Curiosities of Light and Sight Part 4

It is indeed wonderful that an organ affected by peculiarities of which those that have been referred to are merely specimens, should give such well-defined pictures as it does when accommodated for the objects looked at.

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 cla.s.s, 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 quant.i.ties 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 ma.s.s 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 p.r.o.nounces 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 ill.u.s.trative of the general uncertainty of mental estimates.

[Ill.u.s.tration: _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 a.s.similate itself, as regards the quality or condition in question, to the object or other ent.i.ty 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.

[Ill.u.s.tration: _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.

[Ill.u.s.tration: _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.

[Ill.u.s.tration: _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 s.p.a.ce 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.

[Ill.u.s.tration: _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 a.s.sociate 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 a.s.similate itself, as regards the quality or condition to be estimated, to the ent.i.ty in which the same is manifested. This is true, for example, in judging of an angle of inclination or slope; of a motion in s.p.a.ce; 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 circ.u.mstances 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.

[Ill.u.s.tration: _Fig. 30.--Illusion of Inclination._]

This may be ill.u.s.trated 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 cla.s.s of illusion is remarkably well demonstrated by Zollner's lines, Fig. 31; the two thick lines which appear to diverge from left to right, are in truth strictly parallel.

[Ill.u.s.tration: _Fig. 31.--Zollner'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 const.i.tutes 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 pa.s.sing 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.

[Ill.u.s.tration: _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 a.s.sume 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.

[Ill.u.s.tration: _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 a.s.sumption is exactly a.n.a.logous 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.

[Ill.u.s.tration: _Fig. 34.--Illusion of Luminosity._]

The fact is well ill.u.s.trated 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 pa.s.sed 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.