The first group of geometrical optical illusions contains (a) the illusions of reversible perspective. It is a familiar fact that many outline figures—a bowl, an open book, a cube, a stairway—will 'turn inside out' in the most perplexing way as one looks at them. Even two crossed lines, drawn N-wise upon a sheet of paper, may be made to take on the appearance of a right-angled cross, seen in per spective, with. either the lower or the higher point of the line which forms the horizontal arms nearer to the observer. Very little prae tiee suffices to show that the direc tion of perspective depends here upon the point fixated and the course along which the eye moves; the point of fixation is the point nearer the oh server, and movement of the eye toward a given point brings that, in its turn, to the front of the figure. (b) Next follow the illusions of extent, variable and constant. A dotted line looks longer than a drawn line of equal objective length, for the reason that it offers more halting places as the eye moves along it. Draw an outline square; then a group of horizontal lines, filling the same area as the square; and then a similar group of vertical lines. The horizontal group looks higher, the vertical group broader, than the ob jectively equal square, for the reason, again, that the grouped lines offer more obstacles to the passage of the eye over the area of the figure. One of the most disputed figures of this class is the illusion of Altiller-Lyer, or the arrow-head and feather illusion. Draw two vertical or hori zontal lines of equal length. Tip the two ends with oblique lines of the same length directed outward (arrow feathers) ; the latter appears considerably the longer of the two. Wundt's explanation is that the inward-going obliques offer a check to the passage of the eye along the principal line, while the outward-going obliques favor a continuance of eye-movement. The con stant illusions of extent (due to asymmetries of muscular action about the eyeball) are summed up in a right-angled and equal-armed cross. The vertical line in this figure seems to be longer than the horizontal; the upper vertical arm longer than the lower; and, in monocular vision. the outer horizontal arm looks longer than the inner. (e) Thirdly, we have variable and con stant illusions of direction. Draw a large out line square, marking in one of the diagonals, and three or four lines parallel to the diagonal, at equal distances on either side of it. Now pro ceed to cross-hatch the oblique lines, cutting the diagonal with short vertical pieces. the two ad joining obliques with short horizontal pieces. the two oblique lines next beyond these with verticals again, the two next with horizontals, and so forth. Notice that the parallel obliques no longer look parallel, but appear to converge and diverge alternately. The explanation of this and similar illusions is that small angles are over estimated, and large angles relatively underesti mated; and the reason for such overestimation, again, is that it takes more muscular effort and energy to start a movement of the eye than it does to continue a movement already begun. The constant illusion of direction is that, under cer tain conditions of fixation, hyperbolas are per ceived as straight lines, owing to the concavity of the retina. (d) There remains a group of illusions which \Vundt classes as 'associative,' i.e. as psychological, not physiological, in origin.
of the one with oblique lines directed inward (arrow-beads), and the two ends of the other If equal short horizontal lines arc drawn. some grouped closely together, and some widely spaced, the latter appear longer than the former; the length of the line is 'assimilated' to the size of the interspaces. In the same way, if two broad and two narrow rectangles are drawn. of equal height and separated by equal spaces, the space between the larger rectangles will look smaller than the space between the narrower; the inter spaces are differently estimated by 'contrast' with the adjacent figures. (See CONTRAST.) (e) Finally, we may, of course, have figures in which several of the above-mentioned motives, physiological and psychological, eoi;perate to produce the illusion.
We may further include under the general heading of optical illusions: (1 ? the physical illusions produced by mii rors, lenses. prisms, etc. (sec REFLECTIoN ; REFRACTION) ; ( 2 ) the physiological illusions of color (see ArrErt-1 M AGE ; CONTRAST) ; ( ) illusions of movement, such as, e.g. the apparent MOW ment of the moon vhen viewed through drifting clouds; and (4) illusions of distance. Under the latter category falls the apparent enlargement. of sun and moon when seen near the horizon. The distance between the observing eye and the hori zon seems to be longer (owing to the haziness of the air, the number of intervening objects, etc.) than the distance between the eye and the zenith. But if two objects subtend the same visual angle (give the same retinal image) at different distances, the one which is farther off must be larger than the other.
Touch, no less than sight, is subject to spatial illusion. (a) If two compass points are set down upon the skin, first on an area of greater and then on an area of less sensitivity, the dis tance between them will seem to be greater in the former ease than in the latter. (live the points. e.g. a separation that enables them to he clearly perceived as distinct impressions when they are set crosswise upon the skin of the upper arm. Now draw the compasses down the inner surface of the arm, to forearm, wrist, and finger tips. The parallel lines which they doseriW will appear to converge and diverge upon the regions of less and greater sensitivity. Or set the points down, vertically, upon the upper and lower lips, and draw the compasses outward, toward the ear. The points seem to converge as they travel over the skin. (b) Cross the tip of the second over that of the third finger, and place a marble or other small object between the crossed tips. Since the two surfaces now stimu lated are never affected, in ordinary life, by one and the same object, but only by two different objects, the single marble is 'felt' as two. This illusion of localization is described by Aristotle, in his tract Un breams. (e) Draw a given length of coarse thread between the finger and thumb, at first slowly, and then more quickly. The thread appears to be much longer in the for mer case; the separate pressure sensations have a longer time in which to run their course un disturbed by subsequent pressures. and fullness of sensation is interpreted as length of thread. (d) If a point be moved over the skin at a uni form rate, it will seem to travel more quickly as it crosses areas of greater sensitivity, and to become slow again as it enters regions of less sensitivity.
A striking illusion of temperature is described by the English philosopher Locke (q.v.). Hold the one hand in a bowl of heated, the other in a bowl of cold water. After a short time. plunge both hands into a bowl of lukewarm water. This will appear hot to the cooled, and cold to the heated hand. The illusion is due to the pre ceding adaptation of the temperature-organs of the skin. (See CUTANEOUS SENSATION.) An equally striking illusion in the sphere of kin a•sthetie sensation is atTorded by the fact that a small weight always appears heavier than a larger weight of the same objective heaviness. The smaller weight stimulates intensively a lim ited cutaneous area, with its underlying tissues; the larger weight stimulates lightly a large area of skin, and leaves the underlying tissues prac tically unaffected. These instances, which could be multiplied almost indefinitely, show clearly that the term 'illusion' implies nothing more than a discrepancy between perception and ob jective measurement.
BIBLIOGRAPHY. For (1), consult Wundt,Bibliography. For (1), consult Wundt, Physiologische Psychologic (Leipzig, 1S93). (See HALLUCINATION.) For (2), consult: Titehener, Experimental Psychology (New York, 1901) : Sanford, Course in Experimental Psychology (Boston, 189S) ; Wundt, Die geometrisch-opti schen Tauschungen (Leipzig, 1898) ; Lipps, Raum wstlictik nod gcometrisch-optischc Tenschungcn (Leipzig, 1897) ; James, Principles of Psychology (New York. 1S90) ; lloppe, Psychologisch•physio logische Optik (Leipzig, 1SS1).