A multidimensional scaling model for the size-weight illusion

The kinds of individual differences in perceptions permitted by the weighted euclidean model for multidimensional scaling (e.g., INDSCAL) are much more restricted than those allowed by Tucker's Three-mode Multidimensional Scaling (TMMDS) model or Carroll's Idiosyncratic Scaling (IDIOSCAL) model. Although, in some situations the more general models would seem desirable, investigators have been reluctant to use them because they are subject to transformational indeterminacies which complicate interpretation. In this article, we show how these indeterminacies can be removed by constructing specific models of the phenomenon under investigation. As an example of this approach, a model of the size-weight illusion is developed and applied to data from two experiments, with highly meaningful results. The same data are also analyzed using INDSCAL. Of the two solutions, only the one obtained by using the size-weight model allows examination of individual differences in the strength of the illusion; INDSCAL can not represent such differences. In this sample, however, individual differences in illusion strength turn out to be minor. Hence the INDSCAL solution, while less informative than the size-weight solution, is nonetheless easily interpretable.This paper is based on the first author's doctoral dissertation at the Department of Psychology, University of Illinois at Urbana-Champaign. The aid of Professor Ledyard R Tucker is gratefully acknowledged.     

An experimental test of two mathematical models applied to the size-weight illusion.

Two quantitative models, which make different quantitative predictions for the amount of the size-weight illusion, were tested according to the psychophysical methods employed by the respective authors (magnitude estimation versus category ratings). Both models with their corresponding method were supported. This causes uncertainty over Anderson's chaim that the validity of both a model and the applied scale used is sufficiently test by the socalled joint testing procedure.     

Lifting movements in the size-weight illusion

The occurrence of the size-weight illusion is related to the manner in which-objects are lifted. When the SWI occurs, the larger of two objects of equal objective weight is usually lifted with greater acceleration, deceleration, and maximum velocity than the smaller one, but to approximately the same height. These differences are not present when the cans feel equally heavy. The relationship of lifting movements to judgments is consistent with the known behavior of proprioceptors which provide sensory input about muscular and movement events.     

Mechanical advantage in the size-weight illusion

When a hand-held object is lifted by wrist flexion, the lifting system composed of muscles, bones, and the object lifted constitutes a third-class lever. Therefore, objects require greater lifting force as they are supported further distally The small can of the DeMoors size-weight illusion cans is usually supported further distally than the large one, possibly influencing their relative perceived weight When Ss are required to lift the small can through a shorter lever than the large one, there is a significant shift of judgments toward a reversal of the SWI in a paired-comparison situation. It is concluded that mechanical advantage does influence weight judgments and that biomechanical factors should be considered whenever weight judgments are made.     

Application of the method of fixed set to the size-weight illusion

Summary The method of fixed set (Uznadze, 1966) was applied to the size-weight illusion. After the repeated lifting of a small, heavy stimulus and a large, light one with both hands simultaneously, the size-weight illusion diminished. It increased after lifting a small, light stimulus and a large, heavy one. These changes in perception were explained as contrast effects caused by the sets which were fixed during the preceding lifts. The same method was applied to the weight-size illusion and the contrast effect was observed in some cases. The results of the application of the fixed-set method to the size-weight illusion and to the visual size perception were compared. All the results showed analogous patterns of conflicting states between the temporarily fixed set and the set that the subject prepares naturally for perception, such as the size-weight illusion. By way of conclusion, the size-weight illusion was assumed to be a kind of contrast effect in the light of Uznadze's theory of set.     

Charpentier (1891) on the size-weight illusion

This paper offers background for an English translation of an article originally published in 1891 by Augustin Charpentier (1852-1916), as well as a summary of it. The article is frequently described as providing the first experimental evidence for the size-weight illusion. A comparison of experiments on the judged heaviness of lifted weights carried out by Weber (1834) and by Charpentier (1891) supports the view that Charpentier's work deserves priority; review of other experimental studies on the size-weight illusion in the 1890s suggests that the idea that the illusion depended on "disappointed expectations," especially with respect to speed of lift, became dominant almost immediately following the publication of Charpentier's paper. The fate of this and other ideas, including "motor energy," in 20th-century research on the illusion is briefly described.     

Body-based perceptual rescaling revealed through the size-weight illusion

An embodied approach to the perception of spatial layout contends that the body is used as a 'perceptual ruler' with which individuals scale the perceived environmental layout. In support of this notion, previous research has shown that the perceived size of objects can be influenced by changes in the apparent size of hand. The size-weight illusion is a well known phenomenon, which occurs when people lift two objects of equal weight but differing sizes and perceive that the larger object feels lighter. Therefore, if apparent hand size influences perceived object size, it should also influence the object's perceived weight. In this study, we investigated this possibility by using perceived weight as a measure and found that changes in the apparent size of the hand influence objects' perceived weight.     

Psychophysical scales of apparent heaviness and the size-weight illusion

The apparent heaviness of a set of 40 cylindrical objects was scaled by the method of magnitude estimation. The objects varied in weight, volume. and density. There were three main conclusions: (1) For any constant volume, heaviness grows as a power function of weight; the larger the volume. the larger the exponent of the power function. The family of such power functions converge at a common point in the vicinity of the heaviest weight that can be lifted. (2) For any constant density (i:e., weight proportional to volume), heaviness does not grow as a power function of weight. (3) For any constant weight, heaviness decreases approximately as a logarithmic function of volume; the constants of the log function depend systematically on the weight of the object. The outcome furnishes a broad quantitative picture of apparent heaviness and of the size-weight illusion (Charpentier’s illusion).     

The size-weight illusion in 2-D nonlinear psychophysics

An extension of unidimensional nonlinear psychophysics is postulated by using forms of cross-coupling between the parameters of the two single-channel recursions, which have already been shown to model some perceptual phenomena. The size-weight illusion is shown to be reproducible in the topology of its relations, and it is suggested that some so-called illusions are in fact the natural consequences of nonlinear cross-coupling. The conditions that produce the illusion involve partially compensating the cross-coupling of sensory dimensions, and a second equilibrium with no cross-coupling, resembling simpler veridical perception, also exists in the behavior of some subjects.     

The role of preparatory muscular tension in the size-weight illusion

Muscle action potentials were recorded from lifting muscles during the foreperiod before lifts of large and small objects when the size-weight illusion occurred. There were increases in tension throughout the foreperiod of both lifts, culminating in a large increase following the instruction to lift. The increases were greater before lifts of the large can, supporting the peripheral theory of comparative weight judgment. The “set to lift” effect was shown to exist in the action potentials before the foreperiod of the second lift when compared to those just prior to the lift of the first can.     

Independence and separability of volume and mass in the size-weight illusion

Numerous size-weight illusion models were classified in the present article according to general recognition theory (Ashby & Townsend, 1986), wherein the illusion results from a lack of perceptual separability, perceptual independence, decisional separability, or a combination of the three. These options were tested in two experiments in which a feature-complete factorial design and multidimensional signal detection analysis were used (Kadlec & Townsend, 1992a, 1992b). With haptic touch alone, the illusion was associated with a lack of perceptual and decisional separability. When the participant viewed the stimulus in his or her hand, the illusion was associated only with a lack of decisional separability. Visual input appeared to improve the discrimination of mass, leaving only the response bias due to expectation.     

The role of haptic versus visual volume cues in the size-weight illusion

Three experiments establish the size-weight illusion as a primarily haptic phenomenon, despite its having been more traditionally considered an example of vision influencing haptic processing. Experiment 1 documents, across a broad range of stimulus weights and volumes, the existence of a purely haptic size-weight illusion, equal in strength to the traditional illusion. Experiment 2 demonstrates that haptic volume cues are both sufficient and necessary-for a full-strength illusion. In contrast, visual volume cues are merely sufficient, and produce a relatively weaker effect. Experiment 3 establishes that congenitally blind subjects experience an effect as powerful as that Of blindfolded sighted observers, thus demonstrating that visual imagery is also unnecessary for a robust size-weight illusion. The results are discussed in terms of their implications for both sensory and cognitive theories of the size-weight illusion. Applications of this work to a human factors design and to sensor-based systems for robotic manipulation are also briefly considered.     

The role of expectancies in the size-weight illusion: A review of theoretical and empirical arguments and a new explanation

The size–weight illusion (SWI) refers to the phenomenon that objects that are objectively equal in weight but different in size or volume are perceived to differ in weight, such that smaller objects feel heavier than larger ones. This article reviews studies trying to support three different viewpoints with respect to the role of expectancies in causing the SWI. The first viewpoint argues for a crucial role; the second admits a role, yet without seeing consequences for sensorimotor processes; and the third denies any causal role for expectancies at all. A new explanation of the SWI is proposed that can integrate the different arguments. A distinctive feature of the new explanation is that it recognizes the causal influence of expectancies, yet combines this with certain reactive and direct behavioral consequences of perceiving size differences that are independent of experience-based expectancies, and that normally result in the adaptive application of forces to lift or handle differently sized objects. The new account explains why the illusion is associated with the repeated generation of inappropriate lifting forces (which can, however, be modified through extensive training), as well as why it depends on continuous visual exposure to size cues, appears at an early age, and is cognitively impenetrable.     

An illusion of movement complementary to the horizontal-vertical illusion

Blindfolded subjects moved a stylus held in the hand over a standard distance of 4.5 ins. in a given direction. They then attempted to move the same distance in a direction at right angles to the first. Eight combinations of movements were investigated. The results reveal an illusion such that the extent of movements to left or right across the body is underestimated, while the extent of movements towards or away from the body in the mid-line is overestimated. The illusion applies to speed as well as extent of movement. Movement up or down in a vertical plane is equivalent to movement towards or away from the body in a horizontal plane.

The interaction of this illusion with the well-known horizontal-vertical illusion of visual perception explains a failure to find any net illusory effect where lines visually displayed in different orientations were matched for length by unseen movements in similar orientations.

Whether the visual and movement illusions simply co-exist or whether they are functionally related is not yet clear.     

A static geometrical illusion contributes largely to the footsteps illusion

When a black and a white rectangle drifts across a stationary striped background with constant velocity, the rectangles appear to alternately speed up and slow down. Anstis (2001, Perception 30 785-794; 2004, Vision Research 44 2171-2178) suggested that this 'footsteps' illusion is due to confusion between contrast and velocity signaling in the motion detectors of the human visual system. To test this explanation, three experiments were carried out. In experiment 1, the magnitudes of the footsteps illusion in dynamic and static conditions was compared. If motion detectors play an important role in causing the illusion, it should be reduced in the static condition. Remarkably, however, we found that the illusory misalignment between the black and the white rectangle was even more prominent in the static condition than in the dynamic condition. In experiment 2, we measured the temporal-frequency properties of the footsteps illusion. The results showed that the footsteps illusion was tuned to low temporal frequencies. This suggests that the static illusory misalignment can contribute sufficiently to the dynamic illusory misalignment. In experiment 3, the magnitude of the illusion was measured with the rectangles drifting on a temporally modulated background instead of a spatially modulated background. If contrast affects the apparent velocity of the rectangles, temporal modulation of a uniform background should also cause the footsteps illusion. However, the results showed that the magnitude of the illusion was much reduced in this condition. Taken together, the results indicate that the footsteps illusion can be regarded as a static geometrical illusion induced by the striped background and that motion detectors play a minor role at best.