Part 2 (2/2)
[Ill.u.s.tration: Fig. 4.--The vertical line appears longer than the equal horizontal line in each case.]
This type of illusion persists in geometrical figures and may be found on every hand. A perfect square when viewed vertically appears too high, although the illusion does not appear to exist in the circle. In Fig. 4 the vertical line appears longer than the horizontal line of the same length. This may be readily demonstrated by the reader by means of a variety of figures. A striking case is found in Fig. 5, where the height and the width of the diagram of a silk hat are equal. Despite the actual equality the height appears to be much greater than the width. A pole or a tree is generally appraised as of greater length when it is standing than when it lies on the ground. This illusion may be demonstrated by placing a black dot an inch or so above another on a white paper. Now, at right angles to the original dot place another at a horizontal distance which appears equal to the vertical distance of the first dot above the original. On turning the paper through ninety degrees or by actual measurement, the extent of the illusion will become apparent. By doing this several times, using various distances, this type of illusion becomes convincing.
[Ill.u.s.tration: Fig. 5.--The vertical dimension is equal to the horizontal one, but the former appears greater.]
The explanation accepted by some is that more effort is required to raise the eyes, or point of sight, through a certain vertical distance than through an equal horizontal distance. Perhaps we unconsciously appraise effort of this sort in terms of distance, but is it not logical to inquire why we have not through experience learned to sense the difference between the relation of effort to horizontal distance and that of effort to vertical distance through which the point of sight is moved? We are doing this continuously, so why do we not learn to distinguish; furthermore, we have overcome other great obstacles in developing our visual sense. In this complex field of physiological psychology questions are not only annoying, but often disruptive.
As has been pointed out in Chapter II, images of objects lying near the periphery of the visual field are more or less distorted, owing to the structure and to certain defects of parts of the eye. For example, a checkerboard viewed at a proper distance with respect to its size appears quite distorted in its outer regions. Cheap cameras are likely to cause similar errors in the images fixed upon the photographic plate.
Photographs are interesting in connection with visual illusions, because of certain distortions and of the magnification of such aspects as perspective. Incidentally in looking for illusions, difficulty is sometimes experienced in seeing them when the actual physical truths are known; that is, in distinguis.h.i.+ng between what is actually seen and what actually exists. The ability to make this separation grows with practice but where the difficulty is obstinate, it is well for the reader to try observers who do not suspect the truth.
_Illusions of Interrupted Extent._--Distance and area appear to vary in extent, depending upon whether they are filled or empty or are only partially filled. For example, a series of dots will generally appear longer overall than an equal distance between two points. This may be easily demonstrated by arranging three dots in a straight line on paper, the two intervening s.p.a.ces being of equal extent, say about one or two inches long. If in one of the s.p.a.ces a series of a dozen dots is placed, this s.p.a.ce will appear longer than the empty s.p.a.ce. However, if only one dot is placed in the middle of one of the empty s.p.a.ces, this s.p.a.ce now is likely to appear of less extent than the empty s.p.a.ce. (See Fig. 7.) A specific example of this type of illusion is shown in Fig. 6. The filled or divided s.p.a.ce generally appears greater than the empty or undivided s.p.a.ce, but certain qualifications of this statement are necessary. In _a_ the divided s.p.a.ce unquestionably appears greater than the empty s.p.a.ce.
Apparently the filled or empty s.p.a.ce is more important than the amount of light which is received from the clear s.p.a.ces, for a black line on white paper appears longer than a white s.p.a.ce between two points separated a distance equal to the length of the black line. Furthermore, apparently the s.p.a.cing which is the most obtrusive is most influential in causing the divided s.p.a.ce to appear greater for _a_ than for _b_. The illusion still persists in _c_.
[Ill.u.s.tration: Fig. 6.--The divided or filled s.p.a.ce on the left appears longer than the equal s.p.a.ce on the right.]
An idea of the magnitude may be gained from certain experiments by Aubert.
He used a figure similar to _a_ Fig. 6 containing a total of five short lines. Four of them were equally s.p.a.ced over a distance of 100 mm.
corresponding to the left half of _a_, Fig. 6. The remaining line was placed at the extreme right and defined the limit of an empty s.p.a.ce also 100 mm. long. In all cases, the length of the empty s.p.a.ce appeared about ten per cent less than that of the s.p.a.ce occupied by the four lines equally s.p.a.ced. Various experimenters obtain different results, and it seems reasonable that the differences may be accounted for, partially at least, by different degrees of unconscious correction of the illusion.
This emphasizes the desirability of using subjects for such experiments who have no knowledge pertaining to the illusion.
[Ill.u.s.tration: Fig. 7.--The three lines are of equal length.]
[Ill.u.s.tration: Fig. 8.--The distance between the two circles on the left is equal to the distance between the outside edges of the two circles on the right.]
As already stated there are apparent exceptions to any simple rule, for, as in the case of dots cited in a preceding paragraph, the illusion depends upon the manner in which the division is made. For example, in Fig. 7, _a_ and _c_ are as likely to appear shorter than _b_ as equal to it. It has been concluded by certain investigators that when subdivision of a line causes it to appear longer, the parts into which it is divided or some of them are likely to appear shorter than isolated lines of the same length. The reverse of this statement also appears to hold. For example in Fig. 7, _a_ appears shorter than _b_ and the central part appears lengthened, although the total line appears shortened. This illusion is intensified by leaving the central section blank. A figure of this sort can be readily drawn by the reader by using short straight lines in place of the circles in Fig. 8. In this figure the s.p.a.ce between the inside edges of the two circles on the left appears larger than the overall distance between the outside edges of the two circles on the right, despite the fact that these distances are equal. It appears that mere intensity of retinal stimulation does not account for these illusions, but rather the figures which we see.
[Ill.u.s.tration: Fig. 9.--Three squares of equal dimensions which appear different in area and dimension.]
In Fig. 9 the three squares are equal in dimensions but the different characters of the divisions cause them to appear not only unequal, but no longer squares. In Fig. 10 the distance between the outside edges of the three circles arranged horizontally appears greater than the empty s.p.a.ce between the upper circle and the left-hand circle of the group.
[Ill.u.s.tration: Fig. 10.--The vertical distance between the upper circle and the left-hand one of the group is equal to the overall length of the group of three circles.]
_Illusions of Contour._--The illusions of this type, or exhibiting this influence, are quite numerous. In Fig. 11 there are two semicircles, one closed by a diameter, the other unclosed. The latter appears somewhat flatter and of slightly greater radius than the closed one. Similarly in Fig. 12 the shorter portion of the interrupted circ.u.mference of a circle appears flatter and of greater radius of curvature than the greater portions. In Fig. 13 the length of the middle s.p.a.ce and of the open-sided squares are equal. In fact there are two uncompleted squares and an empty ”square” between, the three of which are of equal dimensions. However the middle s.p.a.ce appears slightly too high and narrow; the other two appear slightly too low and broad. These figures are related to the well-known Muller-Lyer illusion ill.u.s.trated in Fig. 56. Some of the illusions presented later will be seen to involve the influence of contour. Examples of these are Figs. 55 and 60. In the former, the horizontal base line appears to sag; in the latter, the areas appear unequal, but they are equal.
[Ill.u.s.tration: Fig. 11.--Two equal semicircles.]
[Ill.u.s.tration: Fig. 12.--Arcs of the same circle.]
[Ill.u.s.tration: Fig. 13.--Three incomplete but equal squares.]
_Illusions of Contrast._--Those illusions due to brightness contrast are not included in this group, for ”contrast” here refers to lines, angles and areas of different sizes. In general, parts adjacent to large extents appear smaller and those adjacent to small extents appear larger. A simple case is shown in Fig. 14, where the middle sections of the two lines are equal, but that of the shorter line appears longer than that of the longer line. In Fig. 15 the two parts of the connecting line are equal, but they do not appear so. This illusion is not as positive as the preceding one and, in fact, the position of the short vertical dividing line may appear to fluctuate considerably.
[Ill.u.s.tration: Fig. 14.--Middle sections of the two lines are equal.]
[Ill.u.s.tration: Fig. 15.--An effect of contrasting areas (Baldwin's figure).]
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