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.