By Professor Ross Day Hon FAPS
School of Psychological Science, La Trobe University
Professor Ross Day Hon FAPS was the recipient of the 2004 APS Distinguished Scientific Contribution Award. He is only the sixth member of the Society to receive this Award, which recognises distinguished theoretical or empirical contributions to psychology. This article is adapted from Professor Day's Keynote address at the 2005 Australian Psychological Society Annual Conference.
Perception can be defined as the immediate and largely effortless awareness of external objects, situations and events and of the self in regard to postures, movements and actions. Illusory perception refers to a consistent and persistent discrepancy between the perceived and real physical properties of a stimulus. Illusions are consistent in the sense that they invariably occur when the particular stimulus is presented and persistent in the sense that they are strongly resistant to efforts to suppress them. Thus a pair of straight lines of equal length in a particular context might appear different in length or, as will be pointed out below, two equal periods of time in a certain context might appear to be quite different in duration. Likewise, we might feel ourselves to be moving when we are stationary or tilted over at an angle when we are upright.
Textbooks almost invariably reproduce illusory figures in the standard form in which they were first observed, thus often conveying the impression that they occur only in that particular context. For example, the Müller-Lyer (M-L) illusion of unequal extents is usually demonstrated in a figure consisting of two equal lines, one with angles directed outward and the other with the same angles directed inward, as shown in Figure 1A. However, the illusion occurs in numerous forms including the highly simplified version shown in Figure 1B consisting merely of one pair of lines forming an acute angle and another pair of exactly the same length forming an obtuse angle. As can be seen, both lines in the acute angle appear shorter than both those in the obtuse angle. Incidentally, this figure was the first in Müller-Lyer’s rather muddled assembly of fifteen figures in his original paper published in 1889. The well known Poggendorff figure shown in Figure 1C is another instance of almost always presenting an illusion in its original form. However, the apparent misalignment of the two perfectly collinear oblique lines occurs also in the much simpler Figure 1D consisting simply of a single oblique aligned with the midpoint of vertical line.
The point of drawing attention to these two well known and frequently reproduced illusions is that an acceptable explanation of an illusory effect must account for its occurrence in all of its forms, including those which are marked simplifications of the original figure. As will be noted, the explanation of the M-L illusion set out below derived largely from the discovery of its occurrence in a highly simplified figure consisting of only three straight, collinear lines. In any case it is reasonable to expect that that an explanation of geometric illusions will be more likely to emerge from simplified figures than from the more elaborate forms in which they were first discovered.
Another point to be emphasised is that many of the illusions shown in textbooks occur also in perceptual modes other than vision. For example, the M-L illusion occurs strongly in the haptic mode – the sense involving the combination of touch and movement as when an extended finger is moved over a model of the M-L figure constructed of thin bars or lengths of wire. It can also be expected that a valid explanation of the illusion can account for its occurrence in both sensory modes.
The conditions for the occurrence of the Müller-Lyer (M-L) illusion
As can be seen in Figure 2A, the M-L illusion of unequal extents also occurs strongly when the two components in the conventional form of the figure are combined, so that the central angle is shared between the two components and the line joining the angles removed. As will be clear from Figure 2, the angles are only one of many terminal elements that give rise to the appearance of unequal extents. The effect is clearly present when the angles are replaced by, inter alia, semicircles (Figure 2B), complete squares (Figure 2C), three different shapes (Figure 2D), and irregular shapes (Figure 2E). Thus it is not the form of the terminal elements that are necessary for the occurrence of the illusion. What then is the critical factor? Inspection of the figures shown in Figure 2 indicates that it is the positions of the elements relative to the equal spaces that they define. In all the apparently shorter components on the left in Figure 2, the elements are 'inboard' of the space and in all the apparently longer components on the right 'outboard' of it. That is to say, when the elements are inboard of a space so that their outer boundaries mark its limits, the space appears shorter than when they are outboard of the space so that the inner boundaries mark its limits. The rule is that outboard elements result in spaces appearing larger and inboard elements result in the same spaces appearing smaller.
If this analysis of the essential condition for the occurrence of the M-L illusion is valid, it follows that the illusion can be expected to occur when the stimulus figure is reduced simply to three collinear lines arranged so that two fall inboard of one space and two outboard of another, equal, space as shown in Figure 2F. Of course in this version of the figure the central element marks the ends of both spaces, i.e., inboard of that on the left and outboard of that on the right. Numerous observers when invited informally to compare the lengths of the two spaces consistently judged that on the left with the lines inboard to be shorter than that on the left with the lines outboard. These informal observations were fully confirmed in two experiments by Christine Mulvihill and the author (see Mulvihill, 2000). In the first of the two experiments with specially constructed apparatus, 16 participants and a standard and highly reliable psychophysical procedure, the M-L illusion proved to be strong and robust in both the visual and haptic modes. In brief, the M-L illusion occurs in both the visual and haptic modes with a simple 3-line stimulus like that in Figure 2F in which the collinear lines are inboard of one space and outboard of the other.
The temporal M-L illusion
It will be obvious that that the three lines in Figure 1F can be transposed into three intervals of time falling 'inboard' and 'outboard' of two equal time intervals. That is to say, the spatial form of the stimulus arrangement in Figure 1F can be converted into a temporal form by converting the lines in Figure 2F into durations of time with silent or blank periods between. When observers either listened to or watched these sequential events informally they reported strong illusions of time, that is, of auditory and visual duration.
Using computer-generated and controlled stimuli, Sam Lloyd and the author (see Lloyd, 2000) confirmed that there is indeed a temporal homologue of the M-L illusion in both the auditory and visual mode. The two equal time intervals were 6 seconds in duration, and the short inboard and outboard episodes of auditory or visual stimulation 2 seconds of either acoustic 'beeps' or of a black square appearing on the monitor screen. It is emphasised that the intervals and the inboard and outboard episodes were strictly in accord with the spatial sequence shown in Figure 1F. Nine participants judged durations in both the auditory and visual conditions. The psychophysical procedure and data analysis were the same as for the spatial illusion. The outcomes of this experiment were also clear-cut. The 6-second interval with 2-second outboard episodes appeared consistently longer than the same interval with inboard episodes. In other words, the M-L illusion occurred over time. Indeed, the illusion is so strong for some participants that they believe that they are being tricked.
It should be pointed out that this is by no means the first evidence for a close association between perceived space and time. Indeed, almost a century ago it was demonstrated that visual judgments of extent are affected by the temporal conditions under which the judgments are made, the tau effect, and judgments of time by the spatial conditions, the kappa effect (see Jones & Huang, 1982 for a review). More recently, Morgan, Findlay and Watt (1982) and Day and Duffy (1988) found that when the conventional form of the M-L figure was progressively exposed by passing it behind a narrow aperture, apparent extent was strongly influenced by the time for which each component was exposed. However, the experiments described here with the highly simplified M-L form are, as far as can be ascertained, the first to show that the same illusion occurs over space and time.
Explanation of illusions of spatial extent and temporal duration
To summarise to this point, the M-L illusion occurs in all the stimulus arrangements shown in Figure 2 and in the in the simplified arrangement shown in Figure 1B consisting of an acute angle and an obtuse angle. It also occurs over space in both the visual and haptic modes in Figure 2F and over time in the temporal equivalent of this figure in both the visual and auditory modes.
How then can this remarkably robust illusion be explained? Consideration of Figure 1B suggests a relatively simple answer to this question. As pointed out above, in Figure 2F both lines forming the acute angle appear to be shorter than both those forming the obtuse angle. It can be seen that the acute angle itself is smaller in overall extent than the obtuse angle or, more simply, the acute-angle figure takes up less space than the obtuse angle. It is proposed that the apparent extents of the lines forming the angles are compromised by the size of the figures of which they are intrinsic parts. In other words, the size of the whole figure determines the apparent size of its intrinsic components. In all the versions of the M-L figure in Figure 2, the apparently shorter components with the terminal elements inboard of the fixed space are smaller overall than those with the elements outboard of an equal space. Thus, the key to the illusion is the overall size of the figure. It can therefore be assumed that the effect of the terminal elements inboard and outboard of equal spaces is to render the figures smaller and larger respectively.
In making this proposal it must be pointed out that it not new. It was first proposed by Müller-Lyer himself in his original paper and later by Max Wertheimer (1923) when he stated: “There are wholes, the behaviour of which is not determined by that of their individual elements, but where the part processes themselves are determined by the intrinsic nature of the whole”. However, in neither of these early formulations was the concept of the whole time in a temporal sequence considered. The overall times have the same effect on apparent durations as that of overall size in the spatial illusion.
In conclusion, two additional points should be made. First, this explanation is not confined to the many forms of the M-L effect. It applies to a wide range of other size illusions, in particular to the Sander parallelogram effect shown in Figure 3A and the Delboeuf circles in Figure 3B. In both figures the overall size of the figure determines the apparent size of its intrinsic parts. The equal diagonals in the Sander figure are intrinsic parts of a large and a small parallelogram, and the circles of the same size in the Delboeuf figure parts of large and small 'rings'.
Day, R.H. & Duffy, F.M. (1988). Illusions of time and extent when the Müller-Lyer figure moves in an aperture. Perception & Psychophysics, 44, 205-210.
Jones, B. & Huang, Y.L. (1982). Space-time dependencies in psychophysical judgment of extent and duration: Algebraic models of the tau and kappa effects. Psychological Bulletin, 91, 128-142.
Lloyd, S.P. (2000). The Müller-Lyer effect for temporal duration in auditory and visual modes. Honours thesis, School of Psychological Science, La Trobe University, Melbourne.
Morgan, M.J., Findlay, J.M. & Watt, R.J. (1982). Aperture viewing: A review and a synthesis. Quarterly Journal ofExperimental Psychology, 34A, 211-233.
Müller-Lyer, F.C. (1889). Optische urteilstauschungen. Archiv für Anatomie und Physiologie, Physiolische Abteilung, 2 (Supplement). 253-270, (See translation by Day, R.H. & Knuth, H. (1981). The contributions of F.C. Müller-Lyer. Perception, 10, 126-146).
Mulvihill, C.(2000). A comparison of the visual and haptic Müller-Lyer illusions using a variant of the Müller-Lyer figure. Honours thesis, School of Psychological Science, La Trobe University, Melbourne.
Wertheimer, M. (1923). Untersuchungen zur Lehre von der Gestalt, II. Psychologische Forshung, 4, 301-350.