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.     

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.     

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).     

Averaging model applied to the size-weight illusion

A theoretical model was given for the size-weight illusion based on a principle of information integration. Judged heaviness of lifted weights was assumed to be an average of two pieces of information, weight and size, with the latter receiving negative weighting in the model formulation. Two experiments based on a Weight by Size design gave fair support to the parallelism prediction of the integration model. The hypothesis that Ss were really judging density was shown to imply a divergence prediction, contrary to the data. The theoretical analysis was generalized to include negative, positive, and comparative illusions; these were differentiated according to whether the contextual information was integrated with negative weighting, positive weighting, or served as a yardstick of judgment.     

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.     

A process-dissociation analysis of semantic illusions

We examine semantic illusions from a dual-process perspective according to which the processes that go into failing or succeeding to detect such illusions can be decomposed into controlled processes (checking the facts in the sentence against the information in memory) and automatic processes (the impression of truth that comes from the semantic associations between the elements in the sentence). These processes, we argue, make largely independent contributions to truth judgments about semantic-illusory sentences. The Process Dissociation Procedure was used to obtain estimates of these two kinds of processes. In Study 1, participants judged whether sentences were true or false while under high or low cognitive load. Cognitive load increased the rate of semantic illusions by specifically affecting controlled processing but not automatic processing. In Study 2, a previous paired-associate learning task also increased the rate of semantic illusions, but it did so by specifically affecting automatic processing, not controlled processing.     

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.     

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.     

Idealism and illusions

According to the idealist, facts about phenomenal experience determine facts about the physical world. Any such view must account for illusions: cases where there is a discrepancy between the physical world and our experiences of it. In this article, I critique some recent idealist treatments of illusions before presenting my own preferred account. I then argue that, initial impressions notwithstanding, it is actually the realist who has difficulties properly accounting for illusions.     

Illusory illusions: the significance of fixation on the perception of geometrical illusions

Some well-known geometrical illusions disappear when the eyes are fixating and saccades are suppressed for a period of time. This disappearance is not accompanied by fading due to stabilisation of the retinal image. Any saccade made on purpose restores the illusion immediately. The fixation time after which some illusions disappeared was measured for four illusions and four subjects each. Effects of practice have been observed after measurements were repeated on successive days. Present theories of vision cannot readily explain the effect.     

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.     

A mathematical theory of optical illusions and figural aftereffects

If it is assumed that spurious enhancement of receptive field excitations near the intersection of image lines on the retina contributes to the cortical determination of the geometry of two-dimensional figures, an equation based on the least-squares fit of data points to a straight line-can be obtained to represent theapparent line. Such a fit serves as anextreemum on the precision with which a data set can be represented by a straight line. The disparity between theapparent line and the actual line that occurs in the case of peripheral (and to a lesser degree in more central regions of the retina) vision is sufficient to produce the perceptual errors that occur in the Poggendorff, Hering, and Mueller-Lyer illusions. The magnitude of the Poggendorff illusion as a function of the line angle is derived and experimentally tested. Blakemore, Carpenter, and Georgeson’s (1970) experimental data on angle perception are shown to fit this same function. Theapparent curve is derived for the Hering illusion. The Mueller-Lyer illusion is found to be a variation of the Poggendorff illusion. The equations are further developed and used to derive Pollack’s (1958) experimental results on figural aftereffects. The results involve onlyone experimentally determined coefficient that can be evaluated, within the limits of experimental error, in terms of physiological data. The use of these concepts provides a foundation for the abstract modeling of the initial phases of the central nervous system data reduction processes, including receptive field structure, that is consistent with the physiological limitations of the retina as a source of visual data, as well as with the findings of Hubel and Wiesel (1962).     

A criticism of the diffraction theory of some geometrical illusions

Chung Chiang (1968) invoked diffraction in the eye to explain Poggendorff’s illusion and extended the discussion to account for other geometrical illusions produced by intersecting lines. But diffraction in the eye cannot account for the displacement and rotation of lines assumed by Chung to produce Poggendorff’s illusion. And even if displacement and rotation do occur, the theory does not account for all illusions of the type considered. I am grateful to R. H. Day and M. Coltheart for critically reading a draft of this paper.     

Imagery and memory illusions

This article provides a summary of current knowledge about memory illusions. The memory illusions described here focus on the recall of imagined events that have never actually occurred. The purpose is to review theoretical ideas and empirical evidence about the reality-monitoring processes involved in memory illusions. Reality monitoring means deciding whether the memory has been perceptually derived or been self-generated (thought or imagined). A few key findings from the literature have been reported in this paper and these focus on internal source-monitoring judgments which distinguish perceptual events from imagined events. Finally, the experimental paradigms used to shed light on processes occurring in the failure of reality monitoring in healthy subjects may be extended to an examination of the causes and the prevention of hallucinations in patients.     

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.