A reexamination of the size weight illusion induced by visual size cues

Transcription

1 Exp Brain Res (2007) 179: DOI /s RESEARCH ARTICLE A reexamination of the size weight illusion induced by visual size cues Satoru Kawai Frank Henigman Christine L. MacKenzie Alex B. Kuang Paul H. Faust Received: 7 September 2005 / Accepted: 13 November 2006 / Published online: 30 November 2006 Springer-Verlag 2006 Abstract The size weight illusion induced by visually perceived sizes was reexamined to investigate whether this illusion is a sensory based or cognitive-based phenomenon. A computer-augmented environment was utilized to manipulate visual size information of target objects independently of their haptic information. Two physical cubes of equal mass (30.0 g) and size ( cm) were suspended in parallel by wires attached to small graspable rings, in order to keep haptically obtained information constant between lifts. Instead of directly seeing each physical cube, subjects viewed 3D graphics of a cube with a wire and a ring that were precisely superimposed onto each physical cube. Seventeen subjects vertically lifted these augmented cubes, one after the other, by grasping the attached rings, and then reported their perception of cube heaviness. The graphical size of a comparison cube pseudo randomly varied for every comparison from to cm, while that of a standard cube remained constant ( cm). S. Kawai (&) Faculty of Psychology and Welfare, Tezukayama University, Gakuen-Minami, Nara, Japan , skawai@tezukayama-u.ac.jp F. Henigman C. L. MacKenzie Human Motor Systems Laboratory, School of Kinesiology, Simon Fraser University, Burnaby, Canada A. B. Kuang Internet Explorer, Microsoft Corporation, Redmond, WA, USA P. H. Faust Professor Emeritus, Tezukayama University, Nara, Japan Results indicated that the size weight illusion frequently and systematically occurred for all the subjects such that when the comparison cube was relatively smaller than the standard cube, it was perceived to be heavier, and vice versa. As the size diverence increased between the standard cube and the comparison cube, more subjects experienced the illusion, and vice versa. Follow-up tests showed occurrence of the size weight illusion was signiwcantly correlated with subject s sensitivity to discriminate weight, but not with sensitivity to discriminate visual size. Results suggest that the size weight illusion induced by only visual size cues in an augmented environment is sensory based, and depends on an individual s integrated perception based on multimodal sensory information. Keywords Heaviness perception Size Weight Vision Virtual environments Augmented objects Introduction When two objects of equal weight but diverent sizes are lifted, the smaller object is normally perceived as heavier than the larger object. This size weight illusion (Charpentier 1891) may derive from haptically and/or visually acquired size information, and/or from a subject s expectation or previous experience. That is, when blindfolded subjects directly grasp and lift two objects of equal weight but of unequal size to compare heaviness, the size weight illusion generally occurs (Ellis and Lederman 1993; Kawai 2002b, 2003b). The same is true of congenitally blind subjects (Rice 1898; Ellis and Lederman 1993). The size weight illusion may also occur, as long as subjects are allowed to view

2 444 Exp Brain Res (2007) 179: objects, even when haptically acquired size cues remain constant, for instance, when test objects are lifted by using hook handles, wire, or a grip apparatus with constant grasp-span attached to diverent-sized cubes (Charpentier 1891; Pick and Pick 1967; Davis and Roberts 1976; Masin and Crestoni 1988; Ellis and Lederman 1993; Gordon et al. 1991a; Mon-Williams and Murray 2000; Flanagan and Beltzner 2000; Flanagan et al. 2001). Similarly, KoseleV (1957) documented the size weight illusion when subjects compared an object s heaviness while viewing it through convex or concave lenses, thus altering its visual size. Psychophysicists and psychologists have long discussed whether the size weight illusion is due to sensory based or cognitive-based events (Jones 1986). In the former, the phenomenon occurs due to the direct integration of weight information with the size information concurrently obtained, whether through visual or haptic senses, during lifting of an object. The Information Integration theory is based on this idea (Sjöberg 1969; Anderson 1970). In the latter view, the phenomenon occurs due to some cognitive process in the perception of heaviness, such as expectation or rationalization based on the visual size of the target objects (Ross 1969; Mon-Williams and Murray 2000; Flanagan and Belzner 2000). With regard to the size weight illusion induced by haptically perceived size, evidence that this phenomenon is sensory based has been provided in a series of the studies involving the lifting of cubes with a precision grasp using the pads of the thumb and index Wnger (Kawai 2002a, b, 2003a, b). Kawai (2003b) indicated that haptically perceived size is constantly and systematically integrated with weight information to form one s perception of heaviness. That is, when a test subject lifts individual cubes to judge heaviness without viewing them, the perceived heaviness is expressed as a ratio of width-to-weight of the cube. He concluded that heaviness perception is not based simply on the physical weight of an object (Kawai 2003a), but that haptically obtained size information is a critical factor contributing to the judgment of heaviness (Kawai 2003b). On the other hand, determining whether the size weight illusion induced by visually perceived size information is sensory based or cognitive-based has been controversial (Ross 1969; Masin and Crestoni 1988; Mon-Williams and Murray 2000; Flanagan and Beltzner 2000). Ross (1969) proposed, as dewned by Expectation theory, that the illusion is the result of a measuring system that takes into account the expected value of an object. For instance, it is a common expectation that the larger of two objects should be heavier than the smaller one. The idea of expectation explains why people generate larger grip and lift forces when lifting larger objects than when lifting smaller objects of the same weight (Gordon et al. 1991a) and describes the size weight illusion as a product of the mismatch between the expected weight and the sensory feedback obtained from the object s actual weight following liftov. Expectation theory, Wrst proposed by Flournoy (1894), is supported by studies observing erroneously programmed motor outputs, as measured by lift velocity (Davis and Roberts 1976), EMG activity in muscles responsible for lifting movements (Davis and Brickett 1977), and peak load and grip force rates (Gordon et al. 1991a, b). These studies have consistently hypothesized that such a mismatch between initial motor commands and feedback from the true weight of the objects might result in perceiving heaviness diverently depending on object size. That is, generating greaterthan-necessary forces for lifting may result in the perception of reduced heaviness, and vice versa. Recent articles, however, have refuted Expectation theory by demonstrating that there is no signiwcant relation between the experienced illusion and erroneously programmed forces (Mon-Williams and Murray 2000; Flanagan and Beltzner 2000; Flanagan et al. 2001). Using a methodology similar to that of Gordon et al. (1991a), Mon-Williams and Murray (2000) investigated, on a trial by trial basis, whether or not subjects reported the larger object to be perceived as lighter than the smaller object while greater forces were applied to the larger object. Their Wndings suggested that there is no close relation between produced forces and verbal reports. The researchers thus concluded that erroneous motor programming is neither necessary nor suycient to produce the size weight illusion. They proposed that, instead of Expectation theory, the size weight illusion induced by visual size cues arises due to a cognitive process in which the subjects form an awareness that the objects have the same weight and so attempt to rationalize, at a cognitive level, the discrepancy between the awareness that the objects are the same in weight and the actual sensory feedback in which the objects are perceived to vary in weight. Flanagan and Beltzner (2000) had subjects grasp a grip apparatus and repeatedly lift two boxes of unequal size but equal weight. While subjects initially generated excessive grip and load forces for the larger object and relatively insuycient forces for the smaller object, they learned to scale their forces equally for the two objects after Wve to ten alternating lifts. Despite this motor adjustment leading subjects to apply equal and appropriate forces to the two objects, the size weight illusion persisted. This provided further evidence against

3 Exp Brain Res (2007) 179: Expectation theory although neither study presented any convincing evidence that the size weight illusion is cognitive-based. Masin and Crestoni (1988), in contrast, insisted that the visually induced size weight illusion was a consequence of sensory origins, as seen in the Information Integration theory (Sjöberg 1969; Anderson 1970). They had subjects estimate the weight of objects after pulling down on a ring attached by a wire tied to the target object and fed through a pulley. The size weight illusion occurred only when the subjects were allowed to view the objects while lifting, but not when there was an absence of visual size cues. This observation was consistent with Flournoy (1894), who requested subjects to close their eyes prior to lifting an object with a hook handle, and with Ellis and Lederman (1993), who requested blindfolded subjects to lift cubes suspended on wires. Masin and Crestoni (1988) furthermore demonstrated that the size weight illusion did not arise when a delay existed between when subjects saw the target objects and when they lifted them. Consequently, they argued against Expectation theory, reasoning that any cognitive expectation should persist even after a once-viewed object disappears from view. Masin and Crestoni, instead, supported the Information Integration theory (Sjöberg 1969; Anderson 1970), in which the size weight illusion arises by direct integration of size information with weight information. Thus, as Wndings relating to the visually induced size weight illusion are few and contradictory (Pick and Pick 1967; Ross 1969; Masin and Crestoni 1988; Ellis and Lederman 1993), it appeared essential to reconsider the fundamental question of how the visually induced size weight illusion occurs among subjects. The premise for the experiments reported here, therefore, was a simple and methodical observation of the visually induced size weight illusion, focusing on such questions as (1) whether or not the visually induced size weight illusion was commonly experienced by all subjects; (2) whether or not visually acquired size cues inxuenced heaviness perception in a similar manner to the haptically acquired size cues; (3) how susceptibility to the visually induced size weight illusion divered amongst the diverent subjects; (4) what individual factors were related to susceptibility to the visually induced size weight illusion and (5) whether or not the erroneously programmed motor commands were related to the occurrence of this illusion. The present study sought to determine whether the visually induced size weight illusion is a cognitivebased or sensory-based event. In addition, we analyzed whether the size weight illusion was related to individual sensitivity to weight discrimination or size discrimination. Finally, we discussed how the size weight illusion occurs in both the perceptual system and the motor system. Materials and methods Subjects Seventeen adults (9 men and 8 women), aged from 20 to 49 years (M = 29.0, SD = 7.4), participated after providing informed consent. The local university ethics committee approved the ethics of the human research. All subjects were right-handed (OldWeld 1971), and none of them exhibited any visual, muscular, or cutaneous problems. In addition, none of the subjects had any previous experience with the experimental tasks nor were they familiar with the hypotheses being tested. Augmented environment Methodologically, an augmented environment allowed for strict isolation of the evect of visual size cues from associated physical and haptic evects, e.g., weight, density, center of gravity, mass distribution, inertia tensor, and haptically perceived size, which avect perceived heaviness more strongly than visual size cues in the size weight illusion (Ellis and Lederman 1993; Amazeen and Turvey 1996; Amazeen 1999; Kawai 2002b). However, all these haptic evects could be kept constant between the standard and comparison stimuli in the augmented environment, since two cubes with identical physical properties were used (30.0 g in mass, cm in size). Therefore, the present study could concentrate solely on the evect of visual size, through graphically augmenting the size of cubes, while other physical and haptic information was kept constant. A schematic drawing of the augmented environment used in these experiments is shown in Fig. 1. The methodological details and original graphic software of the Virtual Hand Laboratory (Simon Fraser University, Canada) have been described previously (Summers 1999; Kawai et al. 2002). Two acrylic physical rings were suspended on 0.01 cm diameter piano wire so that they were 14.0 cm apart and parallel to each other at a height of 14.0 cm beneath a semi-silvered mirror (D in Fig. 1) and 15.0 cm above the table surface. These rings were 0.3 cm in thickness and 1.7 cm in outside diameter and well Wtted the center of the pads of thumb and index Wngers. Subjects established stable precision grasps on the ring during repeated lifting of a test object without

4 446 Exp Brain Res (2007) 179: Fig. 1 Illustration of the augmented environment of the Virtual Hand Laboratory. Subjects were presented with two stereo images (G dotted line) using crystal eyes stereographic goggles (C) and a monitor (A) viewed through a semi-silvered mirror (D). An OPTOTRAK system (B) tracked infrared markers (E) attached to the physical wires of the physical cubes (F) and the goggles (C), and these 3D position data were used to create a graphical image (G) and to analyze the lifting speed for each cube. The physical cubes (F) of identical size ( cm cube) and of identical mass (30.0 g) were invisible to the subjects. While the graphical size (G) of the standard cube placed on the left-hand side of each subject was constant (a cm cube), that of the comparison cube placed on the right-hand side varied from to cm micro-slips, distortion, sweating, or wear and tear on the support surface of their Wngers, eliminating factors that might otherwise avect perceived heaviness (Westling and Johansson 1984; Flanagan et al. 1995). Two physical cubes (F in Fig. 1) of identical size ( cm) and mass (30.0 g) were suspended on sigmoid hooks that were themselves attached to the rings by thin piano wire. Cubes were acrylic boxes whose weight was adjusted by the addition or subtraction of cotton and granular lead. Weight was measured on a digital precision weight scale ( 0.01 g, TANITA, TKP-100, Tokyo, Japan). The distance from the lower edge of the physical ring to the top surface of the physical cube was 4.0 cm. The initial orientation for physical rings was adjusted to approximately 135 relative to the anterior posterior axis respectively so that the subjects, who were all right-handed, could grasp them with the thumb and index Wnger in a natural manner. Computer-generated graphic cubes, rings and wires were displayed on a computer monitor (A in Fig. 1) positioned face-down over the semi-silvered mirror (D in Fig. 1). The size of graphical rings was the same as the physical rings. Images were created independently for the left and right eye, based on subject-speciwc inter-ocular distance measurements, to create the impression of 3D objects when viewed with crystal eyes liquid crystal shutter stereoscopic goggles (Stereo Graphics, San Rafael, CA; C in Fig. 1). Images were rendered at 60 Hz in stereo and goggles were shuttered at 120 Hz to deliver 60 images per second to left and right eyes. An OPTOTRAK 3D motion analysis system with two position sensors (Northern Digital Inc., Waterloo, Canada: B in Fig. 1) allowed for continuous measurement of the 3D position of infrared light emitting diodes (LED; E in Fig. 1) mounted on each physical wire and on the goggles, allowing images to be rexected in the mirror in such a way that the graphic objects were head-coupled, stereoscopic, and accurately superimposed over the physical objects in the workspace between the table and half-silvered mirror. 3D position data were detected and transmitted to the master SGI (Silicon Graphics Indigo II workstation) sampling at 60 Hz. The total time required for the system to sample the LED s position, calculate the object s position and orientation in space, and display the graphical cube was no greater than two to three frames at 60 Hz. All LED position data were measured in millimeters. The size of the workspace in which both the graphical cubes and physical cubes coexisted was approximately cm; an area that easily encompassed the lifting tasks in the present study. The vertical displacement signals from both physical cubes were also recorded during lifting at a frequency of 100 Hz through the OPTOTRAK motion analysis system, from which the peak velocity for each lifting movement was calculated. An occluder was in place beneath the semi-silvered mirror so that neither the physical objects nor the hand of the subjects could be seen. The 3D graphical cubes were adjusted on the basis of subject s point of view to keep object shape constant so that each of the subjects was able to see each graphical cube as a cubic shape from their individual point of view during trials. A diverent color, i.e., red, yellow, green, was used for each surface of the graphical cubes so that subjects perceived them as cubic because a single-colored graphic cube would be perceived as a 2D hexagonal shape. No outlines were added in a diverent color on the surface borders of the graphical cube since the Necker cube illusion could possibly occur (Butler and McManus 1998). The graphical rings and wires (4.0 cm in length) were both ov-white in color, and the background was black. No other graphics evects such as lighting, shading, or texture were added to the graphical image, in order to isolate the evect of visually perceived object size. The size of the graphical cubes was adjustable from to cm, in 0.1 cm increments.

5 Exp Brain Res (2007) 179: As previously described (Summers 1999; Kawai et al. 2002), the properties of these graphically augmented objects are such that they are perceived stereoscopically to be 3D, touchable, and as having weight. Subjects, therefore, have a strong sense of presence and feel as if they are manipulating the perceived graphical image rather than an invisible physical object. As a result, it has been reported that both forceproduction strategy and heaviness perception in an augmented environment are similar to those in a physical environment (Kawai et al. 2002). Procedure The present study relied on one main experiment to investigate the frequency of occurrence of the visually induced size weight illusion using a broad range of volumes, and one supplementary experiment to re-evaluate the relation between the motor program and the illusion. In addition, two brief tests were conducted to determine subject s sensitivity to discriminate weight and size respectively. All experiments took place within the augmented environment of the Virtual Hand Laboratory. Subjects sat in a height-adjustable chair facing an augmented environment (Fig. 1). After putting on the liquid crystal shutter goggles, the laboratory was semidarkened to calibrate the equipment for the subject s point of view and hand workspace. Subjects conwrmed that two 3D graphical cubes suspended by graphical wire and graphical rings existed in parallel in the workspace in front of them. Upon presentation of the two augmented cubes, each subject was requested to grasp the augmented ring of the standard augmented cube (the cube suspended on the left-hand side of the workspace) using the tips of their thumb and index Wnger of the right hand, and to lift. The vertical lift of the standard cube that followed was accomplished with a single Xowing movement to a height of approximately 5 cm, to allow for processing of its perceived heaviness. As soon as the standard cube was back in its original position, the comparison cube, located on the right-hand side of the workspace, was lifted in exactly the same manner. Finally, subjects were requested to state whether they perceived the comparison cube to be Heavier, Lighter, or Similar in comparison to the standard cube. Subjects were instructed to maintain as constant a lifting speed as possible at all times. To facilitate this, each subject was permitted from Wve to ten practice lifts at the beginning of the experiment to become accustomed to the augmented environment, to allow them to properly reach for and grasp the graphically augmented ring and to maintain a stable lifting speed. In addition, they were requested to continually observe the target cube without closing or turning their eyes away from it during the lifting procedure. In the main experiment, the graphical size of the comparison cube (30.0 g) was pseudo randomly varied from a minimum of cm to a maximum of cm (hereafter referred to as the 1.0 and 9.0 cm cube, respectively) while the graphical size of the standard cube (30.0 g) was constant (5.0 cm cube) throughout the experiment. Each subject performed a total of 64 trials with 25 levels for size. As trials in the present study were limited, the trials were reduced to minimize fatigue among the subjects as much as possible. It was reported that subjects could generally experience the size weight illusion when the size diverence was suycient between the standard cube and the comparison cube (Kawai 2003a). Thus, trials were predetermined as follows; one trial for diverences of more than 2.5 cm between the standard and comparison cube [9.0, 8.5, 8.0, 7.5, 2.5, 2.0, 1.5, and 1.0 cm cube], two trials for diverences from 1.0 to 2.0 cm [7.0, 6.5, 6.0, 4.0, 3.5, and 3.0 cm cube], four trials for diverences of less than 1.0 cm [5.8, 5.6, 5.4, 5.2, 5.1, 4.9, 4.8, 4.6, 4.4, and 4.2 cm cube], and four trials for the identical size condition [5.0 cm cube]. Based on the relative size for the standard 5.0 cm cube, trials were allotted into three conditions, i.e., the Smaller condition ( cm cube for the comparison), the Identical condition (5.0 cm cube), and the Larger condition ( cm cube). Following the main experiment, a supplementary experiment was immediately performed to record 3D position data of the augmented cubes during the lifting movement. The subjects performed 12 trials in the same manner as for the main experiment. That is, they were required to judge the perceived diverence in heaviness between the standard cube and the comparison cube. The sizes of the comparison cubes used in this experiment were 7.5 cm for two trials and 6.0 cm for two trials each (Larger condition), 5.0 cm cube for four trials (Identical condition), and 4.0 and 2.5 cm for two trials each (Smaller condition), while the standard cube was constantly 5.0 cm in size. The presentation order for these trials was pseudo-random. After the main and supplementary experiments, a size discrimination test was performed. Subjects were instructed to discriminate graphic size diverences between the standard cube and the comparison cube. The two graphical cubes were displayed for 2 s; subjects compared them visually and stated whether they perceived the size of the comparison cube to be Larger, Smaller, or Similar to the standard cube.

6 448 Exp Brain Res (2007) 179: The size of the comparison cube was pseudo randomly varied, while that of the standard cube was constant (5.0 cm cube). A total of 64 comparisons were performed with the same trials and sizes as those in the main experiment. Finally, a weight discrimination test was performed utilizing fourteen physical cubes of identical size (2.5 cm) with diverent weights (20.0, 22.0, 24.0, 26.0, 28.0, 29.0, 30.0, 30.0, 31.0, 32.0, 34.0, 36.0, 38.0, and 40.0 g). To eliminate any visually induced size evect, graphical cubes and graphical wires were removed from the subject s view leaving only the two graphical rings to be seen in the workspace. Subjects compared heaviness in the same manner as in the main experiment. The standard cube weighing 30.0 g was constantly suspended from the standard ring, and the weight for the comparison ring was pseudo randomly varied. In the Wrst step, each of the subjects performed 21 trials (seven weights of 26.0, 28.0, 29.0, 30.0, 31.0, 32.0, and 34.0 g 3 trials) to investigate their ability to discriminate within 4.0 g (a Weber fraction of ) of the standard cube (30.0 g). If the subject could not successfully discriminate 4.0 g diverence for more than three out of six trials in the Wrst step (34.0 vs g and 26.0 vs g), they went on to a second step in which they performed a further 21 trials (seven weights of 20.0, 22.0, 24.0, 30.0, 36.0, 38.0, and 40.0 g 3 trials) to investigate their ability to discriminate within 10.0 g (a Weber fraction of ). It should be noted that special care was taken to prevent the subjects from becoming aware of the fact that the weight of the physical cubes was constant during most of the experiments. The subjects were neither informed of this fact (cf. Flanagan and Beltzner 2000), nor were there opportunities for the subjects to gain haptic experience relative to the size and weight of the physical cubes at the beginning of the experiment (cf. Gordon et al. 1991b). Further, to avoid a potential cognitive bias on subject s responses (for example, the weight must be the same because the experimenter did not change the physical object ), the experimenters remained seated at the augmented environment with a set of numerous cubes and manipulated the comparison cube after every trial. In this way, the subjects presumably formed the belief that cube weight might change in every trial, despite the fact that only the visual size changed throughout the trials in the main and the supplementary experiments. Such care to detail seemed essential to remove any cognitive bias from subject responses, since such knowledge may, in fact, bias their Wnal decision (Mon- Williams and Murray 2000). In addition, the three categories of Heavier, Lighter, or Similar were used for subject s responses in the present study. Recent articles have frequently used a forced-choice method in which subjects were forced to choose either Heavier or Lighter, even if they truly felt the compared heaviness to be similar (Mon-Williams and Murray 2000), or subjects were asked which of the two objects felt Heavier (or Heaviest) (Flanagan and Beltzner 2000; Gordon et al. 1991a, b). Such leading questions may possibly bias subject s responses. Analysis Percentages of responses were calculated as a function of the visual size of the comparison cube and response categories (Heavier, Similar, and Lighter), for each individual subject. For example, if a subject s response was Heavier in two trials, Lighter in one trial, and Similar in one trial from among four trials for a particular size condition, the percentage of responses for each category in this condition is 50% for Heavier, 25% for Lighter, and 25% for Similar. The individual percentages were then averaged across subjects as a function of the size of the comparison cube and the response category (see Fig. 2). To assess the evect of visual size cues on perceived heaviness, a one-way (size, 25 levels), within-subject ANOVA was performed on the frequency of the subject s response of Similar only, which was the correct response for perceived heaviness since the two cubes were of identical mass. The frequency of the size weight illusion was evaluated for each subject according to the relative size between the standard and comparison cubes (Table 1). That is, the percentages of subject responses of Heavier were averaged for each subject within the range of size conditions ( cm; the Smaller condition), where the comparison cube was relatively smaller than the standard cube (5.0 cm). Likewise, Lighter responses were averaged for each subject within the range of size conditions ( cm; the Larger condition), where the comparison cube was relatively larger than the standard cube (5.0 cm). Finally, correlations were compared between susceptibility to the size weight illusion and sensitivity to visual size diverence, and between size weight illusions and sensitivity to weight diverences (see the second set of three columns from the left in Table 1). The percentage of occurrence of the size weight illusion was calculated for each subject based on 24 trials in which the sizes of the comparison cube were 0.4 cm of the 5.0 cm cube. The percentage of correct responses was also calculated for each subject in the weight discrimination test over 18 trials with the weight of the comparison cubes being 4.0 g of 30.0 g as well as in the size

7 Exp Brain Res (2007) 179: Fig. 2 Mean values for percentage of subject responses as a function of size of the comparison cube (in cm) and response category (Heavier, Similar, and Lighter) in the main experiment. The standard cube and the comparison cube were of identical mass across the trials (30.0 g). The comparison cube is smaller in size than the standard cube in the range of 1.0 to 4.9 cm (the Smaller condition), while that is larger in the range of 5.1 to 9.0 cm (the Larger condition). A major percentage of subjects perceived the comparison cube to be heavier than the standard cube in the Smaller condition (top), and a major percentage of subjects perceived the comparison cube to be lighter in the Larger condition (bottom). As the size diverence between the standard cube and the comparison cube grew smaller (marked in triangle), most subjects tended to perceive the cubes to be similar in heaviness (middle) discrimination test over 24 trials with the size of the comparison cubes being 0.4 cm of the 5.0 cm cube. Results Figure 2 indicates the mean values for the percentages of subject s responses in each response category as a function of size of the comparison cube. A one-way, within-subjects (size condition; 25 levels) ANOVA indicated a signiwcant size evect (F (24, 384) = 6.11, P < 0.001) on perceived heaviness. As shown at the top of Fig. 2, subjects tended to perceive the comparison cube to be heavier than the standard cube in the Smaller condition ( cm sized cube for the comparison) regardless of the fact that both were of equal mass (30.0 g). The frequency of the size weight illusion was 94.1% (16 trials from 16 subjects) for the 1.0 cm cube, 76.5% (13 trials from 13 subjects) for the 2.5 cm cube, 67.6% (23 trials from 13 subjects) for the 3.5 cm cube, 64.7% (44 trials from 17 subjects) for the 4.2 cm, 45.6% (31 trials from 15 subjects) for the 4.6 cm cube, and 26.5% (18 trials from 12 subjects) for the 4.8 cm cube. Thus, the illusory evect of feeling the comparison cube as heavier decreased as the size diverence between comparison and standard cube became smaller. It was when the comparison cube was smaller than cm that all the subjects perceived the comparison cube to be heavier than the 5.0 cm standard cube, in the Smaller condition. Likewise, subjects tended to perceive the comparison cube to be lighter than the standard cube in the Larger condition ( cm sized cube for the comparison, bottom of Fig. 2). The frequency of the size weight illusion was 27.9% (19 trials from 9 subjects) for the 5.2 cm cube, 38.2% (26 trials from 14 subjects) for the 5.4 cm cube, 35.3% (24 trials from 13 subjects) for the 5.8 cm cube, 52.9% (18 trials from 12 subjects) for the 6.5 cm cube, 70.6% (12 trials from 12 subjects) for the 7.5 cm cube, and 82.4% (14 trials from 14 subjects) for the 8.5 cm cube. Thus, the illusory evect of feeling lighter for the comparison cube increased as the size diverence became greater between the comparison and standard cube. It was when the comparison cube was larger than cm that all the subjects perceived the comparison cube to be lighter than the standard cube (5.0 cm). As the size diverence of the comparison cube approached the standard cube (5.0 cm, marked as a triangle in the middle of Fig. 2), a majority of the subjects perceived them to be Similar in heaviness. The frequency of Similar responses was, for instance, 77.9%

8 450 Exp Brain Res (2007) 179: (53 trials from 17 subjects) for the 4.9 cm cube, 60.3% (41 trials from 17 subjects) for the 5.0 cm cube, and 75% (51 trials from 17 subjects) for the 5.1 cm cube. Table 1 summarizes the individual subject results for the frequency of the visually induced size weight illusion (left-most three columns) obtained in the main experiment, the susceptibility to the size weight illusion based on small graphic size diverences in the main experiment and the sensitivity to weight and visual size obtained in the discrimination tests (second set of three columns from the left), and the interval and peak velocity of the lifting movement (the set of six columns on the right) obtained in the supplementary experiment. As shown at the bottom of Table 1, the mean value of the frequency of the size weight illusion was signiwcantly greater for the Smaller condition ( %) than for the Larger condition ( %) (Paired t = 2.431, P < 0.05) which may be due to the greater relative diverences in volume ratio that were used in the Smaller condition (1:0.008 for the comparison between 5.0 and 1.0 cm cubes) than in the Larger condition (1:5.8 for that between 5.0 and 9.0 cm cubes). There were also large individual diverences in the frequency of the size weight illusion, e.g., % for total frequency of the size weight illusion. The second three columns from the left indicate the results of susceptibility to the size weight illusion ( 0.4 cm for 5.0 cm cube) (shown as SW in Table 1), sensitivity to weight ( 4.0 g for 30.0 g), and sensitivity to visual size ( 0.4 cm for 5.0 cm cube). For SW susceptibility, the percentage of frequency of the size weight illusion was calculated from 24 trials with 4.6, 4.8, 4.9, 5.1, 5.2, and 5.4 cm cubes. The diverence threshold for weight discrimination was estimated using the psychometric function (Osaka 1994), although the trials in the present study were limited. The diverence threshold was, on average, g ( g in mass) for 11 subjects who could discriminate 4.0 g diverence in the Wrst step, while it was g ( g in mass) for six subjects who went on to the second step of the discrimination test (10.0 g diverence). In total, the mean value of the diverence threshold for 30 g mass was g with a Weber fraction of ( ). The correlation between the percentage of correct responses and the diverence threshold (Weber fraction) for weight discrimination (Table 1) was 0.96 (P < 0.001). A signiwcant correlation was found between susceptibility to the size weight illusion (SW) and sensitivity Subject Perception Lifting movement Table 1 Individual results for frequency of occurrence of the size weight illusion in the main experiment (three left-most column), for the susceptibility to the visually induced size weight illusion for the small diverence conditions in the main experiment, the sensitivity to weight, and sensitivity to visual size from the weight and size discrimination tests (second set of three columns from left), and for the interval between and peak velocity of lifting movements in the supplementary experiment (right six columns) Frequency of the SW illusion (%) Susceptibility and sensitivity (%) Interval time (s) Peak velocity (cm/s) SW indicates the visually induced size weight illusion; susceptibility to the size weight illusion was tested for the range of 0.4 cm for 5.0 cm graphic cube. The sensitivity to weight was tested in the range of 4.0 g for 30.0 g, while that to visual size was tested in the range of 0.4 cm for 5.0 cm cube Smaller Larger Total SW Weight Size Mean SD CV Mean SD CV Mean SD

9 Exp Brain Res (2007) 179: to weight (r = 0.789, P < 0.001). On the other hand, no signiwcant correlation was observed between susceptibility to the size weight illusion and sensitivity to visual size (r = 0.350, P = 0.169) or between sensitivity to weight and sensitivity to visual size (r =0.147, P = 0.573). A signiwcant correlation was observed between sensitivity to weight and the total frequency of the size weight illusion (shown as total in Table 1) (r = 0.494, P < 0.05), while there was no signiwcant correlation between the total frequency and sensitivity to visual size (r = 0.298, P = 0.245). The second set of three columns from the right in Table 1 indicates mean, standard deviation (SD), and the coeycient of variation (CV) for the interval time, i.e., duration from completion of releasing the standard cube to onset of lifting the comparison cube. These values are regarded as individual characteristics of the lifting movement since these were recorded after the main experiment was completed and, as a result, all the subjects had become accustomed to the lifting tasks. The total frequency of the visually induced size weight illusion was not signiwcantly correlated with the mean interval time (r = 0.031, P =0.907) or with the coeycient of variation (r = 0.098, P = 0.707), indicating that neither the duration nor the consistency of interval time was related to the occurrence of the size weight illusion. The peak velocity of lifts was also examined with respect to the size weight illusions. The right-most set of three columns in Table 1 indicates the mean, SD, and the CV for peak lifting velocity. The total frequency of the visually induced size weight illusion was not signiwcantly correlated with mean peak velocity (r = 0.042, P = 0.873) or with the CV (r = 0.118, P = 0.652), indicating that neither peak velocity nor its stability were related to the occurrence of the visually induced size weight illusion. Table 2 indicates the means of peak velocity in the process of lifting the cubes and subject responses for each trial in the supplementary experiment. Although the subjects were instructed to maintain a constant lifting speed, a greater peak velocity was, on average, exerted for the comparison cube when it was larger than the standard cube and vice versa. As a result, signiwcant diverences were observed in peak velocity in the conditions between the 5.0 and 6.0 cm cube (paired t = 2.136, P < 0.05) and between the 5.0 and 2.5 cm cube (t = 2.355, P <0.05) in Table2. Peak velocity thus had some proportionality to perceived object size, i.e., larger objects had higher peak velocities. However, peak velocity was not correlated with the heaviness judgments, nor was there consistency among the subjects. Average lifting velocity prowles across subjects and trials are depicted in Fig. 3. The velocity prowles for the comparison cube (bold solid line) are graphed to lag by 0.1 s those from the standard cube (thin solid line), to make easier the comparison of velocity prowles. Peak velocities were found to be signiwcantly higher in the Larger condition (Fig. 3a) and signiwcantly lower in the Smaller condition (Fig. 3b), compared to the standard cube size (5.0 cm, see also Table 2). Individual subject velocity prowles are shown for the Larger condition (c). In the Larger condition (Fig. 3c), three subjects, with the reports being for Similar, had peak velocity values that were similar between the standard cube and the comparison cube (like subject 1 in Fig. 3c). Ten subjects had peak velocity values with the comparison cube being greater than the standard cube (like subject 8 in Fig. 3c), while the reports of Wve out of those ten subjects were for Lighter, three for Similar, and two for Heavier. In contrast, four subjects had peak velocity values with the comparison cube being lower than for the standard cube (like subject 11 in Fig. 3c); of these Table 2 Means and standard deviations of peak velocity and subject responses for each trial in the supplementary experiment The size (cm) indicates the comparison cube *Indicate signiwcant diverences in mean values between the standard cube and the comparison cube (P <.05) Condition Comparison Peak velocity (cm/s) Subject response Size(cm) Standard Comparison Lighter Similar Heavier Mean SD Mean SD Larger * Identical Smaller *

10 452 Exp Brain Res (2007) 179: the size weight illusion (Fig. 3, and Tables 1, 2). Below we consider: the signiwcant correlation between frequency of the size weight illusion with sensitivity to weight diverence, implications of results for sensory based and cognitive-based theories of the size weight illusion, multisensory information integration, the generality of the results to objects of greater mass, the role of size information more broadly in heaviness perception and a conceptual model for occurrence of the size weight illusion. Size weight illusion frequency correlates with weight sensitivity but not size sensitivity Fig. 3 ProWles of lifting velocity are averaged for all subjects, in which signiwcant diverences were found in the Larger condition (a 5.0 vs. 6.0 cm cube) and in the Smaller condition (b 5.0 vs. 2.5 cm cube). For comparison purposed, the velocity prowles for the comparison cube (bold solid line) are graphed to start 100 ms later than the standard cube (thin solid line). c Indicates typical examples for individual subject velocity prowles in the same Larger condition as shown in (a) four, the report of one subject was for Lighter, one for Similar, and two for Heavier than the standard cube. Thus, although there were trends for peak velocities to be higher for larger cubes, and lower peak velocities for small cubes, these motor evects were not related to the heaviness judgments (see Table 2). Discussion In summary, the results are as follows: (1) the visual size cues inxuenced perceived heaviness for all subjects under conditions having suycient size diverences between standard and comparison cubes of equal mass (Fig. 2); (2) visual size cues avected perceived heaviness such that when the comparison cube was relatively smaller in size than the standard cube, it was perceived to be heavier, and vice versa (Fig. 2); (3) as the size diverence increased between the standard cube and the comparison cube, more subjects experienced the illusion. Similarly, as the size diverence became smaller, fewer subjects experienced the illusion (Fig. 2); (4) whether or not the subjects experienced the size weight illusion was signiwcantly correlated with their sensitivity to weight discrimination but not their sensitivity to discriminate small diverences in visual size (Table 1); and (5) erroneously programmed motor commands were not systematically related to the heaviness estimates or experience of As the size diverence increased between the standard cube and the comparison cube, more subjects experienced the illusion. Similarly, as the size diverence became smaller, fewer subjects could experience the illusion (Fig. 2). In short, the visual size of handled objects seems to be important factor for all the subjects to experience the visually induced size weight illusion. In addition, experience of the size weight illusion was signiwcantly correlated with each subject s sensitivity to discriminate weight diverences (Table 1). These results suggest that a subject s susceptibility to the size weight illusion may depend partly on the magnitude of size diverence between two target objects, and partly on an individual s sensitivity to small weight diverences. On the contrary, and somewhat paradoxically, the present results (Table 1) show that experience of the size weight illusion was not signiwcantly correlated with a subject s ability to discriminate small diverences in visual size, although visual size was a single independent factor. In short, whether or not subjects can discriminate which of two closely sized objects is larger or smaller is not a critical factor for all the subjects to experience the size weight illusion. Implications for sensory based and cognitive-based theories of the size weight illusion These results imply that cognitive processes for formation of expectation (Ross 1969) or rationalization (Mon-Williams and Murray 2000) are not involved necessarily in the production of the visually induced size weight illusion, as obtained in the present study. In Expectation theory (Ross 1969), involvement of the cognitive process to discriminate size diverence becomes essential in the production process of the size weight illusion. Without such a cognitive process to discriminate which object is larger or smaller, it must be very hard as a next step to form an expectation that a larger object should have greater weight or mass than a

11 Exp Brain Res (2007) 179: smaller object, prior to lifting an object (Ross 1969). Similarly, in Rationalization theory (Mon-Williams and Murray 2000), the cognitive process to discriminate size diverence must be necessary to rationalize in order to resolve the discrepancy between awareness that two objects are the same weight and the sensory feedback that indicates otherwise. Nevertheless, the occurrence of the size weight illusion did not correlate with the sensitivity to small visual size diverences, which absolutely contributes to comparison of object size. Thus, susceptibility to the visually induced size weight illusion may depend partly on visual size magnitudes of target objects, and partly on an individual sensitivity to small weight diverences, rather than sensitivity to small diverences in visual size. This suggests that the visually induced size weight illusion is based mainly on intensity of visual stimulus or sensory based event (Masin and Crestoni 1988) rather than a cognitive-based event (Ross 1969; Mon-Williams and Murray 2000; Flanagan and Beltzner 2000). Reexamination of Expectation theory based on kinematics Kinematic results from the present study reconwrmed two previous Wndings related to the visually induced size weight illusion. Firstly, visual size cues inxuence motor programming during the lifting movements. That is, regardless of the fact that subjects were instructed to lift in a uniform manner for all objects, peak velocity during the lifting movement tended to increase when the comparison cube was larger than the standard cube, and vice versa, in keeping with the results of previous studies (Davis and Roberts 1976; Davis and Brickett 1977; Gordon et al. 1991a, b; Brenner and Smeets 1996; Mon-Williams and Murray 2000; Kawai et al. 2000, 2002), and one proposition of Expectation theory, that a larger object will be lifted with stronger motor commands. The second replicated Wnding, however, is that there is not a strong, systematic relationship between the experienced illusions and erroneously programmed motor commands. In the present study, greater peak velocity did not necessarily correlate with a subject s perceived heaviness on every trial (Fig. 3). This is consistent with the results recently reported by Mon-Williams and Murray (2000), and Flanagan and Beltzner (2000) and poses a problem for Expectation theory. Multisensory information integration and the visually induced size weight illusion As discussed above, the systematic results for perceived heaviness as a function of object size strongly support a direct participation of visual size information to the perceptual system of heaviness, i.e., the Information Integration theory (Sjöberg 1969; Anderson 1970; Masin and Crestoni 1988), rather than less direct or more constructed participation of visual size information, such as Expectation theory (Ross 1969) or the Rationalization theory (Mon-Williams and Murray 2000). Recently, noninvasive imaging techniques, e.g., functional magnetic resonance imaging (fmri) or positron emission tomography (PET), have provided evidence in support of multisensory interaction or integration processing in humans (Macaluso 2006). In a PET experiment, Sathian et al. (1997) found neurons in areas seven or nineteen in normal human cortex, which responded to both visual and somatosensory stimuli when subjects viewed an approaching object. In an fmri study, Amedi et al. (2001) demonstrated functional overlap between visual and tactile object-related activation in the ventral visual pathway when they instructed their subjects to recognize objects either visually or haptically. In a delayed-matching task, James et al. (2002) demonstrated visuo-tactile interactions in the occipital cortex by fmri. Such neurons, therefore, may be involved in the visually induced size weight illusion. Further investigation is required to understand how visual size cues integrate with weight information in heaviness perception, e.g., whether they arrive via the dorsal stream during lifting movements or via the ventral stream during object recognition (Goodale 1994). Generality of the results to objects of greater mass Low-mass (30.0 g) cubes were selected in the present study to minimize subject s fatigue as well as to enhance the visual size evect on perceived heaviness since it was reported to be weak (Ellis and Lederman 1993). The potency of the illusion induced by visual size cues is expected to diminish as weight increases (Ross 1969; Stevens and Rubin 1970; Cross and Rotkin 1975) or in cases where the size and weight increase in a constant ratio fashion (Ross 1969; Ross and Di Lollo 1970; Stevens and Rubin 1970). This does not mean, however, that the size evect will disappear entirely with greater masses. In fact, evects of visual size cues on perceived heaviness have been reported in several studies using more massive stimuli ( g, Ross 1969; g, Masin and Crestoni 1988; 1,030 g, Gordon et al. 1991a, b; g, Ellis and Lederman 1993; 250 g, Mon-Williams and Murray 2000). Thus, visually perceived sizes tend to avect perceived heaviness as long as test objects are of identical mass, though