, but it does not look so; each is regarded as differing less than it really does from an imaginary line of intermediate length.

Fig. 27.—Illusion of Length.

Two divergently oblique lines attached to the ends of a straight line as at A, Fig. 27, suggest to the mind the idea of lengths greater than that of the straight line itself; the latter, being thought of as comparatively small, is therefore estimated in terms of a smaller unit than would be employed if the attachments were absent, and consequently appears longer. If, on the other hand, the attachments are made convergent, as at B, shorter lengths are suggested; the length of the given line is regarded as exceeding an average or mean; the standard applied in estimating it is accordingly increased, and the line is made to seem unduly short. In spite of appearances to the contrary, the two lines A and B are actually of the same length.

By duplicating the attached lines, as shown in Fig. 28, their misleading effect becomes intensified. Here we have a well-known illusion of which several explanations have been proposed. The fallacy is, I think, sufficiently accounted for by variation of the mental standard, in accordance with the law to which I have called attention.

Fig. 28.—Illusion of Length.

A number of other paradoxical effects may be referred to the operation of the same law. Fig. 29 shows a curious specimen. At each end of the diagram is a short upright line; exactly in the middle is another; between the middle and the left hand end are inserted several more lines, the space to the right of the middle being left blank. Any one looking casually at the diagram would be inclined to suppose that it was not equally divided by what purports to be the middle line, the left hand portion appearing sensibly longer than the other.

Fig. 29.—Illusion of Distance.

It is not difficult to indicate the source of the illusion. When we look at the left hand portion we attend to the small subdivisions, and the mental unit becomes correspondingly small; while in the estimation of the portion which is not subdivided a larger unit is applied.

As one more example I may refer to a familiar trap for the unwary. Ask a person to mark upon the wall of a room the height above the floor which he thinks will correspond to that of a gentleman’s tall hat. Unless he has been beguiled on a former occasion, he will certainly place the mark several inches too high. Obviously the height of a hat is unconsciously estimated in terms of a smaller standard than that of a room.

The illusion presented by the horizontal and vertical lines in Fig. 25 (p. 132) depends, though a little less directly, upon a similar cause. We habitually apply a larger standard in the estimation of horizontal than of vertical distances, because the horizontal magnitudes to which we are accustomed are upon the whole very much greater than the vertical ones. The heights of houses, towers, spires, trees, or even mountains are insignificant in comparison with the horizontal extension of the earth’s surface, and of many things upon it, to which our notice is constantly directed. For this reason, we have come to associate horizontality with greater extension and verticality with less, and, in conformity with our law, a given distance appears longer when reckoned vertically than when reckoned horizontally. Hence the illusion in Fig. 25.

But it is not only in regard to lengths and distances that the law in question holds good; in most, if not all cases in which a psycho-optical estimate is possible, the mental standard is unstable and tends to assimilate itself, as regards the quality or condition to be estimated, to the entity in which the same is manifested. This is true, for example, in judging of an angle of inclination or slope; of a motion in space; of luminous intensity, or of the purity of a colour.

Every cyclist knows how difficult it is to form a correct judgment of the steepness of a hill by merely looking at it. Not only may a slope seem to be greater or less than it really is, but under certain circumstances a dead level sometimes appears as an upward or downward inclination, while a gentle ascent may even be mistaken for a descent, and vice versa.

We usually specify a slope by its inclination to a level plane which is parallel to the plane of the horizon, or at right angles to the direction of gravity. At any given spot the level is, physically considered, definite and unalterable. In forming a mental judgment of an inclination, we employ as our standard of reference an imaginary plane which is intended to be identical with the physical level. But our mental plane is not absolutely stable; when we refer a slope to it, we unconsciously give the mental plane a slight tilt, tending to make it parallel with the slope. Hence the inclination of a simple slope, when misleading complications are absent, is always underestimated.

Fig. 30.—Illusion of Inclination.

This may be illustrated by the diagram Fig. 30. If A B represents a truly horizontal line, the slope of the oblique line C D is correctly specified by the angle C O A. But if we have no instrument at hand to fix the level for us, we shall infallibly imagine it to be in some such position as that indicated (in an exaggerated degree) by the dotted line E F, while the true level A B will appear to slope oppositely to C D.

This class of illusion is remarkably well demonstrated by ZÖllner’s lines, Fig. 31; the two thick lines which appear to diverge from left to right, are in truth strictly parallel.

Fig. 31.—ZÖllner’s Lines.

I need not discuss in further detail the various illusions to which a cyclist is subjected when slopes of different inclinations succeed one another: they all follow simply from the same general principle.

A thing is said to be in motion when it is changing its position relatively to the earth, which for all practical purposes may be regarded as motionless. The state, as regards motion, of the earth and anything rigidly attached to it, therefore constitutes the physical zero or standard to which the motion of everything terrestrial is referred. But the corresponding mental standard, especially when it cannot easily be checked by comparison with some stationary object, is liable to deviate from the physical one; it tends in fact to move in the same direction as the moving body which is under observation, and the apparent speed of the body is consequently rather less than it should be.

The influence exerted upon the judgment sometimes even persists for an appreciable period after the exciting cause has ceased to be operative, as when the moving body is lost sight of or has suddenly come to rest; in such cases fixed objects, being compared with the delusive mental standard, appear for a few seconds to be moving in the opposite direction.

I have devised a lantern slide (Fig. 32) by the aid of which this phenomenon may be rendered very evident. In a square plate of metal is cut a vertical slot, which is shaded in the figure; behind the plate is an opaque disk, which, by means of suitable mechanism, can be made to rotate about its centre. The disk has a spiral opening cut in it of the same width as the slot, as indicated by the dotted line. The slide is placed in an optical lantern, and the light passing through the aperture formed where the slot is crossed by the spiral opening, produces a small bright patch upon a white screen hung at a suitable distance from the lantern.

Fig. 32.—Slide for showing Illusions of Motion.

When the disk is turned in the direction indicated by the arrow, the bright patch moves upwards and ultimately disappears; but at the moment of its disappearance a fresh patch starts from below, which also moves in the upward direction; thus there is formed upon the screen a continuous succession of ascending bright patches. After these have been observed for about a quarter of a minute, the disk is suddenly stopped, and the persistence of the fallacious mental standard is at once demonstrated. For the bright patch does not appear to be at rest, as it actually is, but to creep steadily downwards, continuing to do so more and more slowly for perhaps as long as ten seconds. The upward motion of the bright patches had led the observer to assume a slower upward motion as the zero, or standard of no motion, and reference of the really stationary patch to this physically false standard induces the illusion that the patch is descending.

This experiment is most successful when the bright patches are projected upon the middle of a large screen. The disk should turn about three times in a second, and the room should be feebly illuminated, but not quite dark.

Fig. 33.—Illusions of Motion.

A very remarkable illusion which no doubt depends upon the same principle as the last, though its form is entirely different, is that to which the diagram Fig. 33 relates. So far as I am aware, it has not before been noticed.Two intersecting straight lines, the one upright and the other sloping, as shown in the figure, are drawn upon a card. The card is to be held vertically before the eyes at the distance of most distinct vision, and waved up and down through a distance of a few inches. The oblique line will then appear to oscillate transversely, as if it were not rigidly attached to the card.

This is the result of underestimating the speed at which the card is moved. Rather than recognise the true state of things, the mind prefers to accept the suggestion that the upward or downward movement of the point of intersection is in part due to oppositely directed horizontal movements of the lines themselves upon the surface of the card. When the card is descending the vertical line is supposed to slide a little to the right and the oblique line to the left, which would have the effect of lowering their point of intersection independently of the downward movement of the card itself. When the card ascends, these horizontal movements are supposed to be reversed, and the point of intersection consequently raised. The assumption is exactly analogous to that made when an angle of slope is unwittingly minimised.

Another example of the instability of a mental standard occurs in the estimation of luminosity. The luminosity of a bright object, if reckoned in terms of the same unit as that applied in judging of a less bright one, would appear to be greater than it actually does appear, and this quite independently of any effects of fatigue.

Fig. 34.—Illusion of Luminosity.

The fact is well illustrated by a familiar experiment. Fig. 34 is photographed from a transparency made by superposing several different lengths of gelatine film so as to form a series of steps. At the right-hand end of the image the light has passed through only one layer of the film; in the next division it has traversed two layers, in the next, three, and in the last, four. The luminosity of each of the four squares into which the oblong is divided is, in a physical sense, quite uniform, but the mental standard of luminosity varies for different parts of the image, increasing or decreasing, as the case may be, not per saltum, but smoothly and continuously, with the result that each square looks brighter towards the left than towards the right. The appearance, which is often likened to that presented by a fragment of a fluted column, is equally well shown when the diagram is illuminated instantaneously by an electric spark, and cannot, therefore, be accounted for by retinal fatigue.

If the squares are separated from one another by distinct lines of demarcation, however fine, the standard of luminosity becomes uniform for each square, and the illusion vanishes. This fact sufficiently disposes of the hypothesis which has been advanced to the effect that the phenomenon is due to physiological causes.

I now propose to discuss a curious consequence of the fluctuation of unaided judgment as regards the purity of a colour.

When any colour occupies a predominant place in the field of vision, we are apt to consider it as being less pure, or paler, than we should if it were less conspicuous, our standard of whiteness tending to approximate itself to the colour in question.

For the sake of clearness let us first confine our attention to a definite colour—say red. An absolutely pure red is one that is entirely free from any admixture of white; in proportion as it contains more and more white, the more impure, or in other words, the more pale does it become, until at last all trace of perceptible redness is lost and the colour is indistinguishable from white.

Fig. 35.—Illusion of Colour.

A convenient way of picturing the scale of purity is shown in Fig 35. The shaded oblong may be supposed to represent a painted strip of cardboard or paper. At the extreme right hand end the colour is supposed to be absolutely pure red; towards the left the red gradually becomes paler or more dilute, and at the middle of the diagram it has merged into perfect whiteness. The figures 0 to 100 from left to right denote the percentage of free red contained in the mixture at different parts of the scale; the luminosity is supposed to be uniform throughout.

Now the white light with which the red is diluted may be regarded as consisting of two parts, one of which is of exactly the same hue as the pure red itself, and the other an equivalent proportion of the complementary colour, which in the present case will be greenish-blue. The fact therefore really is that, as we pass along the scale from 100 to 0, the total quantity of red in the mixture is not reduced to nothing, but only to one half, while at the same time greenish-blue is added in proportions increasing from nought at the extreme right to 50 per cent. of the whole at the middle of the card. The ordinates of the quadrilateral figure E D B F show the proportion of red, and those of the triangle E F B the proportion of greenish-blue, at different parts of the scale.

Regarding the portion of the strip which lies above the point marked 0, as representing the zero of colour—that is, whiteness or greyness, which is essentially the same as whiteness—let us continue the diagram in the negative direction, gradually reducing the quantity of red until it falls from 50 per cent. of the whole at F to nothing at A, and at the same time increasing that of the greenish-blue from 50 per cent. at F to 100 per cent. at A. The resultant hue in the portion of the card between F and A will be greenish-blue, which begins to be perceptible as a very pale tint just to the left of F, and increases in purity as A is approached, at which point the colour will be entirely free from any admixture with white.

We have in the scale thus presented to our imagination a pair of colours, each occupying one-half of the scale, and gradually diminishing in purity towards the middle line; here only, just at the stage where one colour merges into the other, is there no colour at all, and this region represents the fixed physical zero or standard from which is reckoned the purity of a colour corresponding to any other portion of the scale. The completed scale, it will be observed, though originally intended only for the case of red, turns out to be equally serviceable for greenish-blue: if we consider greenish-blue as positive, then the red, being on the other side of zero, must be regarded as negative. Any other possible pairs of complementary colours may be similarly treated.

This device enables us at once to understand the consequence of mentally displacing the zero, while physically the scale remains unchanged. When red is the prevailing colour in the field of vision, we are inclined to consider it unduly pale; in other words we imagine it to be nearer the zero of the scale than is actually the case, and so are led to shift our standard of whiteness from the middle slightly towards the red end of the scale. The new position assigned to white, being a little to the right of the point marked 0 in Fig. 35, is one where, under customary circumstances, the colour would be called pale red. At the same time, an object which is normally white, and is exactly matched at the middle of the scale, would be a little to the left of the imaginary zero, and would consequently appear to be of a greenish-blue tint.

This apparent transformation of white or grey into a decided colour is most striking when the inducing colour is considerably diluted with white or is of feeble luminosity. A small fragment of neutral grey paper, placed upon a much larger piece of a bright red hue, generally appears at the first glance[11] to be greenish-blue, but if the light is at all strong, only slightly so. If, however, a sheet of white tissue paper is laid over the whole, the greenish-blue tint immediately becomes startlingly distinct, and may even appear more decided than the red itself as seen through the tissue. The same piece of grey paper, when placed upon a green ground, appears rose-coloured, and upon a blue ground, yellow, the effect being always greatly increased by the diluent action of superposed tissue paper.

There seem to be several reasons, partly physical and partly psychological, why these contrast colours, as they are called, are more pronounced when the colour that calls them into existence either has a somewhat pale tint or is feebly illuminated. Probably the most important is of a purely physical character. The refracting media of the eye are much less perfectly transparent than a good glass lens is; they are sensibly turbid or opalescent, and in consequence of this defect some of the light which falls upon them is irregularly scattered over the retina. If we look at a bright red object with a small white patch upon it, the image of the patch as formed upon the retina is not, physically speaking, perfectly white, but slightly coloured by diffused red light; owing however to the psychological influence to which our attention has been directed, the faint red coloration is not consciously perceived; the same mental displacement of the zero which, when the exciting colour was feeble, led us to regard white (or grey) as bluish-green, now causes what is actually pale red to appear white.

There is no need whatever to assume that the contrast colours with which we have been dealing are of physiological origin and due to an inductive action excited in portions of the retina adjacent to those upon which coloured light falls. On the contrary, it would be a matter for surprise if the case in question presented an exception to the comprehensive law which governs the fluctuation of the mental judgment.

Of the operation of this law I have quoted several very diverse instances, and the number might easily have been increased. Nor is it only in relation to optical phenomena that the law holds good; in its most general form, supplemented it may be in some instances by obvious corollaries, it is applicable to almost every case in which physical attributes of whatever kind are the subject of unassisted mental judgment.

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