Exp Brain Res (2007) 179:443–456

DOI 10.1007/s00221-006-0803-1

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 visuallyperceived sizes was reexamined to investigate whetherthis illusion is a sensory based or cognitive-based phe-nomenon. A computer-augmented environment wasutilized to manipulate visual size information of targetobjects independently of their haptic information. Twophysical cubes of equal mass (30.0 g) and size(3.0 £ 3.0 £ 3.0 cm) were suspended in parallel bywires attached to small graspable rings, in order tokeep haptically obtained information constant betweenlifts. Instead of directly seeing each physical cube, sub-jects viewed 3D graphics of a cube with a wire and aring that were precisely superimposed onto each physi-cal cube. Seventeen subjects vertically lifted these aug-mented cubes, one after the other, by grasping theattached rings, and then reported their perception ofcube heaviness. The graphical size of a comparisoncube pseudo randomly varied for every comparisonfrom 1.0 £ 1.0 £ 1.0 to 9.0 £ 9.0 £ 9.0 cm, while that ofa standard cube remained constant (5.0 £ 5.0 £ 5.0 cm).

Results indicated that the size–weight illusion fre-quently and systematically occurred for all the subjectssuch that when the comparison cube was relativelysmaller than the standard cube, it was perceived to beheavier, and vice versa. As the size diVerence increasedbetween the standard cube and the comparison cube,more subjects experienced the illusion, and vice versa.Follow-up tests showed occurrence of the size–weightillusion was signiWcantly correlated with subject’s sensi-tivity to discriminate weight, but not with sensitivity todiscriminate visual size. Results suggest that the size–weight illusion induced by only visual size cues in anaugmented environment is sensory based, and dependson an individual’s integrated perception based onmultimodal sensory information.

Keywords Heaviness perception · Size · Weight · Vision · Virtual environments · Augmented objects

Introduction

When two objects of equal weight but diVerent sizesare lifted, the smaller object is normally perceived asheavier than the larger object. This “size–weight illu-sion” (Charpentier 1891) may derive from hapticallyand/or visually acquired size information, and/or froma subject’s expectation or previous experience. That is,when blindfolded subjects directly grasp and lift twoobjects of equal weight but of unequal size to compareheaviness, the size–weight illusion generally occurs(Ellis and Lederman 1993; Kawai 2002b, 2003b). Thesame is true of congenitally blind subjects (Rice 1898;Ellis and Lederman 1993). The size–weight illusionmay also occur, as long as subjects are allowed to view

S. Kawai (&)Faculty of Psychology and Welfare, Tezukayama University, 3-1-3 Gakuen-Minami, Nara, Japan 631-8585, e-mail: skawai@tezukayama-u.ac.jp

F. Henigman · C. L. MacKenzieHuman Motor Systems Laboratory, School of Kinesiology, Simon Fraser University, Burnaby, Canada

A. B. KuangInternet Explorer, Microsoft Corporation, Redmond, WA, USA

P. H. FaustProfessor Emeritus, Tezukayama University, Nara, Japan

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objects, even when haptically acquired size cuesremain constant, for instance, when test objects arelifted by using hook handles, wire, or a grip apparatuswith constant grasp-span attached to diVerent-sizedcubes (Charpentier 1891; Pick and Pick 1967; Davisand Roberts 1976; Masin and Crestoni 1988; Ellis andLederman 1993; Gordon et al. 1991a; Mon-Williamsand Murray 2000; Flanagan and Beltzner 2000; Flana-gan et al. 2001). Similarly, KoseleV (1957) documentedthe size–weight illusion when subjects compared anobject’s heaviness while viewing it through convex orconcave lenses, thus altering its visual size.

Psychophysicists and psychologists have long dis-cussed whether the size–weight illusion is due to sen-sory based or cognitive-based events (Jones 1986). Inthe former, the phenomenon occurs due to the directintegration of weight information with the size infor-mation concurrently obtained, whether through visualor haptic senses, during lifting of an object. The Infor-mation Integration theory is based on this idea(Sjöberg 1969; Anderson 1970). In the latter view, thephenomenon occurs due to some cognitive process inthe perception of heaviness, such as expectation orrationalization based on the visual size of the targetobjects (Ross 1969; Mon-Williams and Murray 2000;Flanagan and Belzner 2000).

With regard to the size–weight illusion induced byhaptically perceived size, evidence that this phenome-non is sensory based has been provided in a series ofthe studies involving the lifting of cubes with a preci-sion grasp using the pads of the thumb and index Wnger(Kawai 2002a, b, 2003a, b). Kawai (2003b) indicatedthat haptically perceived size is constantly and system-atically integrated with weight information to formone’s perception of heaviness. That is, when a test sub-ject lifts individual cubes to judge heaviness withoutviewing them, the perceived heaviness is expressed as aratio of width-to-weight of the cube. He concluded thatheaviness perception is not based simply on the physi-cal weight of an object (Kawai 2003a), but that haptic-ally obtained size information is a critical factorcontributing to the judgment of heaviness (Kawai2003b).

On the other hand, determining whether the size–weight illusion induced by visually perceived size infor-mation is sensory based or cognitive-based has beencontroversial (Ross 1969; Masin and Crestoni 1988;Mon-Williams and Murray 2000; Flanagan and Beltz-ner 2000). Ross (1969) proposed, as deWned by Expec-tation theory, that the illusion is the result of ameasuring system that takes into account the expectedvalue of an object. For instance, it is a common expec-tation that the larger of two objects should be heavier

than the smaller one. The idea of expectation explainswhy people generate larger grip and lift forces whenlifting larger objects than when lifting smaller objectsof the same weight (Gordon et al. 1991a) and describesthe size–weight illusion as a product of the mismatchbetween the expected weight and the sensory feedbackobtained from the object’s actual weight following lift-oV. Expectation theory, Wrst proposed by Flournoy(1894), is supported by studies observing erroneouslyprogrammed motor outputs, as measured by lift veloc-ity (Davis and Roberts 1976), EMG activity in musclesresponsible for lifting movements (Davis and Brickett1977), and peak load and grip force rates (Gordonet al. 1991a, b). These studies have consistently hypoth-esized that such a mismatch between initial motorcommands and feedback from the true weight of theobjects might result in perceiving heaviness diVerentlydepending on object size. That is, generating greater-than-necessary forces for lifting may result in theperception of reduced heaviness, and vice versa.

Recent articles, however, have refuted Expectationtheory by demonstrating that there is no signiWcantrelation between the experienced illusion and errone-ously programmed forces (Mon-Williams and Murray2000; Flanagan and Beltzner 2000; Flanagan et al.2001). Using a methodology similar to that of Gordonet al. (1991a), Mon-Williams and Murray (2000) inves-tigated, on a trial by trial basis, whether or not subjectsreported the larger object to be perceived as lighterthan the smaller object while greater forces wereapplied to the larger object. Their Wndings suggestedthat there is no close relation between produced forcesand verbal reports. The researchers thus concludedthat erroneous motor programming is neither neces-sary nor suYcient to produce the size–weight illusion.They proposed that, instead of Expectation theory, thesize–weight illusion induced by visual size cues arisesdue to a cognitive process in which the subjects form anawareness that the objects have the same weight and soattempt to rationalize, at a cognitive level, the discrep-ancy between the awareness that the objects are thesame in weight and the actual sensory feedback inwhich the objects are perceived to vary in weight. Flan-agan and Beltzner (2000) had subjects grasp a gripapparatus and repeatedly lift two boxes of unequal sizebut equal weight. While subjects initially generatedexcessive grip and load forces for the larger object andrelatively insuYcient forces for the smaller object, theylearned to scale their forces equally for the two objectsafter Wve to ten alternating lifts. Despite this motoradjustment leading subjects to apply equal and appro-priate forces to the two objects, the size–weight illusionpersisted. This provided further evidence against

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Expectation theory although neither study presentedany convincing evidence that the size–weight illusion iscognitive-based.

Masin and Crestoni (1988), in contrast, insisted thatthe visually induced size–weight illusion was a conse-quence of sensory origins, as seen in the InformationIntegration theory (Sjöberg 1969; Anderson 1970).They had subjects estimate the weight of objects afterpulling down on a ring attached by a wire tied to thetarget object and fed through a pulley. The size–weightillusion occurred only when the subjects were allowedto view the objects while lifting, but not when therewas an absence of visual size cues. This observationwas consistent with Flournoy (1894), who requestedsubjects to close their eyes prior to lifting an objectwith a hook handle, and with Ellis and Lederman(1993), who requested blindfolded subjects to lift cubessuspended on wires. Masin and Crestoni (1988) fur-thermore demonstrated that the size–weight illusiondid not arise when a delay existed between when sub-jects saw the target objects and when they lifted them.Consequently, they argued against Expectation theory,reasoning that any cognitive expectation should persisteven after a once-viewed object disappears from view.Masin and Crestoni, instead, supported the Informa-tion Integration theory (Sjöberg 1969; Anderson 1970),in which the size–weight illusion arises by direct inte-gration of size information with weight information.

Thus, as Wndings relating to the visually inducedsize–weight illusion are few and contradictory (Pickand Pick 1967; Ross 1969; Masin and Crestoni 1988;Ellis and Lederman 1993), it appeared essential toreconsider the fundamental question of how the visu-ally induced size–weight illusion occurs among sub-jects. The premise for the experiments reported here,therefore, was a simple and methodical observation ofthe visually induced size–weight illusion, focusing onsuch questions as (1) whether or not the visuallyinduced size–weight illusion was commonly experi-enced by all subjects; (2) whether or not visuallyacquired size cues inXuenced heaviness perception in asimilar manner to the haptically acquired size cues; (3)how susceptibility to the visually induced size–weightillusion diVered amongst the diVerent subjects; (4)what individual factors were related to susceptibility tothe visually induced size–weight illusion and (5)whether or not the erroneously programmed motorcommands were related to the occurrence of this illu-sion. The present study sought to determine whetherthe visually induced size–weight illusion is a cognitive-based or sensory-based event. In addition, we analyzedwhether the size–weight illusion was related to individ-ual sensitivity to weight discrimination or size discrimi-

nation. Finally, we discussed how the size–weightillusion occurs in both the perceptual system and themotor system.

Materials and methods

Subjects

Seventeen adults (9 men and 8 women), aged from 20to 49 years (M = 29.0, SD = 7.4), participated after pro-viding informed consent. The local university ethicscommittee approved the ethics of the human research.All subjects were right-handed (OldWeld 1971), andnone of them exhibited any visual, muscular, or cutane-ous problems. In addition, none of the subjects had anyprevious experience with the experimental tasks norwere they familiar with the hypotheses being tested.

Augmented environment

Methodologically, an augmented environment allowedfor strict isolation of the eVect of visual size cues fromassociated physical and haptic eVects, e.g., weight, den-sity, center of gravity, mass distribution, inertia tensor,and haptically perceived size, which aVect perceivedheaviness more strongly than visual size cues in thesize–weight illusion (Ellis and Lederman 1993; Amaz-een and Turvey 1996; Amazeen 1999; Kawai 2002b).However, all these haptic eVects could be kept con-stant between the standard and comparison stimuli inthe augmented environment, since two cubes withidentical physical properties were used (30.0 g in mass,3.0 £ 3.0 £ 3.0 cm in size). Therefore, the presentstudy could concentrate solely on the eVect of visualsize, through graphically augmenting the size of cubes,while other physical and haptic information was keptconstant.

A schematic drawing of the augmented environmentused in these experiments is shown in Fig. 1. The meth-odological details and original graphic software of theVirtual Hand Laboratory (Simon Fraser University,Canada) have been described previously (Summers1999; Kawai et al. 2002).

Two acrylic physical rings were suspended on0.01 cm diameter piano wire so that they were 14.0 cmapart and parallel to each other at a height of 14.0 cmbeneath a semi-silvered mirror (D in Fig. 1) and15.0 cm above the table surface. These rings were0.3 cm in thickness and 1.7 cm in outside diameter andwell Wtted the center of the pads of thumb and indexWngers. Subjects established stable precision grasps onthe ring during repeated lifting of a test object without

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micro-slips, distortion, sweating, or wear and tear onthe support surface of their Wngers, eliminating factorsthat might otherwise aVect perceived heaviness (Wes-tling and Johansson 1984; Flanagan et al. 1995).

Two physical cubes (F in Fig. 1) of identical size(3.0 £ 3.0 £ 3.0 cm) and mass (30.0 g) were suspendedon sigmoid hooks that were themselves attached to therings by thin piano wire. Cubes were acrylic boxeswhose weight was adjusted by the addition or subtrac-tion of cotton and granular lead. Weight was measuredon a digital precision weight scale (§0.01 g, TANITA,TKP-100, Tokyo, Japan). The distance from the loweredge of the physical ring to the top surface of the phys-ical cube was 4.0 cm. The initial orientation for physi-cal rings was adjusted to approximately 135° relative tothe anterior–posterior axis respectively so that the sub-jects, who were all right-handed, could grasp them withthe thumb and index Wnger in a natural manner.

Computer-generated graphic cubes, rings and wireswere displayed on a computer monitor (A in Fig. 1)positioned face-down over the semi-silvered mirror (Din Fig. 1). The size of graphical rings was the same asthe physical rings. Images were created independentlyfor the left and right eye, based on subject-speciWcinter-ocular distance measurements, to create the

impression of 3D objects when viewed with crystal eyesliquid crystal shutter stereoscopic goggles (StereoGraphics, San Rafael, CA; C in Fig. 1). Images wererendered at 60 Hz in stereo and goggles were shutteredat 120 Hz to deliver 60 images per second to left andright eyes. An OPTOTRAK 3D motion analysis sys-tem with two position sensors (Northern Digital Inc.,Waterloo, Canada: B in Fig. 1) allowed for continuousmeasurement of the 3D position of infrared light emit-ting diodes (LED; E in Fig. 1) mounted on each physi-cal wire and on the goggles, allowing images to bereXected in the mirror in such a way that the graphicobjects were head-coupled, stereoscopic, and accu-rately superimposed over the physical objects in theworkspace between the table and half-silvered mirror.3D position data were detected and transmitted to themaster SGI (Silicon Graphics Indigo II workstation)sampling at 60 Hz. The total time required for thesystem to sample the LED’s position, calculate theobject’s position and orientation in space, and displaythe graphical cube was no greater than two to threeframes at 60 Hz. All LED position data were measuredin millimeters. The size of the workspace in which boththe graphical cubes and physical cubes coexisted wasapproximately 25.0 £ 33.0 £ 20.0 cm; an area that eas-ily encompassed the lifting tasks in the present study.The vertical displacement signals from both physicalcubes were also recorded during lifting at a frequencyof 100 Hz through the OPTOTRAK motion analysissystem, from which the peak velocity for each liftingmovement was calculated. An occluder was in placebeneath the semi-silvered mirror so that neither thephysical objects nor the hand of the subjects could beseen.

The 3D graphical cubes were adjusted on the basisof subject’s point of view to keep object shape constantso that each of the subjects was able to see each graph-ical cube as a cubic shape from their individual point ofview during trials. A diVerent color, i.e., red, yellow,green, was used for each surface of the graphical cubesso that subjects perceived them as cubic because a sin-gle-colored graphic cube would be perceived as a 2Dhexagonal shape. No outlines were added in a diVerentcolor on the surface borders of the graphical cube sincethe Necker cube illusion could possibly occur (Butlerand McManus 1998). The graphical rings and wires(4.0 cm in length) were both oV-white in color, and thebackground was black. No other graphics eVects suchas lighting, shading, or texture were added to thegraphical image, in order to isolate the eVect of visuallyperceived object size. The size of the graphical cubeswas adjustable from 1.0 £ 1.0 £ 1.0 to 16.0 £ 16.0 £16.0 cm, in 0.1 cm increments.

Fig. 1 Illustration of the augmented environment of the VirtualHand Laboratory. Subjects were presented with two stereo imag-es (G dotted line) using crystal eyes stereographic goggles (C) anda monitor (A) viewed through a semi-silvered mirror (D). AnOPTOTRAK system (B) tracked infrared markers (E) attachedto 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 physicalcubes (F) of identical size (3.0 £ 3.0 £ 3.0 cm cube) and of identi-cal mass (30.0 g) were invisible to the subjects. While the graphi-cal size (G) of the standard cube placed on the left-hand side ofeach subject was constant (a 5.0 £ 5.0 £ 5.0 cm cube), that of thecomparison cube placed on the right-hand side varied from1.0 £ 1.0 £ 1.0 to 9.0 £ 9.0 £ 9.0 cm

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As previously described (Summers 1999; Kawaiet al. 2002), the properties of these graphically aug-mented objects are such that they are perceived stereo-scopically to be 3D, touchable, and as having weight.Subjects, therefore, have a strong sense of presenceand feel as if they are manipulating the perceivedgraphical image rather than an invisible physicalobject. As a result, it has been reported that both force-production strategy and heaviness perception in anaugmented environment are similar to those in a physi-cal environment (Kawai et al. 2002).

Procedure

The present study relied on one main experiment toinvestigate the frequency of occurrence of the visuallyinduced size–weight illusion using a broad range of vol-umes, and one supplementary experiment to re-evalu-ate the relation between the motor program and theillusion. In addition, two brief tests were conducted todetermine subject’s sensitivity to discriminate weightand size respectively. All experiments took placewithin the augmented environment of the VirtualHand Laboratory.

Subjects sat in a height-adjustable chair facing anaugmented environment (Fig. 1). After putting on theliquid crystal shutter goggles, the laboratory was semi-darkened to calibrate the equipment for the subject’spoint of view and hand workspace. Subjects conWrmedthat two 3D graphical cubes—suspended by graphicalwire and graphical rings—existed in parallel in theworkspace in front of them. Upon presentation of thetwo augmented cubes, each subject was requested tograsp the augmented ring of the ‘standard’ augmentedcube (the cube suspended on the left-hand side of theworkspace) using the tips of their thumb and indexWnger of the right hand, and to lift. The vertical lift ofthe standard cube that followed was accomplished witha single Xowing movement to a height of approxi-mately 5 cm, to allow for processing of its perceivedheaviness. As soon as the standard cube was back in itsoriginal position, the comparison cube, located on theright-hand side of the workspace, was lifted in exactlythe same manner. Finally, subjects were requested tostate whether they perceived the comparison cube to be‘Heavier’, ‘Lighter’, or ‘Similar’ in comparison tothe standard cube. Subjects were instructed to main-tain as constant a lifting speed as possible at all times.To facilitate this, each subject was permitted from Wveto ten practice lifts at the beginning of the experimentto become accustomed to the augmented environment,to allow them to properly reach for and grasp thegraphically augmented ring and to maintain a stable

lifting speed. In addition, they were requested to con-tinually observe the target cube without closing orturning their eyes away from it during the lifting proce-dure.

In the main experiment, the graphical size of thecomparison cube (30.0 g) was pseudo randomly variedfrom a minimum of 1.0 £ 1.0 £ 1.0 cm to a maximumof 9.0 £ 9.0 £ 9.0 cm (hereafter referred to as the 1.0and 9.0 cm cube, respectively) while the graphical sizeof the standard cube (30.0 g) was constant (5.0 cmcube) throughout the experiment. Each subject per-formed a total of 64 trials with 25 levels for size. As tri-als in the present study were limited, the trials werereduced to minimize fatigue among the subjects asmuch as possible. It was reported that subjects couldgenerally experience the size–weight illusion when thesize diVerence was suYcient between the standardcube and the comparison cube (Kawai 2003a). Thus,trials were predetermined as follows; one trial fordiVerences of more than 2.5 cm between the standardand comparison cube [9.0, 8.5, 8.0, 7.5, 2.5, 2.0, 1.5, and1.0 cm cube], two trials for diVerences from 1.0 to2.0 cm [7.0, 6.5, 6.0, 4.0, 3.5, and 3.0 cm cube], four tri-als 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 trialsfor the identical size condition [5.0 cm cube]. Based onthe relative size for the standard 5.0 cm cube, trialswere allotted into three conditions, i.e., the Smallercondition (1.0–4.9 cm cube for the comparison), theIdentical condition (5.0 cm cube), and the Larger con-dition (5.1–9.0 cm cube).

Following the main experiment, a supplementaryexperiment was immediately performed to record 3Dposition data of the augmented cubes during the liftingmovement. The subjects performed 12 trials in thesame manner as for the main experiment. That is, theywere required to judge the perceived diVerence inheaviness between the standard cube and the compari-son cube. The sizes of the comparison cubes used inthis experiment were 7.5 cm for two trials and 6.0 cmfor two trials each (Larger condition), 5.0 cm cube forfour trials (Identical condition), and 4.0 and 2.5 cm fortwo trials each (Smaller condition), while the standardcube was constantly 5.0 cm in size. The presentationorder for these trials was pseudo-random.

After the main and supplementary experiments, asize discrimination test was performed. Subjects wereinstructed to discriminate graphic size diVerencesbetween the standard cube and the comparison cube.The two graphical cubes were displayed for 2 s; sub-jects compared them visually and stated whether theyperceived the size of the comparison cube to be‘Larger’, ‘Smaller’, or ‘Similar’ to the standard cube.

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The size of the comparison cube was pseudo randomlyvaried, while that of the standard cube was constant(5.0 cm cube). A total of 64 comparisons were per-formed with the same trials and sizes as those in themain experiment.

Finally, a weight discrimination test was performedutilizing 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, and40.0 g). To eliminate any visually induced size eVect,graphical cubes and graphical wires were removedfrom the subject’s view leaving only the two graphicalrings to be seen in the workspace. Subjects comparedheaviness in the same manner as in the main experi-ment. The standard cube weighing 30.0 g was con-stantly suspended from the standard ring, and theweight for the comparison ring was pseudo randomlyvaried. In the Wrst step, each of the subjects performed21 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 todiscriminate within §4.0 g (a Weber fraction of 0.03–0.13) of the standard cube (30.0 g). If the subject couldnot successfully discriminate 4.0 g diVerence for morethan three out of six trials in the Wrst step (34.0 vs.30.0 g and 26.0 vs. 30.0 g), they went on to a secondstep in which they performed a further 21 trials (sevenweights of 20.0, 22.0, 24.0, 30.0, 36.0, 38.0, and40.0 g £ 3 trials) to investigate their ability to discrimi-nate within §10.0 g (a Weber fraction of 0.20–0.33).

It should be noted that special care was taken toprevent the subjects from becoming aware of the factthat the weight of the physical cubes was constant dur-ing most of the experiments. The subjects were neitherinformed of this fact (cf. Flanagan and Beltzner 2000),nor were there opportunities for the subjects to gainhaptic experience relative to the size and weight of thephysical cubes at the beginning of the experiment (cf.Gordon et al. 1991b). Further, to avoid a potentialcognitive bias on subject’s responses (for example,“the weight must be the same because the experi-menter did not change the physical object”), theexperimenters remained seated at the augmentedenvironment with a set of numerous cubes and manip-ulated the comparison cube after every trial. In thisway, the subjects presumably formed the belief thatcube weight might change in every trial, despite thefact that only the visual size changed throughout thetrials in the main and the supplementary experiments.Such care to detail seemed essential to remove anycognitive bias from subject responses, since suchknowledge may, in fact, bias their Wnal decision (Mon-Williams and Murray 2000). In addition, the three cat-egories of Heavier, Lighter, or Similar were used for

subject’s responses in the present study. Recent arti-cles have frequently used a forced-choice method inwhich subjects were forced to choose either Heavieror Lighter, even if they truly felt the compared heavi-ness to be similar (Mon-Williams and Murray 2000),or subjects were asked which of the two objects feltHeavier (or Heaviest) (Flanagan and Beltzner 2000;Gordon et al. 1991a, b). Such leading questions maypossibly bias subject’s responses.

Analysis

Percentages of responses were calculated as a functionof the visual size of the comparison cube and responsecategories (Heavier, Similar, and Lighter), for eachindividual subject. For example, if a subject’s responsewas Heavier in two trials, Lighter in one trial, and Sim-ilar in one trial from among four trials for a particularsize condition, the percentage of responses for eachcategory in this condition is 50% for Heavier, 25% forLighter, and 25% for Similar. The individual percent-ages were then averaged across subjects as a functionof the size of the comparison cube and the responsecategory (see Fig. 2). To assess the eVect of visual sizecues on perceived heaviness, a one-way (size, 25 lev-els), within-subject ANOVA was performed on thefrequency of the subject’s response of Similar only,which was the correct response for perceived heavinesssince the two cubes were of identical mass.

The frequency of the size–weight illusion was evalu-ated for each subject according to the relative sizebetween the standard and comparison cubes (Table 1).That is, the percentages of subject responses ofHeavier were averaged for each subject within therange of size conditions (1.0–4.9 cm; the Smaller condi-tion), where the comparison cube was relativelysmaller than the standard cube (5.0 cm). Likewise,Lighter responses were averaged for each subjectwithin the range of size conditions (5.1–9.0 cm; theLarger condition), where the comparison cube was rel-atively larger than the standard cube (5.0 cm).

Finally, correlations were compared between sus-ceptibility to the size–weight illusion and sensitivity tovisual size diVerence, and between size–weight illusionsand sensitivity to weight diVerences (see the second setof three columns from the left in Table 1). The percent-age of occurrence of the size–weight illusion was calcu-lated for each subject based on 24 trials in which thesizes of the comparison cube were §0.4 cm of the5.0 cm cube. The percentage of correct responses wasalso calculated for each subject in the weight discrimi-nation test over 18 trials with the weight of the compar-ison cubes being §4.0 g of 30.0 g as well as in the size

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discrimination test over 24 trials with the size of thecomparison cubes being §0.4 cm of the 5.0 cm cube.

Results

Figure 2 indicates the mean values for the percentagesof subject’s responses in each response category as afunction of size of the comparison cube. A one-way,within-subjects (size condition; 25 levels) ANOVAindicated 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 per-ceive the comparison cube to be heavier than the stan-dard cube in the Smaller condition (1.0–4.9 cm sizedcube for the comparison) regardless of the fact thatboth were of equal mass (30.0 g). The frequency of thesize–weight illusion was 94.1% (16 trials from 16 sub-jects) for the 1.0 cm cube, 76.5% (13 trials from 13 sub-jects) for the 2.5 cm cube, 67.6% (23 trials from 13subjects) for the 3.5 cm cube, 64.7% (44 trials from 17subjects) for the 4.2 cm, 45.6% (31 trials from 15 sub-jects) for the 4.6 cm cube, and 26.5% (18 trials from 12subjects) for the 4.8 cm cube. Thus, the illusory eVectof feeling the comparison cube as heavier decreased asthe size diVerence between comparison and standard

cube became smaller. It was when the comparison cubewas smaller than 4.0 £ 4.0 £ 4.0 cm that all the subjectsperceived the comparison cube to be heavier than the5.0 cm standard cube, in the Smaller condition.

Likewise, subjects tended to perceive the compari-son cube to be lighter than the standard cube in theLarger condition (5.1–9.0 cm sized cube for the com-parison, 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 sub-jects) for the 5.4 cm cube, 35.3% (24 trials from 13subjects) for the 5.8 cm cube, 52.9% (18 trials from12 subjects) for the 6.5 cm cube, 70.6% (12 trialsfrom 12 subjects) for the 7.5 cm cube, and 82.4% (14trials from 14 subjects) for the 8.5 cm cube. Thus, theillusory eVect of feeling lighter for the comparisoncube increased as the size diVerence became greaterbetween the comparison and standard cube. It waswhen the comparison cube was larger than 7.0 £ 7.0 £7.0 cm that all the subjects perceived the comparisoncube to be lighter than the standard cube (5.0 cm).

As the size diVerence of the comparison cubeapproached the standard cube (5.0 cm, marked as a tri-angle in the middle of Fig. 2), a majority of the subjectsperceived them to be Similar in heaviness. The fre-quency of Similar responses was, for instance, 77.9%

Fig. 2 Mean values for percentage of subject responses as a func-tion of size of the comparison cube (in cm) and response category(Heavier, Similar, and Lighter) in the main experiment. The stan-dard cube and the comparison cube were of identical mass acrossthe trials (30.0 g). The comparison cube is smaller in size than thestandard cube in the range of 1.0 to 4.9 cm (the Smaller condi-tion), while that is larger in the range of 5.1 to 9.0 cm (the Larger

condition). A major percentage of subjects perceived the compar-ison cube to be heavier than the standard cube in the Smaller con-dition (top), and a major percentage of subjects perceived thecomparison cube to be lighter in the Larger condition (bottom).As the size diVerence between the standard cube and the compar-ison cube grew smaller (marked in triangle), most subjects tendedto perceive the cubes to be similar in heaviness (middle)

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(53 trials from 17 subjects) for the 4.9 cm cube, 60.3%(41 trials from 17 subjects) for the 5.0 cm cube, and75% (51 trials from 17 subjects) for the 5.1 cm cube.

Table 1 summarizes the individual subject results forthe frequency of the visually induced size–weight illu-sion (left-most three columns) obtained in the mainexperiment, the susceptibility to the size–weight illusionbased on small graphic size diVerences in the mainexperiment and the sensitivity to weight and visual sizeobtained in the discrimination tests (second set of threecolumns from the left), and the interval and peak veloc-ity of the lifting movement (the set of six columns onthe right) obtained in the supplementary experiment.

As shown at the bottom of Table 1, the mean valueof the frequency of the size–weight illusion was signiW-cantly greater for the Smaller condition (60.3 § 13.0%)than for the Larger condition (49.5 § 17.2%) (Pairedt = 2.431, P < 0.05) which may be due to the greater rel-ative diVerences in volume ratio that were used in theSmaller condition (1:0.008 for the comparison between5.0 and 1.0 cm cubes) than in the Larger condition(1:5.8 for that between 5.0 and 9.0 cm cubes). Therewere also large individual diVerences in the frequencyof the size–weight illusion, e.g., 32.3–83.3% for totalfrequency of the size–weight illusion.

The second three columns from the left indicate theresults 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 sensitivityto visual size (§0.4 cm for 5.0 cm cube). For SW sus-ceptibility, 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 discriminationwas estimated using the psychometric function (Osaka1994), although the trials in the present study were lim-ited. The diVerence threshold was, on average,2.34 § 0.77 g (1.03–3.48 g in mass) for 11 subjects whocould discriminate 4.0 g diVerence in the Wrst step,while it was 4.99 § 0.72 g (4.35–6.34 g in mass) for sixsubjects who went on to the second step of the discrim-ination test (10.0 g diVerence). In total, the mean valueof the diVerence threshold for 30 g mass was3.28 § 1.50 g with a Weber fraction of 0.11 § 0.05(0.034–0.211). The correlation between the percentageof 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 suscep-tibility to the size–weight illusion (SW) and sensitivity

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 illusionfor the small diVerence conditions in the main experiment, the sen-

sitivity to weight, and sensitivity to visual size from the weight andsize discrimination tests (second set of three columns from left),and for the interval between and peak velocity of lifting move-ments in the supplementary experiment (right six columns)

SW indicates the visually induced size–weight illusion; susceptibility to the size–weight illusion was tested for the range of §0.4 cm for5.0 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 rangeof §0.4 cm for 5.0 cm cube

Subject Perception Lifting movement

Frequency of the SW illusion (%)

Susceptibility andsensitivity (%)

Interval time (s) Peak velocity (cm/s)

Smaller Larger Total SW Weight Size Mean SD CV Mean SD CV

1 75.0 45.8 60.4 16.7 27.8 54.2 0.86 0.15 0.17 53.3 4.10 0.08 2 77.1 12.5 44.8 25.0 22.2 41.7 0.61 0.14 0.23 62.5 4.94 0.08 3 54.2 52.1 53.1 25.0 33.3 58.3 1.04 0.29 0.28 60.3 7.11 0.12 4 60.4 41.7 51.0 29.2 55.6 37.5 1.48 0.20 0.14 37.2 4.07 0.11 5 56.3 52.1 54.2 12.5 22.2 37.5 0.90 0.13 0.14 36.5 4.12 0.11 6 68.8 77.1 72.9 45.8 66.7 37.5 0.68 0.12 0.18 42.4 4.23 0.10 7 58.3 35.4 46.9 16.7 0.0 58.3 1.05 0.09 0.09 43.8 4.12 0.09 8 45.8 60.4 53.1 8.3 16.7 33.3 0.89 0.09 0.11 60.0 6.22 0.10 9 45.8 39.6 42.7 29.2 50.0 45.8 1.47 0.27 0.19 32.5 4.75 0.15 10 47.9 56.3 52.1 29.2 38.9 41.7 1.42 0.23 0.16 39.6 5.13 0.13 11 56.3 50.0 53.1 16.7 44.4 41.7 0.86 0.05 0.06 62.9 5.26 0.08 12 64.6 58.3 61.5 25.0 38.9 58.3 1.26 0.15 0.12 37.3 4.78 0.13 13 60.4 47.9 54.2 45.8 61.1 54.2 1.91 0.56 0.30 50.7 5.71 0.11 14 47.9 45.8 46.9 25.0 22.2 54.2 0.79 0.23 0.29 54.1 6.40 0.12 15 41.7 22.9 32.3 16.7 38.9 50.0 0.89 0.07 0.08 51.9 3.11 0.06 16 83.3 83.3 83.3 50.0 77.8 70.8 0.96 0.07 0.08 50.0 3.52 0.07 17 81.3 60.4 70.8 37.5 33.3 50.0 1.03 0.13 0.13 53.3 4.10 0.08 Mean 60.3 49.5 54.9 26.7 38.2 48.5 1.06 – 0.16 48.7 – 0.10 SD 13.0 17.2 12.2 12.2 19.7 10.1 0.34 – 0.07 9.9 – 0.02

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to weight (r = 0.789, P < 0.001). On the other hand, nosigniWcant correlation was observed between suscepti-bility to the size–weight illusion and sensitivity to visualsize (r = 0.350, P = 0.169) or between sensitivity toweight and sensitivity to visual size (r = 0.147,P = 0.573). A signiWcant correlation was observedbetween sensitivity to weight and the total frequency ofthe size–weight illusion (shown as total in Table 1)(r = 0.494, P < 0.05), while there was no signiWcant cor-relation between the total frequency and sensitivity tovisual size (r = 0.298, P = 0.245).

The second set of three columns from the right inTable 1 indicates mean, standard deviation (SD), andthe coeYcient of variation (CV) for the interval time,i.e., duration from completion of releasing the standardcube to onset of lifting the comparison cube. These val-ues are regarded as individual characteristics of the lift-ing movement since these were recorded after the mainexperiment was completed and, as a result, all the sub-jects had become accustomed to the lifting tasks. Thetotal frequency of the visually induced size–weight illu-sion was not signiWcantly correlated with the meaninterval time (r = ¡0.031, P = 0.907) or with the coeY-cient of variation (r = 0.098, P = 0.707), indicating thatneither the duration nor the consistency of intervaltime was related to the occurrence of the size–weightillusion.

The peak velocity of lifts was also examined withrespect to the size–weight illusions. The right-most setof three columns in Table 1 indicates the mean, SD,and the CV for peak lifting velocity. The total fre-quency of the visually induced size–weight illusion wasnot 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 itsstability were related to the occurrence of the visuallyinduced size–weight illusion.

Table 2 indicates the means of peak velocity in theprocess of lifting the cubes and subject responses foreach trial in the supplementary experiment. Althoughthe subjects were instructed to maintain a constant lift-ing speed, a greater peak velocity was, on average,exerted for the comparison cube when it was largerthan the standard cube and vice versa. As a result, sig-niWcant diVerences were observed in peak velocity inthe conditions between the 5.0 and 6.0 cm cube (pairedt = ¡2.136, P < 0.05) and between the 5.0 and 2.5 cmcube (t = 2.355, P < 0.05) in Table 2. Peak velocity thushad some proportionality to perceived object size, i.e.,larger objects had higher peak velocities. However,peak velocity was not correlated with the heavinessjudgments, nor was there consistency among the sub-jects.

Average lifting velocity proWles across subjects andtrials are depicted in Fig. 3. The velocity proWles for thecomparison cube (bold solid line) are graphed to lag by0.1 s those from the standard cube (thin solid line), tomake easier the comparison of velocity proWles. Peakvelocities were found to be signiWcantly higher in theLarger condition (Fig. 3a) and signiWcantly lower in theSmaller condition (Fig. 3b), compared to the standardcube size (5.0 cm, see also Table 2). Individual subjectvelocity proWles are shown for the Larger condition (c).In the Larger condition (Fig. 3c), three subjects, withthe reports being for Similar, had peak velocity valuesthat were similar between the standard cube and thecomparison cube (like subject 1 in Fig. 3c). Ten sub-jects had peak velocity values with the comparisoncube being greater than the standard cube (like subject8 in Fig. 3c), while the reports of Wve out of those tensubjects were for Lighter, three for Similar, and two forHeavier. In contrast, four subjects had peak velocityvalues with the comparison cube being lower than forthe 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

Condition Comparison Peak velocity (cm/s) Subject response

Size(cm) Standard Comparison Lighter Similar Heavier

Mean SD Mean SD

Larger 7.5 44.6 9.2 47.2 10.0 11 6 07.5 50.4 7.4 51.5 10.4 12 5 06.0 47.6 12.4 49.8 11.5* 6 7 46.0 49.9 10.5 50.4 9.9 10 5 2

Identical 5.0 47.7 10.8 47.8 11.6 3 13 15.0 49.2 9.7 50.4 11.5 5 9 35.0 48.7 10.6 47.6 12.5 3 13 15.0 50.1 11.9 50.2 12.7 2 12 3

Smaller 4.0 52.2 8.4 50.0 10.9 2 9 64.0 53.8 8.3 51.1 9.4 1 6 102.5 48.4 10.8 46.8 11.4 0 2 152.5 50.4 11.7 47.6 11.4* 0 3 14

The size (cm) indicates thecomparison cube

*Indicate signiWcant diVer-ences in mean values between the standard cube and the comparison cube (P < .05)

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four, the report of one subject was for Lighter, one forSimilar, and two for Heavier than the standard cube.Thus, although there were trends for peak velocities tobe higher for larger cubes, and lower peak velocitiesfor small cubes, these motor eVects were not related tothe heaviness judgments (see Table 2).

Discussion

In summary, the results are as follows: (1) the visualsize cues inXuenced perceived heaviness for all subjectsunder conditions having suYcient size diVerencesbetween standard and comparison cubes of equal mass(Fig. 2); (2) visual size cues aVected perceived heavi-ness such that when the comparison cube was relativelysmaller in size than the standard cube, it was perceivedto be heavier, and vice versa (Fig. 2); (3) as the sizediVerence increased between the standard cube andthe comparison cube, more subjects experienced theillusion. Similarly, as the size diVerence becamesmaller, fewer subjects experienced the illusion(Fig. 2); (4) whether or not the subjects experiencedthe size–weight illusion was signiWcantly correlatedwith their sensitivity to weight discrimination but nottheir sensitivity to discriminate small diVerences invisual size (Table 1); and (5) erroneously pro-grammed motor commands were not systematicallyrelated to the heaviness estimates or experience of

the size–weight illusion (Fig. 3, and Tables 1, 2). Belowwe consider: the signiWcant correlation between fre-quency of the size–weight illusion with sensitivity toweight diVerence, implications of results for sensorybased and cognitive-based theories of the size–weightillusion, multisensory information integration, the gen-erality of the results to objects of greater mass, the roleof size information more broadly in heaviness percep-tion and a conceptual model for occurrence of the size–weight illusion.

Size–weight illusion frequency correlates with weight sensitivity but not size sensitivity

As the size diVerence increased between the standardcube and the comparison cube, more subjects experi-enced the illusion. Similarly, as the size diVerencebecame smaller, fewer subjects could experience theillusion (Fig. 2). In short, the visual size of handledobjects seems to be important factor for all the subjectsto experience the visually induced size–weight illusion.In addition, experience of the size–weight illusion wassigniWcantly correlated with each subject’s sensitivity todiscriminate weight diVerences (Table 1). These resultssuggest that a subject’s susceptibility to the size–weightillusion may depend partly on the magnitude of sizediVerence between two target objects, and partly on anindividual’s sensitivity to small weight diVerences.

On the contrary, and somewhat paradoxically, thepresent results (Table 1) show that experience of thesize–weight illusion was not signiWcantly correlatedwith a subject’s ability to discriminate small diVerencesin visual size, although visual size was a single indepen-dent factor. In short, whether or not subjects can dis-criminate which of two closely sized objects is larger orsmaller is not a critical factor for all the subjects toexperience the size–weight illusion.

Implications for sensory based and cognitive-based theories of the size–weight illusion

These results imply that cognitive processes for forma-tion of expectation (Ross 1969) or rationalization(Mon-Williams and Murray 2000) are not involved nec-essarily in the production of the visually induced size–weight illusion, as obtained in the present study. InExpectation theory (Ross 1969), involvement of thecognitive process to discriminate size diVerencebecomes essential in the production process of the size–weight illusion. Without such a cognitive process to dis-criminate which object is larger or smaller, it must bevery hard as a next step to form an expectation that alarger object should have greater weight or mass than a

Fig. 3 ProWles of lifting velocity are averaged for all subjects, inwhich 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 forthe comparison cube (bold solid line) are graphed to start 100 mslater than the standard cube (thin solid line). c Indicates typicalexamples for individual subject velocity proWles in the same Larg-er condition as shown in (a)

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smaller object, prior to lifting an object (Ross 1969).Similarly, in Rationalization theory (Mon-Williams andMurray 2000), the cognitive process to discriminate sizediVerence must be necessary to rationalize in order toresolve the discrepancy between awareness that twoobjects are the same weight and the sensory feedbackthat indicates otherwise. Nevertheless, the occurrenceof the size–weight illusion did not correlate with thesensitivity to small visual size diVerences, which abso-lutely contributes to comparison of object size.

Thus, susceptibility to the visually induced size–weight illusion may depend partly on visual size magni-tudes of target objects, and partly on an individualsensitivity to small weight diVerences, rather than sen-sitivity to small diVerences in visual size. This suggeststhat the visually induced size–weight illusion is basedmainly on intensity of visual stimulus or sensory basedevent (Masin and Crestoni 1988) rather than a cogni-tive-based event (Ross 1969; Mon-Williams andMurray 2000; Flanagan and Beltzner 2000).

Reexamination of Expectation theory based on kinematics

Kinematic results from the present study reconWrmedtwo previous Wndings related to the visually inducedsize–weight illusion. Firstly, visual size cues inXuencemotor programming during the lifting movements. Thatis, regardless of the fact that subjects were instructed tolift in a uniform manner for all objects, peak velocityduring the lifting movement tended to increase when thecomparison cube was larger than the standard cube, andvice 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, thata larger object will be lifted with stronger motor com-mands. The second replicated Wnding, however, is thatthere is not a strong, systematic relationship between theexperienced illusions and erroneously programmedmotor commands. In the present study, greater peakvelocity did not necessarily correlate with a subject’sperceived heaviness on every trial (Fig. 3). This is consis-tent with the results recently reported by Mon-Williamsand 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 per-ceived heaviness as a function of object size strongly

support a direct participation of visual size informationto the perceptual system of heaviness, i.e., the Informa-tion Integration theory (Sjöberg 1969; Anderson 1970;Masin and Crestoni 1988), rather than less direct ormore constructed participation of visual size informa-tion, such as Expectation theory (Ross 1969) or theRationalization theory (Mon-Williams and Murray2000).

Recently, noninvasive imaging techniques, e.g.,functional magnetic resonance imaging (fMRI) or posi-tron emission tomography (PET), have provided evi-dence in support of multisensory interaction orintegration processing in humans (Macaluso 2006). In aPET experiment, Sathian et al. (1997) found neuronsin areas seven or nineteen in normal human cortex,which responded to both visual and somatosensorystimuli when subjects viewed an approaching object. Inan fMRI study, Amedi et al. (2001) demonstrated func-tional overlap between visual and tactile object-relatedactivation in the ventral visual pathway when theyinstructed their subjects to recognize objects eithervisually or haptically. In a delayed-matching task,James et al. (2002) demonstrated visuo-tactile interac-tions in the occipital cortex by fMRI.

Such neurons, therefore, may be involved in thevisually induced size–weight illusion. Further investiga-tion is required to understand how visual size cues inte-grate with weight information in heaviness perception,e.g., whether they arrive via the dorsal stream duringlifting movements or via the ventral stream duringobject recognition (Goodale 1994).

Generality of the results to objects of greater mass

Low-mass (30.0 g) cubes were selected in the presentstudy to minimize subject’s fatigue as well as toenhance the visual size eVect on perceived heavinesssince it was reported to be weak (Ellis and Lederman1993). The potency of the illusion induced by visualsize cues is expected to diminish as weight increases(Ross 1969; Stevens and Rubin 1970; Cross and Rotkin1975) or in cases where the size and weight increase ina constant ratio fashion (Ross 1969; Ross and Di Lollo1970; Stevens and Rubin 1970). This does not mean,however, that the size eVect will disappear entirelywith greater masses. In fact, eVects of visual size cueson perceived heaviness have been reported in severalstudies using more massive stimuli (60–270 g, Ross1969; 150–765 g, Masin and Crestoni 1988; 1,030 g,Gordon et al. 1991a, b; 140–904 g, Ellis and Lederman1993; 250 g, Mon-Williams and Murray 2000). Thus,visually perceived sizes tend to aVect perceived heavi-ness as long as test objects are of identical mass, though

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its eVect is consistently weaker than the eVect of theactual mass when comparing objects of diVerent sizes(Ross 1969; Ellis and Lederman 1993). However, fur-ther investigation is required to clarify the relationshipbetween mass magnitude, magnitude of size diVer-ences, and the frequency of the size–weight illusion.

The role of size information in heaviness perception

The eVects of size cues, whether haptically or visuallyacquired, have been regarded as an interesting bias tonormal weight perception. As such, the size–weightillusion has long been discussed separately from weightperception amongst psychologists and psychophysicists(Jones 1986). It is possible, however, that size informa-tion is a fundamental, rather than simply intriguing,aspect to heaviness perception.

Kawai (2003a) recently attempted to link the size–weight illusion and weight perception into a singleframework deWned as heaviness perception. He foundthat haptically perceived size cues are constantly andsystematically involved in weight discrimination evenwhen the objects are composed of identical material,i.e., density (Kawai 2002a). He also found that subjectscould detect density information as well as weight, inspite of the fact that subjects should be unable todirectly detect density information from the handledobjects (Kawai 2002b). He, therefore, suggested thatsubjects might integrate haptically acquired size infor-mation with haptically acquired weight information toacquire not exactly density but density-like informa-tion, as opposed to weight information (Kawai 2002b,2003a, b).

The idea that human beings may acquire density-like information rather than weight information inthe perception of heaviness suggests that the size–weight illusion is not an illusion at all, but rather asimple phenomenon caused by an accurate integra-tion of size and weight information obtained fromthe object being grasped. This idea was discussedpreviously in relation to the human motor systems byClaparede (1901) who proposed that the formationof the internal neural representation of the objectweight may be based on a predicted relationshipbetween the size and weight. Gachoud et al. (1983)also proposed that the properties of the object mustbe compared in relation to the size and weight usingassociative algorithms.

Furthermore, the present Wnding that visuallyacquired size information may also Xow into the per-ceptual system for heaviness implies that such a sys-tem may not simply perceive object weight, but rathermay serve to identify a uniWed, wholistic object by

integrating several pieces of information from multi-ple modalities (Shimojo and Sham 2001; Maravitaet al. 2003; Lloyd et al. 2003). If so, other inXuentialfactors related to lifting movement, e.g., friction, tex-ture, conWguration, and rotational dynamics, mightXow into the same, integrated perceptual system forheaviness. Although the concept that all informationrequired for grasp and lifting movement may con-verge in the perceptual system for heaviness requiresfurther investigation, the signiWcant eVects of surfacetexture, slipperiness, conWguration, and rotationaldynamics on perceived heaviness have been alreadyreported (Johansson and Westling 1988; Edin 1992;Flanagan et al. 1995; Amazeen and Turvey 1996;Kinoshita et al. 1997; Jenmalm 1998; Flanagan andBandomir 2000).

A conceptual model for the occurrence of the size–weight illusion

Although the motor system related to lifting move-ment may operate independently of the perceptual sys-tem for heaviness (Goodale 1994; Flanagan andBeltzner 2000; Grandy and Westwood 2006), it seemsnatural and reasonable to think that there should besome degree of linkage enabling the exchange ofweight information between the two systems (Maschkeet al. 2006). For example, Ross (1969) posited Expecta-tion theory to interpret the size–weight illusion. There-fore, an attempt was made in this study to reconsiderhow the size–weight illusion occurs, taking the linkagebetween the two systems into account.

Figure 4 demonstrates a conceptual model based onWndings and concepts previously established. Weight/Size is used as an internal model (Kawai 2003b), notweight itself as is generally considered (Wolpert andKawato 1998; Davidson and Wolpert 2004). The den-sity-like information obtained in the previous lift isselected as the internal model for the current lift of atarget object (Westling and Johansson 1984; Johanssonand Westling 1988; Cadoret and Smith 1996). Thisinternal model (Weight/Size; a in Fig. 4) is integratedin a multiplication process with the visual size cues(Size�; b) in the process of grasping and lifting phase(Masin and Cresotoni 1988), resulting in only weightinformation being extracted (Weight’; c). In this pro-cess, if the size of the object being lifted is larger thanthat of the previous object (Size� > Size), Weight’ willbecome greater than Weight and vice versa (ifSize� < Size, Weight� < Weight). Thus, the weightinformation of a target object can be accurately com-puted prior to lifting whether it is larger or smallerwithout any cognitive process.

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Exp Brain Res (2007) 179:443–456 455

This information (Weight�) may be used as motorcommands to generate forces in the Wnger and handmuscles (c in Fig. 4). Once the target object is lifted, trueweight (Weight�) and size (Size�) is obtained from theobject being lifted and is then integrated through a divi-sion manner (Weight�/Size�) or a multiplication manner(Weight� £ Size�¡1) to become the true internal repre-sentation (d in Fig. 4) as suggested by Kawai (2003a, b).Weight�/Size� may be compared with the previous inter-nal model (Weight/Size) in the perceptual system whileupdating Weight/Size into Weight�/Size� to become thenext short-term memory item (e in Fig. 4).

If appearance of the target object is similar to theprevious object, as in the case of the size–weight illu-sion, this updated memory will be used as the internalmodel for the following lift (Westling and Johansson1984; Johansson and Westling 1988; Mon-Williams andMurray 2000). However, if object appearance variesfrom that of the previous object, as when presentedwith a novel or unfamiliar object, the internal modelmay be extracted from learned memory (Gordon et al.1993; Flanagan et al. 2001). This model makes it possi-ble to understand previous Wndings in which visual sizecues provided paradoxical eVects in the size–weightillusion on the perceptual system (i.e., the larger objectbeing perceived as lighter) and on the motor system(i.e., the larger object being lifted with greater motoroutput).

In conclusion, the visually induced size–weight illu-sion occurred in accordance with the magnitude ofvisual size cues, and with a subject’s sensitivity toweight diVerence, indicating systematic and directinvolvement of visual size information in the percep-tual system of heaviness. In contrast, the susceptibilityto the illusion did not correlate with a subject’s sensi-tivity to small diVerences in visual size, indicating thatsuch a cognitive process as deciding which object islarger or smaller is not necessary for production of theillusion. These aspects suggest that the size–weight illu-sion may be basically and systematically induced byneural integration of visual or haptic information aboutsize and sensorimotor information about weight, andmay then be modiWed by highly cognitive factors suchas expectation, experience or rationalization.

Acknowledgments This research was supported in part bygrants (C18500209) from Japan Society for the Promotion of Sci-ence and the Tezukayama Educational Institution, and the Natu-ral Sciences and Engineering Research Council of Canada.Gratitude is expressed to Professor H. E. Ross of the Universityof Stirling for oVering her valuable data as well as to Professor R.G. Marteniuk, R. Metcalfe, A. Tao, M. Zahariev, and B. Zheng ofSimon Fraser University.

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Fig. 4 A conceptual model. Density information (a Weight/Size)obtained in the previous lift is used for an object for the currentlift and is integrated with the size cues (Size�) currently obtainedduring grasping and initial lifting phase, so that weight informa-tion (Weight�) is extracted in a multiplication process (b). Thisinformation (Weight�) is transformed into motor commands togenerate the necessary amount of forces to lift a target object (cForce). Once the target object is lifted, true weight (Weight�) andsize (Size�) are both haptically obtained and integrated in a divi-sion process (d Weight�/Size�). This true internal model (Weight�/Size�) may be compared with the previous internal model(Weight/Size), and then be updated as the new short-term mem-ory in the perceptual system (e). In the size–weight illusion,Weight� should constantly be equivalent to Weight, while Size�varies from Size

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