A Brief Taxonomy of Tactile Illusions and

Demonstrations That Can Be Done In a Hardware Store

Vincent HaywardHaptics Laboratory, Centre for Intelligent Machines, McGill University,

3480 University Street, Montreal, H3A 2A7, Canada

Author’s version. The final version appeared in Brain Research Bulletin, 2008, Vol 75, No 6, pp 742-752(Special issue on Robotics and Neuroscience, D. Prattichizzo and S. Rossi, Eds.)

Abstract

This paper surveys more than twenty types of tac-tile illusions and discusses several of their aspects.These aspects include the ease with which they canbe demonstrated and whether they have clear vi-sual analogs. The paper also shows how to con-struct equipment made of simple supplies able todeliver well controlled tactile signals in order toconveniently demonstrate four different tactile il-lusions.

Keywords:Tactile illusions, haptic illusions, hapticperception, tactile perception

1 Introduction

Perceptual illusions have furnished considerablematerial for study and amusement, probably muchbefore Aristotle discussed them. Tactile and hapticillusions are frequently discussed in terms of simil-itude with visual counterparts, if one excludes, ofcourse, those resulting from cross modal interac-tions. An example of the parallels that are oftendrawn between tactile and visual illusions is foundin the comments of Rivers regarding the “reverseAristotle illusion” [67]. This illusion is when peo-ple feel only one surface (sometimes three) whentwo surfaces are in contact with the outer sides ofthe crossed fingers. In the classic Aristotle illu-sion most people feel two objects when only one istouched with crossed fingers (see Fig. 1). Riversregarded this as an analog to stereopsis, to use amodern terminology. A further example, more re-cently discussed by Benedetti is diplesthesia that

was viewed as a tactile equivalent to diplopia, ordouble vision [5]. Pushing gently on the corner ofone eye causes diplopia, while pressing two fingerstouching the same object can cause a doubling ofthe sensation, or diplesthesia. The analogy wasthus motivated by the observation that in the twocases the perceptual disjunction results from exter-nal mechanical perturbation.

Generally, however, far fewer tactile illusionsthan visual or even auditory illusions have beendescribed. A likely contributing factor to the rela-tively small number of known tactile illusions is notthat there are few of them, but that many visual il-lusions can be created out of simple materials suchas pencil and paper, or even simply by looking ata natural scene under the right conditions. More-over, with the development of computers and ofthe Internet, uncountable websites provide a hugerepository of visual illusions which are easily ac-cessible. To a lesser extent, this is also true ofauditory illusions. But for touch, there are veryfew that are easily accessible with the exception ofan amusing version of what could be said to be acase of diplesthesia occurring when holding a penbetween the lips while pulling the mouth cornersdiagonally [56]. To demonstrate and study tactileillusions, one is often required to set up equipmentthat can create the proper conditions, and rarelydo they arise naturally in an obvious manner.

A first aim of this paper is to describe a tax-onomy of tactile illusions, concluding that certainare quite specifically tactile and do not have clearvisual analogs. As we will proceed in listing theseknown tactile illusions, we will indicate the easewith which they can be demonstrated. In a second

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part of this article, the means for producing someof these effects with commonly available supplieswill be described. For more systematic studies,the generation of computer-controlled stimuli canbe accomplished with special purpose, or robotic-like electromechanical equipment.

Several definitions exist for what is an illusion.These definitions can include or exclude differenttypes of phenomena. An extreme view is that allperceptual processes are illusions to some extent.Another view is that an illusion is a wrong per-ception. What constitutes a wrong perception cannevertheless be subject of debate. The idea of il-lusions being when the senses are deceived is notquite satisfactory, even if illusions can be employedfor deception, as in camouflage. Different stimulican produce the same percept. For example, incolor perception it is known that different spectracan elicit the same color [14]. Thus, a color perceptis always wrong given a class of equivalent stimuli,yet it is not an illusion. On the other hand, equiv-alent stimuli form a rich source of illusions.

In the view of the author, an illusion is a perceptarising from a specific stimulus delivered underspecific conditions that gives a different consciousexperience when the conditions are changed. Inother words, the information available to the per-ceiver should be separable into a constant part anda variable part, and the percept produced by theconstant part should be contingent on the variablepart which can include endogenous neural states.In addition, the change should be surprising, unex-pected, even amusing when the perceiver becomesaware of it. Consider for example the “moon illu-sion” [41]. The moon disk creates the same reti-nal image whether it is near the horizon or up inthe sky, yet its perceptual size changes. With the“Necker cube illusion”, prolonged viewing can pro-duce perceptual switches even when the viewingconditions do not vary [44]. In the former case,the visual context modifies the perception of thesame disk. In the latter case, the conditions refersto endogenous neural states since the whole of thevisual input is essentially invariant.

There are many motivations for the study of il-lusions in general, and of tactile illusions in par-ticular. Some of these motivations are practical.Illusions are at the basis of virtually all technolog-ical displays, from cinematography, to computer

screens, to audio reproduction systems. This isalso true of haptic interfaces. More generally, theyprovide important clues regarding the processes atall levels that allow the brain to perceive and to beconscious. They have theoretical value since theysuggest methods to test models, but also have clin-ical applications to detect sensory dysfunction.

2 A Brief Taxonomy

We now attempt to catalog tactile illusions as theyare reported in the literature. In the interest ofbrevity, were excluded those illusions related to theawareness of one’s own body, such as phantom limbphenomena or limb position-sense effects. Thosecould be the topic of a separate survey. Here wecollect phenomena related to the perception of theworld outside the body. Table 1 can be consultedfor a summary.

2.1 Object Perceptual Disjunction andConjunction

As was commented in the Introduction, object dis-junction/conjunction” effects are often discussedwith reference to analogous visual notions such asstereoscopic image fusion [67, 5]. The Aristotle il-lusion is particularly effective when touching one’snose with crossed fingers and hence belongs to theset of those illusions that can be very easily demon-strated, although it may not succeed with everyone(Fig. 1).

Figure 1: The classic “Aristotle illusion” demon-stration involves touching a pea. (A) Fingers arecrossed and the nose is touched instead. Oneshould feel two noses. Try different places. (B) Thereverse illusion can be experienced by touching aninside corner with finger crossed. One should feelone surface, not two.

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2.2 Mislocalization

At least two well-known tactile illusions fall intothe category of mislocalization of stimulation onthe skin. The oldest known is funneling describedby von Bekesy [81]. Producing it is rather sim-ple. It requires to deliver short and simultaneousvibratory signals (of the order of 5 ms) at differ-ent locations of the skin (spatial separation of theorder of 2 cm on the forearm). Under proper con-ditions, only one pulse is felt, for example, half waybetween two contact locations in the case of justtwo contactors. Many other variants have been re-ported in terms of locations of the body and num-bers of contactors. It was studied by Gardner andSpencer who performed peripheral and central mi-croneurographic recordings in the cat [31]. Thisillusion has recently been used to investigate neu-ral correlates of tactile perception using corticaloptical imaging [12].

A second well-know mislocalization illusion wasdescribed by Geldard and Sherrick who gave it thename of the “cutaneous rabbit”. Here, one alsoneeds ‘vibrotactors’ causing short pulses (a fewmilliseconds) at discrete locations on the skin (ofthe order to 10 cm separation on the arm), but thistime their firing must be spread through time atintervals of a few tens of milliseconds, typically inone burst of five pulses at one location, then an-other five at the next location and so-on. What isfelt is a progression of pulses on the path from onelocation to the next. In that, it can be viewed as akinetic variant of the funneling illusion. Since then,truly many variations have been investigated in-cluding two-dimensional variants induced througha electro-cutaneous stimulation [75]. It also wasthe basis of neural correlate studies using func-tional magnetic resonance imaging (fMRI) [8]. Re-lationships, or lack thereof, with visual illusionswere discussed in terms of the phi effect (appar-ent movement) and tau effect (apparent distancereduction) by Geldard [32].

One should expect that many more mislo-calization illusions remain to be found, hav-ing in common methods of production involvingelectronically-driven vibrotactile pulses generators.

2.3 Distance Misjudgment

Taylor-Clarke et al. studied an illusion that wasdescribed by E. H. Weber [85]. Two objects incontact with the skin which are kept at a constantdistance appear to be closer when transiting froma region of high acuity to one of lower acuity (lips-forehead, fingertips-forearm). Conversely, for twoobjects to be felt at the same distance, they mustbe closer in the regions of high acuity. This illusionindicates that tactile size constancy, like in vision,is effective only within limits [76]. It is easy todemonstrate with a paperclip bent so that the twosharp ends are about 1 cm apart. The twin contactthat can be created with this apparatus is thenmoved from the fingertip of the index, to the palm,to the inside of the wrist, to the forearm, or vice-versa.

2.4 Audiotactile Interaction for Rough-ness, Crispiness, Stiffness, ...

Without much doubt, it is under the effect ofcross-modal interactions that the largest numberof tactile illusions have been reported. This typeof illusions is not particularly specific to touch.Some are reviewed in this and the next five sub-sections. Most have analogs in the auditory andvisual modalities.

Since under a wide range of conditions manysurfaces produce an audible sound when touched,one may argue for the ecological prevalence of thesimultaneous production of auditory and tactilestimulation [9]. This was studied by Lederman andothers [51, 35]. A particularly effective demonstra-tion suggested by the present author is to use chalkto write on a blackboard with and without wearingear plugs. Attending to the roughness of the board,it is obvious to most that the blackboard feelssmoother when wearing earplugs (or other sound-blocking or sound-masking device). A similar ef-fect may be created by rubbing one’s hands againsteach other while similarly changing the acousti-cal conditions of the experience. DiFranco et al.showed that subjects tend to rank object stiff-ness differently for identical synthetically producedhaptic objects when the auditory cues vary [20].Whether these effects qualify as illusions is debat-able since they are instances of sensory integrationeffects [25]. In the best conditions, however, the

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interaction can be sufficiently surprising to meritthis status, as in the “parchment-skin” illusion de-scribed by Jousmaki and Hari [45]. Here in con-trast to the blackboard demonstration, the soundmade by rubbing the hands against each other ispicked up by a microphone, the high-frequenciesare enhanced, and the result given to the per-ceiver through headphones. The result is a mod-ified sensation of skin roughness/smoothness ordryness/moisture. This type of illusory perceptionhas practical implications for everyday life such asduring food appreciation [91].

It is also the case that vision interacts with touchin the perception of size, texture, stiffness andprobably most other object attributes [70, 39, 73].This fact was noted long ago by Katz “When onecuts into some soft wood with a knife under astrong magnifying glass, the resulting visual en-largement gives rise to the impression that oneis cutting deeply into a soft mass, such as cork”,quoted by Krueger [48].

2.5 Weight

The “size-weight” or Charpentier illusion is a clas-sic and is remarkably robust [11]. It refers to thefact that when lifting two boxes of equal weightbut of different sizes, the greatest majority of peo-ple are convinced that the smaller boxes are heav-ier than the bigger. It has been described andstudied many times and like many classic illusionsserved as a basis to test hypotheses about percep-tion and action [34]. It is very easy to demonstrateby procuring two or three boxes having the sameaspect but of different sizes (or blocks of wood)and loading them to equalize the weights. Anotherweight illusion known since the nineteenth centurywas described E. H. Weber who found that objectsof equal weight felt heavier when they felt cold thanwhen they felt warm [71]. Recently, Reiner and col-leagues demonstrated that objects labeled “heavy”felt heavier than objects labeled “light” althoughthey had the same mass in a variant of the Stroopeffect [64]. Weight judgement illusions can be de-clined in very many variations [27, 1, 23, 24, 28].

2.6 Numerosity

An effective way to create touch-related illusionsis to ask subjects to count fast-paced auditory and

tactile events. Bresciani et al. report that un-der the conditions of sufficient simultaneity (of theorder of a few tens of milliseconds) the numberof felt taps (2, 3, or 4) depended on the numberof heard beeps [10]. Moreover, Violentyev et al.found that observers would see two flashes whenonly one was produced, if two tactile taps were de-livered within a 60 millisecond interval [79]. Theseinteractions collectively provide evidence for multi-modal cortical circuits. As already mentioned theyhave many equivalents with combinations involv-ing vision. Cross-modality numerosity effects seemto occur for touch as much as they do for vision andaudition.

2.7 Change Numbness

This type of illusion is astonishing to those whoexperience it and then are made aware of its exis-tence. In vision, change blindness, which is wherepeople fail to see major changes in a scene as theresult of a distractor, or from coincidence witha blink or a saccade, has been extensively stud-ied [65, 72]. A similar phenomenon exists for audi-tion, change deafness [78]. It is thus natural thatsomething analogous should occur for touch, andindeed, it does with distractors which are eithertactile or visual [29, 30].

2.8 Temporal Ordering

Craig et al. found that there was a correlation as-sociated with the location on the body where tac-tile stimuli are applied and the judgement of theorder in which they occurred. This was tested us-ing one finger, two fingers of the same hand, orfingers of two hands [16]. But recently, Yamamotoand Kitazawa revealed that the judgement of thetemporal ordering of taps in the bilateral conditionwas reversed from the mere fact of crossing one’sarms, and furthermore found that the effect couldbe cancelled when holding sticks that crossed to‘undo’ the crossing of the arms! [89]. This findingraises new questions regarding the brain mecha-nisms responsible for temporal ordering of eventsand body representations. It may also have a con-nection with the distal attribution phenomena dis-cussed in Section 2.13.

Numerosity, change numbness, and temporal or-dering effects have much in common in the type of

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stimuli that cause them and in the inability of thebrain to disentangle fast paced events.

2.9 Pseudo-Haptic Effects

A series of surprising pseudo-haptic effects was de-scribed by Lecuyer et al. [49, 50]. The commonthread behind these effects is that, in the properconditions, visual cues can create haptic sensa-tions that have no basis in the physical mechan-ical signals experienced by the subject. For exam-ple, when sliding a computer mouse on a smoothand uniform surface, if the velocity of the cursorrelatively to that of the mouse is modulated as afunction of its location on the screen in correlationwith seen items, haptic sensations such as viscosityor shape are typically experienced [49].

2.10 Shape From Distributed Cuta-neous Deformation

Under this heading may be collected perceptual ef-fects that occur when distributed deformation pat-terns are created on the skin in an orderly andcontrolled fashion. What these effects have in com-mon are skin deformation patterns that resemble insome key aspects those that arise naturally. Theycan create a robust percept.

With an ordinary plastic comb and a pencil (seemore detailed description in the next section), aprogressive wave of shearing deformation can becreated in the skin of the fingerpad. While thenormal indentation is invariant, one typically ex-periences the sensation of a raised dot traveling onthe finger, as described by Hayward and Cruz [37].This may be called the “comb illusion”. It is ef-fective enough, using computer controlled devices,to enable blind subjects to read Braille-like pat-terns [54].

Kikuuwe et al. described an effect which, be-cause of its effectiveness, should also fall into thecategory of illusions. The undulations of a surfacecan be magnified when a brush-like structure isinterposed between the surface and the skin [47].This structure is a deformable membrane withdensely distributed rigid posts. When scanning asurface that is not perfectly flat, the membrane isdeformed causing the skin in contact with the poststo be laterally stretched and compressed. The re-sult is a sensation of shape. In that, it probably

appeals to mechanisms similar to that of the combillusion.

Recently Nakatani et al. described a related phe-nomenon that is produced by rubbing a finger onsurfaces divided into strips made of different ma-terials and/or textures [60]. One possibility callsfor a smooth strip with ridges milled orthogonallyon each side, hence the “fishbone illusion”. Rub-bing the finger along the strip results in a sensa-tion where the surface is no longer flat. Severalvariants obtained by manufacturing surfaces withnon-uniform adhesion properties and that can eas-ily be demonstrated will be described later.

Taking advantage of another type of orderly skindeformation, Dostmohamed and Hayward showedthat when eliminating all shape information orig-inating from within the contact area, and despitethe complete absence of proprioceptive cues inthe normal direction, the movement of contact onthe fingerpad skin, alone, gave the perception ofshape [22]. In other words, a flat plate can feel likean illusory “curved plate”. This, combined withother haptic cues, makes for powerful haptic shapedisplays [62].

With the exception of illusions related to tac-tile flow such as the tactile version of “barber poleillusion” caused by moving a slippery undulatedsurface under the fingers [6], the effects createdby distributed cutaneous deformation often do nothave clear analogs in other modalities, or if theydo, they may be too speculative to be discussedwithin the scope of this brief survey. This illusioncan be demonstrated by gluing a set of metal rodsside to side and then asking an assistant to movethe stimulus in various directions under a soapedfinger.

2.11 Geometrical Illusions, Bourdon,Muller-Lyer, and Others

A large number of tactile illusions which, thistime, have perfect analogs in vision have beendescribed and studied. In general, they requirethe production of raised line drawings which areexplored in haptic mode, that is via tactile ex-ploration. Day comments that they have beendescribed for a long time [18, 66]. Suzuki andArashida looked at the relative effectiveness of var-ious figures, Muller-Lyer, Oppel-Kundt, Bourdon,

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Ponzo, Poggendorf, vertical-horizontal, Zollner,Delbœuf [74], while Heller and Joyner consideredthe horizontal-vertical effect comparing the behav-ior blind and sighted people [40]. These effectsmotivated a significant number of recent stud-ies [77, 57, 33]. Generally speaking, in the hap-tic domain, the weakest of these illusions is that ofDelbœuf and the strongest that of Muller-Lyer [33].

A setup to demonstrate the vertical-horizontalillusion can be made of two chopsticks glued in aL shape configuration on a firm backing. Then,their respective lengths is appreciated with theeyes closed. Embossed drawings of adequate qual-ity can be produced manually by writing whilepressing firmly with a ball pen on heavy paper laidon soft backing.

2.12 Kinaesthetic Effects

Here is a series of effects which may also fall un-der the category of illusions and which all share atask of estimation of metric properties of objects,real or virtual, such as size or distance. Theseeffects have a very long history. Krueger notedthat W. James in 1890 wrote that “The interiorof one’s mouth cavity feels larger when exploredby the tongue than when looked at. The craterof a newly extracted tooth, and the movementsof a loose tooth feel quite monstrous” [48]. Someof these effects carry clear relationships to visualillusions, but some do not. Reid described thevertical-horizontal illusion occurring when gaugingthe length of identical objects at different orienta-tion as analog to that in vision [63]. Davidon andCheng reported that subjects consistently overes-timated the lengths of objects when using a radialmovement rather than a lateral one, but disputedanalogy with visual effects [17]. In any case, thistype of effect invariably involves the performanceof significant movement by the limbs, fingers orarms [13, 42, 3].

Judgement of orientation can also yield surpris-ing results [46]. It can easily be demonstratedby asking a blind-folded volunteer to orient twopencils on a table in the same direction, say bysixty degrees toward the right, with one pencilin each hand. The directions in which the pen-cils point will be quite different. Recently, a newseries of studies reveals a variety of new effects

involving this type of judgments, in conjunctionwith vision [7], complex movements [26], and forcecues [88]. In this section we may also include aneffect described by Cormack that involves rotatinga disk using two passive fingers of one hand andtwo active fingers from the other [15]. The disk nolonger feels round but oval.

A force perception effect resulting from a peri-odic, yet asymmetric acceleration profile of a boxheld in the hand was described by Amemiya etal. [2]. Inside the box, a slider-crank mechanismcreates peaks of high accelerations separated bysegments of lower acceleration. While momentumis conserved, one experiences the feeling of beingpulled out of thin air.

2.13 Distal Attribution

Many discussed it. Katz, Gibson, and Merleau-Ponty wrote about it [48]. For Katz “while sewing,our perception seems to be immediately present inthe point of the needle”. This is even more as-tonishing as this happens even when wearing athimble that transforms in a most radical man-ner the mechanical coupling of the needle withthe finger. For Merleau-Ponty “to get used to ahat, a car or a stick is to be transplanted intothem, or conversely, to incorporate them into thebulk of our own body.” The cane for the blindhas often been commented to produce a similarphenomenon. Wilson gives this and other exam-ples [86]. Here the author suggests doing a simpleexperiment. First, hit with the fist a table topto appreciate its resistance. From the oscillations,there is a clear perception of its elasticity. If thesame fist rests the surface but an assistant bangsthe table at some distance, then effectively thesame tactile stimulus gives rise to the perceptionof a distant shock rather than something about themechanics of the table.

Fortunately for the success of electronicallydriven haptic displays distal attribution seems tohappen under an extraordinary range of condi-tions [38]. Back-y-Rita’s tvss enabled blind sub-jects to feel objects exterior to their bodies viasubstitution of vision by artificially produced vi-brotactile patterns [4]. A most interesting, mini-malist variant is described by Lenay et al. wheredistal attribution is reported to occur for single-

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site, single-taps vibrotactile stimuli given under theproper sensorimotor coupling [52, 36]. Recently, adynamic form a distal attribution was reported byYao and Hayward to occur when the tactile stim-ulation’s frequency spectrum is appropriately cor-related with the movement of an observer holdinga stick. What is felt is a ball rolling in the stickwhere there is none [90].

2.14 After-Effects

After-effects may also be put into their own cat-egory. Motion after-effects are well known in vi-sion, such as the classic “waterfall illusion” andwere more recently found in audition [21]. Theyexist for tactile motion [53], although their occur-rence was initially not evidenced [87]. Since then,they have been better characterized [43, 84]. The“weight after-effect”, which can easily serve as a‘party trick’ like the other weight effects mentionedearlier, was confirmed by de Mendoza to be a trueperceptual effect [19]. The “shape after-effect” de-scribed by Vogels et al. is most effective and sur-prising [80]. It can be demonstrated with saladbowls large enough to contain the hand. For in-stance, once having experienced the concavity ofa bowl for about 10 seconds by statically pressingthe hand inside it, a flat surface will feel convexfor a few seconds. Unlike the motion after-effect,it has no obvious visual analog.

2.15 Shape Effects From Force Fields

Every object responds mechanically to externalperturbation. Therefore, every object can be de-scribed, not by one single force field, but by an in-finite collection of them. This continuum of fieldsis in most cases quite complicated [55]. Force feed-back devices rely on the human ability to processthese fields, even very crude or highly simplifiedones, to yield the perception of touching virtualobjects. This is known since the invention of re-mote manipulators in the 50’s.

Minsky commented that textures would be feltby the users of a joystick-like force-feedback de-vice which would oscillate laterally only [58]. Mor-genbesser and Srinivasan took advantage of a sim-ilar effect to smooth the corners of virtually cre-ated objects experienced via a 3D force-feedbackdevices [59]. Certain very simple force fields were

shown by Robles-De-La-Torre and Hayward to beable to give the perception of raised or recessedshapes in the absence of normal proprioceptivecues [68]. Even when a subject’s finger would fol-low the shape of a raised bump that provided thecorresponding proprioceptive information, the sen-sation of a hole would still be experienced if theforce field corresponded to that of a hole, an “in-verted bump” so-to-speak [69]. The combinationof the geometry of a given shape with the forceresponse of another is an instance of a ‘paradoxi-cal’ stimulus that could not arise naturally. Forcefields can also be used to achieve an effect oppositeto smoothing. They can be used to perceptuallysharpen an otherwise geometrically smooth virtualobject [61].

2.16 Discussion

It is a haunting thought to consider that in the actsof everyday activity such as preparing food, or inthe skilled perceptual activity of a physician usingpalpation and percussion to feel organs throughtissues, the effects that have been reviewed are, tovarious extents, all at play! They show that theconscious or the unconscious perception of objectattributes, weight, location, size, movement, tex-ture, stickiness, shape, compliance, time of colli-sion with the body or with other objects, internalstructures, are potentially subject to profound dis-tortions. Yet, skilled activities, such as peeling aslippery potato, are accomplished successfully andeffortlessly by most.

The taxonomy just proposed has undoubtedlysome weaknesses. In particular, some of the illu-sions could belong to two or more categories. Thatthere are so many types of cross-modal interactionsis actually quite interesting and is a fact worthconsidering for future refinements of the presentproposal. In Table 1, these effects are collectedtogether with a judgment of whether they have asingularly tactile quality and whether they haveclear analogs in vision and audition.

3 Demonstrations of ModestComplexity

Some of the cases we have surveyed (see Ta-ble 1), can readily be demonstrated with ready-

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Table 1: Summary of tactile illusions. Illusions with “Household” demonstrability can be producedimmediately or with ordinary supplies as explained in the corresponding section. “Setup” means thattheir production requires computer-driven electromechanical equipment having various degrees of so-phistication. “Hardware” means that an apparatus for systematic demonstration can be made withsupplies found in hardware stores. “Hardware” illusions are further explained in the next section.

Sec. Name Demonstrability Stability Analogs2.1 Diplesthesia Household Not robust Debatable2.2 Funneling Setup Robust Debatable2.2 Cutaneous rabbit Setup Robust Debatable2.3 Size constancy failure Household Robust Visual2.4 Blackboard and parchment-skin Household & setup Robust Cross modal2.5 Weight-size and weigth-X Household Robust Cross modal2.6 Numerosity of taps from beeps Setup Robust Cross modal2.6 Numerosity of flashes from taps Setup Robust Cross modal2.7 Change numbness Setup Robust Auditory and visual2.8 Temporal ordering Setup Robust Auditory and visual2.9 Pseudo-haptic effects Any computer Moderate Cross modal2.10 Comb Household & hardware Robust Tactile specific2.10 Tactile lens Specialized device Robust Tactile specific2.10 Fishbone Household & hardware Robust Tactile specific2.10 Curved plate Household & hardware Robust Tactile specific2.10 Tactile barber pole Hardware Robust Visual analog2.11 Muller-Lyer et alia Household & hardware Moderate Visual analogs2.12 Kinaesthetic effects Household Robust Visual analogs2.12 Force by acceleration asymmetry Setup Robust Tactile specific2.13 Distal attribution Household Robust Visual and auditory2.13 Rolling ball Setup Robust Auditory2.14 Tactile Motion after-effect Setup Moderate Visual and auditory2.14 Weight after-effect Household Robust Visual and auditory2.14 Shape after-effect Household Robust Visual2.15 Texture force fields Setup Robust Haptic specific2.15 Corner smoothing Setup Robust Haptic specific2.15 Bump/holes Hardware Robust Haptic specific

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Figure 3: Mechanical delivery of the “comb illusion”. It is critical that the slider be free to move andnot be preloaded (if needed, it should be loosened up). It is preferable to have play in the mechanismrather than friction. (A) A comb section is epoxy-glued on the moving surface of a slider screwed to awood base. (B) Close up. The wheel of the roller (diameter 10 mm or less) must be set up to deflect theteeth by 1-2 mm sideways. For structural reasons, the optimal placement of the wheel is at about 2/3from the root of the teeth [83]. Of course, many other alternatives could achieve similar results. Theonly critical points are that the comb should slide effortlessly and the teeth spatial period be 1.5 mmor smaller. (C) Finger exploring the illusory bump.

Figure 2: Manual demonstration of the “comb il-lusion” [37]. An ordinary comb and a pencil is allwhat is needed. Stroking the teeth back and forthgently shears the skin locally.

made household items such as salad bowls or chop-sticks. Some require specific electromechanicalequipment. In this section we look at a third cat-egory that can be demonstrated with moderatelycomplex equipment realizable with supplies foundin hardware stores.

These illusions are astonishing, robust, easy todemonstrate almost immediately, and in each casecan be created in more elaborate and controlledmanners using robotic-like equipment. Moreover,the construction of the equipment described belowwill eliminate the need to rely on the manual dex-terity of the experimenter.

3.1 The “Comb Illusion”

In its simplest form, all what is required is a plasticcomb, see Fig. 2. It can be demonstrated on one-self with two hands, as in the figure, or with thehelp of an assistant. Like most tactile illusions,its success often depends on vision being blockedor by voluntarily directing the gaze elsewhere thanon the setup. Most people report that they expe-rience the sensation of a raised object moving onthe finger when, in fact, since the teeth have a con-stant length, the skin is sheared but indentation isinvariant along the line.

To achieve repeatable results, a demonstrationdevice may be constructed out of a rolling slidernormally used to support kitchen drawers, seeFig. 3 and caption. The effect can be experiencedby setting the apparatus on a table and then byexploring the region where the teeth are deflected.The illusory bump is then stationary. When hold-ing the comb on the skin and moving the support,the illusory bump moves. With this apparatus it isthen easy to demonstrate that the illusion is spe-cific to the ridged glabrous skin. It is effective atall places inside the hand where the ridged skin isvisible and also on the sole of the foot, but fails onany other areas of the body. Computer controlledversions of this stimulation method are describedin several publications, for example [54, 82].

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A B C

3 mm

2.5 mm

3 mmFixed Surface

Fixed SurfaceA

dh

esiv

e

Ad

hes

ive

Figure 4: Demonstration of the “ridge/trough illusion” (variants of the “fishbone illusion” [60]).(A) Two larger strips of the sticky section of PostIt notes are glued to a stiff backing with the ad-hesive side exposed. The 3 mm central strip is filled with the same paper but with the sticky sideunder. (B) Opposite case. (C) A 2.5 mm strip of card paper sliding between two glued sections accom-plishes a similar purpose. This configuration requires to push down a little harder. The opposite caseis not as convenient to realize but can be done with some care.

3.2 The “Ridge/Trough Illusion”

Several variants of the “fishbone illusion” describedin Section 2.10 can easily be demonstrated. Thefirst variant involves the use of PostIt R© notes.Figs. 4A and 4B show strips of the notes that havebeen glued on a stiff backing, such as a businesscard. The strips shaded in grey indicate that thesticky surface is exposed. White strips indicatethat the non-sticky side is exposed. Adhesion ismuch larger where the sticky side is exposed thanelsewhere, yet the upper surface is almost perfectlygeometrically flush. When the finger rubs the cen-tral strip in the direction of the arrow, for the caseof Fig 4A, a trough is typically experienced wherethe central strip is located. In the case of Fig 4B,a ridge is experienced. A similar effect can be ob-tained with two business cards or similar material,and paper glue. This time a strip is cut preciselyand inserted between two half-card as indicatedin the figure Fig 4C. These half-card are glued tothe backing and serve as a guide. Since the cen-tral strip can slide freely, adhesion is larger on thefixed surfaces, especially if the finger is moist. Theresult is similar. During exploration, typically, aconcave trough is experienced. In all cases explor-ing in the direction orthogonal to the strips makesit obvious that the upper surface is flush.

3.3 The “Curved Plate Illusion”

This illusion, also described in Section 2.10, canbe demonstrated manually. But to succeed, it re-quires some dexterity from the experimenter. One

method is to get hold of a small rigid item such asa match box or a plastic card with straight edges,as indicated in Fig. 5. It can be demonstrated ononeself, or to someone else. Again, vision may playa role. When the box moves as indicated by arrow1 (Fig. 5A), it is clear that the edge feels straight.Next, the same object is rotated about its centeras per arrows 2 (Fig. 5B). This causes the loweredge to slide on the finger, but also causes the con-tact to move on the finger surface. At a speed ofabout one oscillation per second, the edge will feelcurved.

Figure 5: Manual demonstration of the “CurvedPlate Illusion”. (A) Straight motion. (B) Rotatingmotion.

Reference [22] describes a computer controlledrobotic arrangement that is able to roll a plate onthe fingertip without significant vertical finger dis-placement. For one-dimensional, fixed profiles, itis possible to achieve the same result with simplecams. As seen on Fig. 6, a small carriage withtwo rollers mounted on ball-bearings is guided by

10

Figure 6: Mechanical delivery of the “curved plate illusion” [22]. (A) The device has a cam madeof a bent metal strip which is secured to a wood base and a carriage having two rollers mounted onball-bearings. Dimensioning is given in appendix. (B) Finger exploring the illusory curvature. Forsome subjects, the effect is more pronounced when the exploration is fore-aft rather than sideways. Inany case it is important that the mechanism has little friction and produces little mechanical noise.These types of disturbances are prone to destroy or weaken the illusion. It is also important to pressdown lightly.

a cam in such way that the plate rocks accordingto its horizontal displacement but keeps the fingeron a straight line. For exploration speeds of aboutone oscillation per second, the upper plate will feelcurved, provided that the exploring finger’s orien-tation remains invariant. Please see the Appendixfor design details.

3.4 The “Bump/Hole Illusion”

Here, a simple device made of a slider connectedto magnets can create lateral force fields similarto those described in [69]. It is best to refer di-rectly to Fig. 7A where a wood base supportinga kitchen drawer slider is shown. On the uppermoving surface, a pair of magnets were glued sotheir poles faced downward. Two pairs of magnetshave been embedded in the wood base and glued.The magnetic poles must be such that the movingmagnets are attracted by one pair of fixed mag-nets and repelled by the other pair. Fig. 7B showsa finger exploring an illusory bump where there is arepelling region, and an illusory hole where there isan attracting region. Please see the figure and cap-tion for more detail. Because the lateral force fieldis invariant and independent from the intensity ofthe normal pressing force applied by the subject,one should not press down very hard but with anequal force.

4 Discussion

Demonstrations of illusions are valuable becausemany people can experience them, not just a fewsubjects. They are portable and communicable.The spontaneous comments of many observers maysometimes be illuminating. But of course, demon-strations do not replace systematic scientific inves-tigations where the stimuli and the conditions un-der which they are delivered are rigorously con-trolled.

It is usually a significant electromechanical chal-lenge to design machines that can deliver, un-der computer control, the mechanical signals de-scribed in the previous sections. In fact, if oneemploys commercially available force feedback de-vices, their limitations may cause the stimuli tobe delivered with a lower quality than those givenby the hardware devices just described. They canhave too much friction, not be stiff enough, be tooweak or too heavy, cause mechanical noise, and so-on. Any of these defects may affect the strength oreven eliminate the resulting percept. On the otherhand, mechanical non-programmable devices couldmake systematic studies such searching as for de-tection thresholds, or multi-modal controlled con-ditions cumbersome or impossible to set up, yetthey have advantages.

Demonstrations can fail for a variety of reasons.These are the same that can make visual or au-ditory illusions fail, for instance because of strongprior cognitive bias. There are other factors too.

11

Figure 7: Magneto-mechanical delivery of the “bump/hole illusion” [69]. (A) The slider must beadjusted to minimize play and yet have little friction. The pair of magnets is useful to balance thevertical load when the magnetic fields interfere. With good quality ferrite magnets 15 × 10 × 8 mmin size, an air gap of about 3 mm will create a lateral force field of appropriate intensity. Roundmagnets would also work. Inserting washers under the slider allows one to adjust the air gap foroptimal effect. (B) Finger exploring an illusory bump. Fore-aft movements may be more effective thansideways exploration. The finger may be in contact with any location of the moving surface.

Just as some people may never fuse Julesz’ randomdot stereograms, some people may never experi-ence the illusions described herein. In our expe-rience, however, they are consistently experiencedby most perceivers and can create considerable sur-prise when the mechanism that produces them isexplained.

In this survey article, each instance of tactile il-lusion could only be briefly described and muchmore information is available in the listed refer-ences. It is also natural to try to explain these il-lusions. Some categories already have their contin-gent of explanations but these cannot be discussedin the scope of this survey. To the knowledge ofthe author, considerable work remains to be doneto provide explanations which would be based onspecific brain mechanisms. Are there generally ap-plicable explanation categories, or has each case itsspecific explanation? These questions are open.

5 Acknowledgments

This research was supported by a discovery grantfrom the Natural Sciences and Engineering Councilof Canada. The author would like to thank McGillUniversity for a sabbatical leave. Edouard Gen-taz, Jim Clark, Anatole Lecuyer, Hanifa Dostmo-hamed, Maarten Wijntjes, Mounia Ziat, MasashiNakaniti, Vincent Levesque, and Gabriel Robles-De-La-Torre provided helpful comments.

Appendix: Dimensioning of BentPlate Illusion Mechanism

An infinite number of profiles can guide a plate incontact with a finger such that the contact changesbut the finger stays on a straight line. Here, a sim-ple approximate solution is provided. Referring toFig. 8A, the apex of the isosceles triangle is locatedinside the guided finger and is required to move in astraight line along x. Its location is parametrizedby x = t, y = 0, t ∈ [−1, +1]. We then specifyan inclination that varies proportionally with thehorizontal position. Locally, this will approximatethe inclination that would result from exploring acylinder. Call a the length of one side of the tri-angle. If we imagine the plate to be guided by twosliding contacts L and R, we can write the para-metric equation of the path of these contacts asthe inclination varies from −π

8 to π8 , see Eq. (1).

Optimizing a for path straightness yields a valueof a ≈ 1.5. See Fig. 6. It is then possible to makea cam as in Fig. 6 by shaping an aluminum plateaccording to the profile in Fig. 8B. The cam is thensecured on a wood base. The carriage may be madeas indicated by Fig. 8C,D and caption.

Right branch:[

xy

]=

[t + a cos(π

8 (t + 2))−a sin(π

8 (t + 2))

]Left branch:

[xy

]=

[t + a cos(π

8 (t + 6))−a sin(π

8 (t + 6))

](1)

12

A y

x

L R

t = 0 t = +1t = -1

a = 1.5

10

15

50

50

36

20

3

1316

C

B

20

20D

14

Figure 8: (A) Graphical solution of the shape of a cam having almost straight edges that can guide aplate through a varying orientation while keeping the apex on a straight line. (B) Cam dimensions inmm. (C) and (D) Carriage made of normalized aluminum U profile, four flanged ball-bearing (outerdiameter 6 mm, inner diameter 3 mm) and two 3 mm shafts. Note that other variants exists and thatthe scale can changed to make the illusory shape feel more of less curved. These dimensions give thecurvature of about that of a golf ball.

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