Part 4 (1/2)
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.