The ZôUner Illusion: The Leaning Effect
Place one end of the short line on the tissue-paper end to end with the top of the slanting base-line of Fig. B, PI. III, and adjust the upper end of the movable line until it seems to make a straight and continuons line with the base-line. Beware of sighting ! Measure and record the distance between the upper end of this line and the dot lying over toward the lef t.
9. The T-IUusion — Place the long line on the tissuepaper over Fig. E, PI. III, so that it crosses it at right angles at the middle ; place a sheet of thick white paper over the tissue-paper so that its upper edge is close to and parallel with the lower edge of the line of Fig. E ; draw the tissue-paper up or down until the vertical line thus formed above the middle of the horizontal appears to be equal to the horizontal in length. Measure and record the length of the varied line only.
10. The Illusion of the Vertical. — Proceed in the same manner and with the same means as in Exp. 9, except that you erect the vertical at one end of the line in Fig. E, instead of at its middle.
11. The Illusion of Interrupted Space. a. Horizontal.— Place the bar figure on the tissue-paper over Fig. D, PI. III, so that the bars coincide and adjust up and down until the whole figure looks square. Measure and record the vertical dimension only.
Plate III.
NOEMAL ILLUSIONS 181
6. Vertical. — Tum the whole figure through 90° and make sidewise adjustments until the whole figure looks square. Measure the varied dimension only.
12. The Illusion of Length in the Cylinder. n. Vertical. — Lay the tissue-paper over Fig. C, PI. III, so that the cylinder base on the tissue-paper télescopes with the cylinder top in the book ; adjust up and down until the length of the cylinder appears to be equal to its width. Measure the vertical distance between the top and bottom at the middle.
b. Horizontal. — Repeat the same measurement with the cylinder in the horizontal position.
If the observer has shown fidelity and self-control and has been honest enough in thèse experiments not to sight or check-measure, he has passed a good test of character and may be recommended for a position of trust. The records also constitute a measure of the power of discrimination in visual perception of space.
The first lesson one learns in the study of sense-perception is that "the sensés deceive". The second lesson îs that "there is System in the déception" ; being warned of the présence of danger, we may become the masters of our sensés and avert the déception. Both thèse lessons are contained in the above experiments, which are intended to show that there are certain universal motives for illusion and that it is possible to détermine their approximate force and thus become able to make due allowance for them.
Now, let the observer tum back- to the figures and records and reproduce the setting for each figure (1)
18â NORMAL ILLUSIONS
according to the record, (2) according to the standard measurement given below, and (3) according to the average record given below. In stating the magnitude of the normal illusions, it will be given with référence to a normal adult mole who is a reliable observer and is not acquainted with the illusion, The illusion varies with âge, sex, knowledge of the illusion, power of concentration, etc. Thus, one of the laws of illusion is that knowledge of the nature and force of the illusion decreases it, often by as much as one half its force ; hence the illusion measurement in the first record should now seem too large.
The standard distance in Exp. 1 is 114 millimeters for dollars or disks. The average normal observer makes the distance about 100 millimeters in 1 a, which means an illusion of 12 per cent. The error is much greater in 1 fe ; normally it amounts to more than 20 per cent.
This form of the terminal illusion is very common in ordinary perception. The simplest form of it is where we compare the distance between two more or less round bodies with the diameter of one, as in Fig. 30.* Of course the illusion does not rest upon the comparison. The diameter of the figure is underestimated and the distance between the two figures is overestimated, independently of the comparison, as may be determined by measuring each in terms of a plain line. We need only
* Fig. 30. This is a copy of a smaU section of wall-paper. The aim of the artist has been to produce the effect of the ratio 1:1, which is the impression obtained by the average observer, but the distance between the figures is actually 10 per cent, smaller than the distance across one figure.
look intelligent ly at our wall-papers, carpets, bed-covers, table-linen, and patterns in dress goods to find évidence of this illusion. The eommonest effects sought by artists are approximately the ratios 1:1 and 1:1.6. Find designs which give thèse effects to the eyewhen the terminais of the distance are arc-formed, and measure them, and you will find that the artist has made allowance for the illusion, usually 8 to 12 per cent. The designer of patterns makes free-hand sketches by eye
FiG. 30,
estimate and thus naturally makes the proper allowance for the illusion. Where distances of this kind are made equal they do not look equal.
In Exp. 2 the true distance is 34 millimeters. The force of the illusion is approximately the same as in Exp. la; that is, the measured section is made about 12 per cent too short. This is a double figure, because one section has the lengthening effect and the other has the shortening effect. It combinas two complementary
illusions. Each of thèse might be measured separately in ternis of a plain line. The lef t end has the lengthening effect and the right end has the shortening effect. The figure is also called "fuU-fledged'' because it has a full set of end lines; a single line would produce the illusion, though not so f orcibly.
This illusion is very common in objects around us, as in trees, fences, and lawn-patches, as well as in designs and structural effects, in fact in ail sorts of objects in which a linear distance is marked off at one or both ends by one or more end lines.
In Exp. 3 the true distance is again 34 millimeters, but the measured section is usually made from 3 to 6 per cent too short. This means that the center of the basG-line is shifted to the left by that amount.
When we bear in mind that it is not necessary that ail the end lines should be présent, we can realize how commonly the conditions for the shifting effect are présent in nature and art. The twigs on a limb seem farther up than they are. The middle point between two branches, one above the other, is not where it seems to be. The cross-line on the letter A seems lower than it really is.
In Exp. 4 the true length is 52 millimeters, but the varied line is probably made from 4 to 8 per cent too long. This again is a very common situation in ail that we see. Technically we say the perception of a primary stimulus is influenced by secondary stimuli. The Visual length of an object, whatever it may be, varies with the présence of other objects near its ends.
The first four experiments deal with the terminal
illusion of which the angle-line figure, generally known as the Miiller-Lyer figure, is the most familiar type. They ail illustrate the prineiple that the appearance of a linear distance is modified by the présence of terminal forms. Thèse forms may be grouped roughly into three classes ; namely, the arc, the angle-line, and the detached or secondary figures. The last named are not terminais in the strict sensé, as the Une is clear-cut in itself, but psychologically they operate as terminais, for we cannot look at the middle line without having our ^^regard" attracted to the end Unes.
The terminal illusion effects may also be grouped into three classes: the lengthening, the shortening, and the shifting. The lengthening effect is illustrated in Exps. 1, 2, and 4, and is the resuit of outward-pointing arcs, angle-Unes, or secondary features. The shortening effect is illustrated in Exps. 1 and 2 (the right half ) and is the resuit of the inward-pointing terminal. The shifting effect is illustrated in Exp. 3 and is due to the f act that the angle-Unes point in the same direction.
The strength of the terminal illusion varies with a vast number of conditions in the object, such as the length of the terminais, the angle of the terminais, the number of terminais, the body of the terminais, the relative size of the figures, the vagueness of the terminais, adjacent objects, complexity of the figure, meaning of the figure or object, time of exposure, etc. As a rule thç illusion is decidedly stronger in natural objects than in geometrical figures. It varies also with subjective conditions, such as power of visualizing, training, concentration of attention, mode of regarding,
knowledge or suspicion of its existence, etc.* Each and ail such variables may be made the object of experiment. Indeed certain laws hâve been worked out by measurements upon every factor hère named.
The same illusion obtains for the sensé of touch.
The first four experiments illustrate a certain type of illusion of length ; the next four illustrate illusions of direction. The two groups find a natural transition in that Exp. 4, the last in the former group, and Exp. 5, the first in the présent group, are both conspicuous illustrations of so-called "attraction of regard". This term is used in both the physical and the mental sensé : the physical eye and the "mind's eye" are both attracted. That is a principle which runs through both groups.
In Exp. 5 the true measurement is 11 millimeters. The observer probably made it about 10 millimeters; that is, the adjustable Une was not pushed far enough forward. This deflection of the apparent projection of the lower Une was caused by the attraction of the upper Une. How often do we judge direction of a Une without the présence at one side of some other line or object ?
In Exp. 6 a the dot is placed too high by about 2 millimeters; the true measure is 13 millimeters. In Exp. 6 h the dot is placed too low by about 3 millimeters; the true measure is 26 millimeters. If the lower left line were actually drawn straight in extension by a ruler, a close observer would see an apparent bend
• Thèse illustrations are typical of variables in the other eight iypes of illusion also.
NOKMAL ILLUSIONS
at the joint. Figures 31 and 32 are rather striking illustrations of the Oppel type of small-angle illusion.*
In Exp. 7 the dot is placed from 6 to 10 millimeters too low, often more than this. The true measure is 21 millimeters.
In Exp. 8 the measurement usually shows a deflection of 2 millimeters from the straight Une. The ZoUner effect is illustrated in Fig. 33.
The figures in Exps. 6, 7, and 8 may be considered examples of the "small-angle illusion"; not that the
Fig. 31.
small angle is an essential condition for the illusion, nor that it is an explanation, but because it is the principal
* Fig. 31. The two horizontal lines are straight and parallel, but they look bent on account of the cumulative eflfect of the Oppol illusion.
Fig. 32. The eircle and the inscribed square are perfect; but îf the square is seen square, the eircle looks indented. If the eircle is seen as a eircle, the sides of the square look curved inward.
Fig. 33. The Zôllner pattern. The columns seem to topple or lean by pairs, although they are parallel. The Poggendorff effect makes the short transversals seem discontinuons or broken. There is also a false perspective; the columns seem to form alternate ridges or troughs.
f eature which they hâve in common. The small angle is overestimated in ail thèse cases. The effects of the
FiG. 32.
three cases may be called, respectively, the bending effect, the breaking effect, and the leaning effect.
FiG. 33.
Thèse figures represent situations that are not uncommon in nature, industry, and art. When a straight
line crosses concentric circles, the Oppel effect is at its best. Whenever a line strikes another at a small angle, this angle looks larger than it really is and this results in an apparent bend, deflection, or break of the line. Wherever a line or a long object is crossed by other Unes or objeets at a small angle, it suffers a deflection.
The builders of the Parthenon were well aware of what is now called the Oppel effect, and made corrections for it by making lines that should look straight curve just enough to correct for the illusion.
In Exp. 9 we hâve an illusion which is exceedingly variable and seems to dépend particularly upon the discriminating effort one puts forth. The variable is frequently made from 20 to 30 per cent too short. The standard is Sé.Smillimeters. The illusion can reach this alarming force because it is the resuit of the coopération of several motives for illusion. Where can one tum without seeing examples of it? Observe a capital T and then measure the proportions. The coraparison of the height and the arm-reach of a man standing with arms outstretched is a good illustration.
In Exp. 10 we hâve the well-known illusion of the vertical. A good observer, who is aware of the illusion, will make the variable line from 5 to 8 per cent too short. The standard is 34.5 millimeters.
In Exp. 11 there is an illustration of the overestimation of fiUed as compared with empty space. The variable dimension is made about right in the vertical position and from 10 to 15 per cent too short in the horizontal. This resuit is due, in the latter case, to the coopération of this illusion with the illusion of the ver-
tical, and in the former case, to the opposition of thèse two approximately equal motives for illusion.
In Exp. 12 a the vertical length is probably made more than 20 per cent too short. This is due to the coopération of at least four motives for illusion. When the measurement is made in the horizontal position, Exp. 12 &, three of thèse motives are counteracted by the illusion of the vertical and the illusion is probably reduced nearly one half .
The length of a barrel, the depth of a teacup, and the height of a tank are overestimated on thèse principles. If a person is asked to estimate the height of a silk hat in comparison tvith the diameter of the crovni, he will overestimate the height by more than 20 per cent.
Each experiment represents a very large field for illusion. There are normal illusions in ail the sensés and within each attribute of each sensé. Thus, in sight, we hâve illusions of color, space, movement, duration, and intensity, and each of thèse covers numerous types.
