Beyond Illusions - — Open MIND

Beyond IllusionsOn the Limitations of Perceiving Relational Properties

Heiko Hecht

Explaining the perception of our visual world is a hard problem because the visualsystem has to fill the gap between the information available to the eye and themuch richer visual world that is derived from the former. Perceptual illusions con-tinue to fascinate many researchers because they seem to promise a glimpse ofhow the visual system fills this gap. Illusions are often interpreted as evidence ofthe error-prone nature of the process. Here I will show that the opposite is true.To do so, I introduce a novel stance on what constitutes an illusion, arguing thatthe traditional view (illusion as mere discrepancy between stimulus and percept)has to be replaced by illusion as a manifest noticed discrepancy. The two views,unfortunately, are not necessarily related. On the contrary; we experience themost spectacular illusions where our perception is pretty much on target. Onceour interpretation of the sensory data is off the mark, we usually no longer experi-ence illusions but live happily without ever noticing the enormous perceptual andconceptual errors we make. The farther we move away from simple pictorial stim-uli as the subject of our investigations, the more commonplace a discrepancybetween percept and reality does become—and the less likely we are willing tocall it illusory. Two case studies of our perception of relational properties willserve to illustrate this idea. The case studies are based on the conviction thatperceiving is more than mere sensation, and that some degree of (unconscious)judgment is a necessary ingredient of perception. We understand little about howto balance objects and we make fundamental mistakes when perceiving the slip-periness of surfaces. All the while, we never experience illusions in this context.Thus, when dealing with simple percepts, illusions may be revealing. But when itcomes to percepts that involve relational properties, illusions fail to arise, as per-ception is not concerned with veridicality but appears to be satisfied with the firstsolution that does not interfere with our daily activities.

KeywordsError | Illusion | Intuitive physics | Underspecification

Author

Heiko [email protected] Johannes Gutenberg-UniversitätMainz, Germany

Commentator

Axel [email protected] Universität OsnabrückOsnabrück, Germany

Editors

Thomas [email protected] Johannes Gutenberg-UniversitätMainz, Germany

Jennifer M. [email protected] Monash UniversityMelbourne, Australia

1 Illusion?

1.1 The underspecification problem (UP)

Visual perception can be seen as the process bywhich the visual system interprets the sensorycore data that come in through the retinae ofthe eyes (see e.g., Hatfield & Epstein 1979). Thesensory core is not sufficient to specify the per-cept; that is, there is an explanatory gapbetween the information present at the retina—which is in essence two-dimensional (2D)—andthe information present in the three-dimensional(3D) objects that we see. Let us call the prob-

lem that arises in having to fill this gap the“underspecification problem” (see Hecht 2000).Figure 1 illustrates the UP (underspecificationproblem). A given object can only project oneparticular image onto the projection surface(retina); however, a given projection could havebeen caused by an indefinite number of objectsin the world. Because of this anisotropy in themapping between the 3D object and its 2D pro-jection, information is lost during the projectiveprocess, which cannot be regained with cer-tainty. One could argue that the history of per-

Hecht, H. (2015). Beyond Illusions - On the Limitations of Perceiving Relational Properties.In T. Metzinger & J. M. Windt (Eds). Open MIND: 18(T). Frankfurt am Main: MIND Group. doi: 10.15502/9783958570290 1 | 26

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ception theories is more or less the history offinding solutions to reconstruct the 3D objectthat has caused a given projection.

Figure 1: Underspecification: The 3D origin of a givenimage on the retina (here approximated by the verticalprojection screen) is provided by an indefinite number ofobjects at various orientations in space. Illustration fromGibson (1979).

In order to assess the quality of the solu-tion offered by a given perceptual theory, wehave to evaluate how it describes the gapbetween sensory core and percept and themechanism by which it suggests that the gapis being bridged. The Gibsonian theory of dir-ect perception aside—which denies the prob-lem altogether (e.g., Gibson 1979)—we have avariety of theories to choose from. They areall constructionist in the sense that the sens-ory data have to be interpreted and arrangedinto the configuration that is most likely ormost logical. The theories differ in the mech-anisms they make responsible for the recon-structive process. For instance, Hermann vonHelmholtz (1894) supposes inferences of un-conscious nature that arrive inductively ormaybe abductively at a preferred solution.Roger Shepard (1994), on the other hand sup-poses a recurrence to phylogenetically-ac-quired knowledge. He takes the regularities ofthe physical world or of geometry to havebeen internalized through the course of evolu-tion and to be used to disambiguate compet-ing solutions. An example of such internalizedknowledge is the fact that light usually comesfrom above (see Figure 2). A shading gradientfrom light (at the top of an object) to dark(at its bottom) would thus be compatible witha convex but not with a concave object.

Figure 2: Solution of the underspecification by drawingon internalized knowledge that light comes from above.The sphere in the right panel looks convex because it islighter at the top, whereas the same image rotated by180° (left panel) looks concave. Have we created an illu-sion by juxtaposing them?

Others have proposed that the system con-siders statistical probabilities by defaulting tocontextually appropriate, high-frequency re-sponses (Reason 1992) or by applying theBayes-theorem (e.g., Knill & Richards 1996;Kersten et al. 2004), or predictive processing(Clark this collection; Hohwy this collection)Here we are not concerned with the exactnature of how the construction is accomplished.Note, however, that all the solutions that havebeen proposed abound with cognitive ingredi-ents. The process of constructing a 3D objectfrom the 2D retinal input is usually thought todraw on memory and on some sort of inferen-cing, albeit unconsciously. The next step to ar-riving at meaningful percepts on the basis ofthe 3D object—which is just as essential in per-ception—involves even more cognitive elements,be they unconscious or amenable to conscious-ness.

Here I would like to include a brief aside,which may seem obvious to the psychologist butnot so obvious to the philosopher. Perceivingcannot be dissected successfully into a sensa-tional part and a judgmental part when we aredealing with the everyday perception of mean-ingful objects. Perceiving is always judgmentalwhen we see a stick or a bird, or when it comesto seeing that we can pick up the stick and thatit falls down when we release it. In other words,pure sensations may be possible introspectively—sensing red, sensing heat etc.—but they are


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no longer possible in everyday object percep-tion, that is a separation of sensation and judg-ment is not ecologically valid. Take, for in-stance, the falling object as given in phenom-enal perception. In the sub-field of experimentalpsychology called “intuitive physics”, investigat-ors have doctored physical events to contradictNewtonian physics and presented visual anima-tions to novice or expert observers. Many of thelatter do not see anything wrong with objectsfalling straight down when released, as opposedto following the proper parabola that theyshould (see section 1.3.1 on so-called cognitiveillusions). This perception is reflected in motoraction—people release the object in the wrongplace when trying to hit a container; this per-ception arises in toddlers unable to reflect uponthe event, and it persists after formal physicstraining in cases where observers have to makequick decisions. Thus, a separation into a sensa-tion and perceptual judgment is not meaningfulhere. Perception of (everyday) objects andevents necessarily includes a judgmental aspect,which may or may not enter consciousness.

Now, we are concerned with the question ofwhether the errors that arise during the percep-tual process can be used to gauge where thevisual system fails to capture the 3D world. Wewill argue that this is not the case. Research fo-cusing on so-called optical illusions is particularlyill-suited to gain insight into how the visual sys-tem solves the UP. Illusions typically arise whenerrors are rather small, thus the presence or mag-nitude of an illusion is no predictor of the size ofthe UP. By and large, perceptual error is rathersmall when it comes to simple object properties,such as size, distance, direction of motion, etc. Er-rors become much larger, more interesting, andpotentially dangerous when it comes to relationalproperties, such as seeing if an object can be lif-ted or if I will slip and fall when treading on agiven surface. The case studies below will showthat in the context of relational properties wemake errors but we do not experience illusions.

1.2 The Luther illusion

Please take a close look at this painting of Mar-tin Luther. You have certainly seen pictures of

the great protestant reformer before. Does any-thing about this painting strike you as strange?

Figure 3: Martin Luther as painted by Lukas Cranachthe Elder (1529), Hessisches Landesmuseum Darmstadt.

You may have found that he looks wellnourished, as is appropriate for a monk whose en-joyment of worldly pleasures is well documented.However, I am sure you did not notice the illu-sion. Well, I have photoshopped the photographand made it 15% wider than it should be. Thereis a discrepancy between the painting (or veridicalphotograph thereof) and the picture presented inFigure 3. Such discrepancies are typically con-sidered to be the essence of illusion. For instance,Martinez-Conde & Macknik (2010, p. 4) define anillusion as “the dissociation between the physicalreality and the subjective perception of an objector event”. The physical reality of the picture isdistorted by 15%, but your perception was that ofa correct rendition of a famous painting. Now letus add another twist to the Luther illusion (Fig-ure 4).



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Figure 4: Martin Luther right side up and upside down.

Have I taken the original photograph orhave I turned around the 15% wider version?Surely, Luther looks to be slimmer in the panelon the right. If you turn the page upside down,you will see that both panels show the samepicture that is 15% wider than the original. Letus assume that the inversion effect—also namedfat-face-thin-illusion by Peter Thompson(Thompson & Wilson 2012)—is exactly 15 % inmagnitude. Has the illusion that I introducedinitially been nullified by the inversion?

The fictitious Luther illusion is meant tomake the point that the mere discrepancybetween physical reality and a percept shouldnot be conceived of as illusory. It may not evenbe reasonable to conceive of it as an error. Thestretched image may be a better representationof what we know about Luther than the “cor-rect” picture. For instance, the picture may typ-ically be viewed from an inappropriate vantagepoint that could make the stretched versionmore veridical even when compared to the ac-tual Luther, were he teleported into our time.Take Figure 5. I have stretched Luther by an-other 50%. Now he seems a bit distorted, butnot to an extent that would prevent us from re-cognizing him or from enjoying the picture.There is a fundamental property that needs tobe added for something to be considered an illu-sion. I contend that this is a dual simultaneouspercept that tells us that what we see is so andnot so at the same time (for a detailed defenceof this position see Hecht 2013). For an illusion1

1 Note that I will differentiate between illusiond (being the old notionof discrepancy between object and percept) and illusionm (the mani-

to be called thus, it has to be manifest immedi-ately and perceptually. Calling something an il-lusion is only meaningful if it refers to a dis-crepancy that we can see. It is not meaningful ifit refers to some error that we have to infer.

Figure 5: Martin Luther stretched by another 50%.

Take for instance the often-cited stick inthe water that looks bent. The static imagepresented in Figure 6 is not an illusion. We seea bent stick; note that its shadow is bent aswell, and without recourse to our experience ofrefraction that occurs where two media adjoin,we would not know if the stick were actuallybent or if some effect of optics had created thepercept. However, the moment we move thestick up and down we see the illusionm. We seethe stick being bent and being straight at thesame time. The illusion becomes manifest. Thatis, the discrepancy if not contradiction betweenthe two percepts (here the straight and the bentstick) is available in our working memory, webecome aware of it, often without being able toresolve which of the two discrepant percepts iscloser to reality. In the case of the stick, the loc-ation of the bending at water level reveals that

fest illusion that is perceived rather than inferred with the help ofphysics text books). I will only refer to illusionm as illusion, whereas Iwill refer to illusiond as mere error or discrepancy. See also the re-lated distinction between phenomenally opaque and phenomenallytransparent illusions (e.g., Metzinger 2003a, 2003b). My distinctionbetween illusiond and illusionm is meant to be merely perceptual.



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the stick is really straight; however, in mostcases the illusionm remains unresolved, as for ex-ample in the case of the Ebbinghaus illusion.

Figure 6: Is the stick bent?

1.3 Thesis: Illusionsm are not evidence of error but rather unmasking of error

It would make no sense to call the circles in Fig-ure 7 an illusionm, even if a researcher could showwith a large dataset that the inner circle is repro-duced 2% bigger than it was on the picture. How-ever, as soon as we allow for a direct comparisonand put a ruler to the center circles in Figure 8,the illusionm arises (see Wundt 1898; an interact-ive demonstration of the Ebbinghaus illusion canbe found at http://michaelbach.de/ot/cog-Ebbinghaus/index-de.html).

Illusionsm are perceptually immediate butthey appear to require some form of comparisonand judgment, which supports the argumentthat phenomenal perception cannot be dividedinto a merely sensational core and a cognitiveelaboration. For instance, in the case of aNecker cube or a bi-stable apparent motionquartet, the illusionm can become manifest by amere deliberate shift of attention.

Given the severity of the UP, we should notbe fascinated by the existence of error (illusionsd),but should instead be fascinated by the fact thatour perceptions are pretty much on target most ofthe time. It is truly amazing that among theenormous range of possible interpretations of theretinal image, we usually pick the appropriate

one. Illusionsm are rare special cases of ubiquitoussmall errors that become manifest because ofsome coincidence or another. Note that this as-sessment does not only apply to visual perceptionbut also to other sensory modalities in whichsensory information has to be interpreted and in-tegrated. For instance, the cutaneous rabbit illu-sionm arises when adjacent locations on the skinof our arm are stimulated in sequence. We experi-ence one coherent motion (a rabbit moving alongour arm) rather than a sequence of unrelatedtaps. This “inference” can be explained by prob-abilistic reasoning (Goldreich 2007) and may beconsidered the tactile analogue of apparent mo-tion: just as we cannot perceptually distinguish asequence of static stimuli from real motion in themovie theater. As a matter of fact, the pausesbetween the intermittent frames of the movie areindispensable for motion pictures to look smoothand continuous.

Gestalt psychologists have described theconstructive process by which meaningful ob-jects emerge from the various elements in oursensory core (see e.g., Max Wertheimer 1912for the case of apparent motion). For goodreason, they have avoided the term illusion,and introduced the term emergent property forthe phenomenal result of the (unconscious)process of perceptual organization. It would vi-olate our everyday experience to call somethingwe see an illusion just because we know a little


Figure 7: Is the circle in the middle perceived to be big-ger than it really is? Possibly an illusiond.

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bit about the underlying physics. Just becausewe know that our continuous motion percept isderived from a sequence of discrete images, thisdoes not make the percept an illusion (neitherillusionm nor llusiond).2 By the same token,knowing that light is a wave (or a stream ofphotons) does not make objects in the world il-lusory. In fact, a discrepancy between what isreally there and what we perceive is the norm,not the exception. Given my conceptual dis-tinction, I will show how the perceptual systemdeals with the ubiquitous discrepancy, with thenormal case of illusiond. The relatively rarecases illusionsm arise a by-product of this pro-cess. For something to deserve the name illu-sion, this discrepancy has to become manifest.The Ebbinghaus illusion only turns into an il-lusionm when we perceive a conflict, when theinner circles are seen (or inferred) to be equalin size and they look different in size at thesame time. Thus, it is not the ubiquitous pres-ence of error that makes an illusionm but therather unusual case where this error is un-masked by a perceptual comparison process.

2 Note, that a discrepancy between stimulus and percept is necessarybut not sufficient for an illusionm. Thus, all illusions require an illu-siond but will only become illusionsm in some cases. My distinction iscapable of sorting out illusions as relevant to perceptual psychology,it does, however, not speak to the question of how we can describethe physical stimulus in the first place, i.e., the grand illusion argu-ment (see http://www.imprint.co.uk/books/noe.html).

1.3.1 A note on so-called cognitive illusionsd

In our everyday perception, once we considerthat objects are often in motion and carrymeaning at the perceptual level (see Gibson’sconcept of affordance, e.g., 1979) the UP is ex-acerbated but not changed. I argue that thenature of perceptual error is akin to cognitiveerror when it comes to the more complex andmeaning-laden percepts of everyday perception,as opposed to line drawings that are typicallyreferred to in the context of illusionsm. Just aswith perceptual errors, cognitive errors often donot become manifest. However, if they do be-come manifest, they can typically be correctedwith much greater ease than can perceptual il-lusionsm, which may well be the distinguishingfeature between perceptual and cognitive error.Cognitive errors become noticeable more indir-ectly by recurring to a short-term memory of adissenting fact or by reasoning—which is oftenfaulty by itself. The literature about cognitiveerror is enormous. To give one classical ex-ample, we have trouble with simple syllogisticreasoning, in particular if negations are used.Wason’s famous selection task (Wason & John-son-Laird 1972) shows how limited our abilitiesare (Figure 9). Imagine you have four envelopesin front of you. You are to test the statement “ifthere is sender information on the back sidethen there is a stamp on the front”. Which ofthe 4 envelopes do you have to turn over? Donot turn over any envelope unnecessarily.

Figure 9: Which envelopes do you have to turn to testthe statement “If there is sender information on the backside then there is a stamp on the front”?

Well—it is easy to see that envelope 1 hasto be turned (modus ponens), but then it getsharder. Many observers think that envelope 2needs to be turned. However, this is not thecase. Only 4 has to be turned in addition to 1.


Figure 8: Is the circle surrounded by smaller circlesperceived to be bigger than it really is, or is the centercircle on the right perceived to be too small? This isthe famous Titchener illusionm that was invented byHermann Ebbinghaus and first reported by WilhelmWundt (1898).


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A sender on its back would violate the rule(modus tollens). The majority of college stu-dents fail to solve this problem, but as soon asthe context is changed, all mistakes can be elim-inated. In the context of screening for drinkingunderage, all observers perform accurately (seeFigure 10). Here again 1 and 4 need to be“turned over”. Only by thinking the problemthrough or by noticing that the problem struc-ture is identical to the envelope scenario andthe wine drinking scenario does the error be-come manifest. We may or may not want to callit a cognitive illusion. This term is not widelyused for such mistakes or fallacies, with the ex-ception of Gerd Gigerenzer and his researchgroup (see e.g., Hertwig & Ortmann 2005).However, even if we call these mistakes cognit-ive illusions, they are different in nature fromperceptual illusionsm (which typically contain ajudgmental aspect). We do not readily noticecognitive illusions. Although the distinctionbetween perception and cognition has outliveditself (and cannot me made with clarity to be-gin with, see above), for practical convenience, Iwill continue to use the terms to emphasizecases where deliberate thought processes enterthe equation. We happily live with many a fal-lacy without ever noticing. Millions wentthrough their lives believing in impetus theoryand seeing the sun circle around the earth, letalone holding seemingly absurd beliefs aboutthe shape of our planet.

Figure 10: Whom do you have to query about age orbeverage type to test if “Only adults have alcoholicbeverages in their glass”? It is obvious that the juicedrinker and the elderly person need not be queried.

Errors only turn into illusionsm when webecome aware of them and at the same timecannot correct the error (easily). Just try to seethe earth rotate rather than see the sun rise. Itis impossible. We continue to see the sun rise

above a stable horizon, never the other wayaround. And we continue to misjudge implica-tion rules or widen the grasp of our fingers atad more when reaching for an Ebbinghausstimulus even if we know about the illusion (seeFranz et al. 2000). Other errors can only bespotted when large data samples are collectedand analyzed statistically. For instance, to ex-pert golfers, the putting hole on the green lookslarger than it does to novices (Witt et al. 2008;Proffitt & Linkenauger 2013). They will neverbecome aware of this fact, although the fine-grained scaling of perception as function of skillmight be functional during skill acquisition.Spectacular as they may be, such errors ofwhich we are unaware should not be called illu-sionsm because almost all our perceptions andcognitions contain some degree of error. Wemay believe that a rolling ball comes to a stopbecause it has used up its impetus, or we mayhold that we should aim where we want a mov-ing ball to go rather than using the appropriatevector addition to determine where to aim. Aslong as our action results do not force us to re-consider, our convictions will remain un-changed. One could say that we have a model ofthe world, or its workings, that suffices for ourpurposes.

Figure 11: Technical illustration explaining the traject-ory of a cannon projectile by Daniel Santbech (1561):Problematum Astronomicorum, Basel.



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Why are so many researchers willing tocall a small manifest discrepancy between twopercepts of the same object an illusion, whilegross deviations of perception or conceptionfrom physical reality are not deemed to deservethe same name? Take the straight-down belief(not illusion). Many observers take an objectthat is being released from a moving carrier tofall straight down rather than in a parabola(McCloskey et al. 1983). Figure 11 illustratesthis belief as it was state-of-the-art physicsknowledge from Aristotle through the MiddleAges. It persists today in cognition and percep-tion. Even when impossible events of straightdown trajectories are shown in animatedmovies, to some observers they look better thando the correct parabolas (Kaiser et al. 1992).

Note that there was a discussion at thetime whether or not the transition from the up-ward impetus to the downward impetus was im-mediate or if a third circular impetus inserteditself, such that there were be two trajectorychanges. The intermediary could only bethought of as linear or as a circular arc—any-thing else would have been too far from divineperfection. Presumably, the more principledphysicists before Galileo favored the simpletransition. Others, such as Aristotle himself,presumably preferred the interstition of the cir-cular arc, as it would reconcile trajectory obser-vation with the physics of the time. The pre-Newtonian thinking about projectile motionnicely illustrates that we see the world as in ac-cord with our actions. To the medieval cannon-eer, what he saw and understood about pro-jectiles was sufficiently accurate, given the vari-ance introduced by the inconsistent quality ofthe gunpowder and the fluctuation in theweight of cannon balls at the time.

Thus, we have argued that visual illusionsm,just as cognitive illusionsm, have to become mani-fest to be called such. They are a special and rarecase in which the discrepancy between a perceptand what an ideal observer should have seen in-stead is noticed. Normally this discrepancy goesunnoticed. We will now take a look at why it goesunnoticed and argue that an illusiond will only al-ter perception if it interferes seriously with ouraction requirements. As the latter vary among

people, illusionsd can be private and may be veryfar from the truth—as, for instance, in the con-text of projectile motion (see Hecht & Bertamini2000). The private aspect of perception is to betaken as unconscious in the sense of Helmholtz.For instance, we do not only think that a baseballthrown toward a catcher will accelerate after ithas left the thrower’s hand (which may even beincompatible with impetus theory), but doctoredvisual scenes in which the ball does accelerate arejudged as perfectly natural looking. This amountsto the perceptual analogue of what Herbert Si-mon (1990) has called satisficing in the domain ofreasoning and intuitive judgment. The visual sys-tem searches until it has found a solution that issatisfactory, regardless of how far away it is froma veridical representation of the world.

To conclude this section, we believe thatperception of objects, be it the stick in the wa-ter or a falling brick, is a solution to the under-specification problem. Perception is alwaysfraught with error in the sense of a discrepancybetween the percept and the underlying physics.This error only becomes manifest when a simpleperceptual judgment or comparison reveals acontradiction. In all other cases the error goesunnoticed. Two such cases will now be describedat length to make the point that perceptual illu-siond is the rule rather than the exception.

2 Two case studies or how we deal with error

The study of geometric illusions or overestimationof slope, distance, and size as a function of situ-atedness misleads us into believing that percep-tion normally reveals the true state of affairs. Thefinding that golf holes look slightly bigger to ex-perts as compared to inexperienced golfers isspectacular because and only if we assume thatperception is normally veridical. This is, however,not the case. Normally, our grasp of the physicalworld is rather limited. I present novel data fromtwo everyday domains that differ from the stand-ard examples of intuitive physics in a crucial way.They deal with the understanding (first casestudy) and the perception (second case study) ofrelational properties, rather than with morestraight-forward perception of simple properties.



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Seeing the color of an object or its size, predictingits motion trajectory, etc., refer to simple proper-ties. Most everyday activities, however, involve re-lational properties. We need to see and predicthow we might interact with objects in the world.This interaction depends on our own makeup, onthe object’s properties, and on the relationbetween the two. For instance, to judge whether aslope might be too slippery for us to walk on de-pends on the quality of the soles of my shoes, thesurface texture of the slope, and also on their in-teraction. A polished hardwood ramp may beslippery if I am wearing shoes with leather soles,but it may be very sticky if I am barefoot.

The two case studies that follow are inten-ded to illustrate in detail how limited our un-derstanding of relational properties is in gen-eral, and to show that we have to make de-cisions in the face of poor perception that mayhave serious consequences.

2.1 Case study: Balancing as a relationalproperty

Before you read on, please take a minute to solvesix questions about the depicted falling rods. Solu-tions will be provided later. Note that in tasks 1

through 3 (see Figure 12, 13, 14), the scenario isas follows. Two rods are held upright, but they arevery slightly tipped to one side (by exactly equalamounts), such that they will fall once released.They are released at exactly the same moment.Which one will hit the ground sooner? In tasks 4–6, you are to judge the ease of balancing such arod on the tip of your index finger.

Task 4 asks about the same rods as inTask 1, but the question is whether the woodenor the steel rod would be easier to balance onthe tip of your index finger.

Task 5 asks whether the short steel rod orthe longer wooden rod of equal weight would beeasier to balance on the index finger. And finally,Task 6 asks whether a weight attached to a givenrod would make it easier to balance, and if so,where it best be attached (top, center, bottom).In a large survey, we tested the intuitive know-ledge of a large number of college students aboutthese tasks. Note that we tested such that eachsubject only had to solve one of the six tasks.

2.1.1 Methods detail

180 college students (123 women, 57 men, ageM = 24.9 SD = 5.9, ranging from 18 to 53


Figure 12: Task 1: The rod on the left is light, it ismade of wood; the rod on the right is heavier because itis made of iron. If they begin to tip over at the same mo-ment in time, which one will fall faster?

Figure 13: In Task 2 the rods are equally heavy buthave different lengths. The left rod is made of wood; therod on the right is shorter but has the same weight as itis made of steel. Which one will fall faster?


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years) volunteered to participate in the survey.We used a paper-and-pencil test to investigatethe subjects’ knowledge and to obtain their es-timates about which objects would be easier tobalance. The six tasks were explained carefullyand illustrated with drawings similar to thoseshown in Figure 12, 13 and 14.

Each task was presented to 30 students.Tasks 1–3 were used to test intuitive knowledgewithout referring or alluding to the act of bal-ancing. Merely the process of falling from an al-most upright position to a horizontal positionhad to be judged. In the first task (Figure 12),subjects saw two rods of equal length (1m) butof different material and weight. The woodenrod was said to weigh 40g, the steel rod 400g.The accompanying information text indicatedthat both rods were slightly tipped over at theexact same time, for instance by a minimalbreeze. The wooden rod was to take exactly 1.5seconds to fall from its upright position to thehorizontal. We had tested the falling speed ofsuch rods and measured it to be approximately1.5s. The subjects were asked to estimate thefall-duration of the steel rod. The second (Fig-ure 13) task showed two rods of equal mass(40g) but different length (rod 1 = 100cm, rod

2 = 36cm). The information text was the sameas in Task 1. The third task (Figure 14) showedtwo rods of equal length (1m) and weight(220g). However, an additional small object(220g) was placed respectively toward the topor the bottom of the rod (rod 1 = 10cm fromthe bottom, rod 2 = 90cm from the bottom).The accompanying information text indicatedthat both rods would be tipped over by a min-imal breeze and that it took rod 1 exactly 1.5seconds to fall to a horizontal position. Subjectswere to estimate the fall-duration of rod 2.

Tasks 4–6 used the same rods but thequestions about them were couched in the con-text of balancing. This should evoke experiencesthat subjects may have made when balancing orhefting objects. Thus, rather than asking whichrod would fall quicker, we asked which would beeasier to balance.

The fourth task showed the same two rodsof equal length (1m) but different weights(wooden rod = 40g, heavy steel rod = 400g)that had been used for Task 1 (Figure 12). Thesubjects were asked to indicate which rod theythought they could better balance on the tip ofone finger, typically the index finger. The pos-sible answers ranged from 1 (“rod 1 much bet-ter than rod 2”) to 7 (“rod 2 much better thanrod 1”). The fifth task (Figure 13) showed tworods of equal weight (40g) but different length(rod 1 = 100cm, rod 2 = 36cm). Again, thesubjects were asked to indicate which rod theycould better balance with one finger. Task 6showed one rod (length = 1m, weight = 220g).Subjects had to indicate the position that theywould place an additional small object (mass =220g) to get optimal balancing characteristics(from 10cm = bottom to 100cm = top). It wasmade clear that the weight would not come intocontact with the balancing hand even when itwas placed at the bottom.

2.1.2 Results

People who cannot draw on formal physicstraining to answer the six tasks have a ratherpoor intuitive understanding of falling rods.Neglecting air resistance, the rate of falling isdetermined by how high the center of gravity


Figure 14: In Task 3, the two rods are identical in ma-terial, length, and weight. An additional weight is at-tached either at the bottom or at the top. Which rod willfall faster?


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(barycenter) is above the ground. The rod’smass is irrelevant. Thus, rods of equal length(mass distribution is assumed to be uniform)fall at the same rate, but the shorter rod fallsquicker than its longer counterpart. By thesame token, a weight attached to the tip of therod should cause it to fall more slowly becauseit moves the barycenter closer to the tip.

In general, the subjects estimated theirknowledge in the natural sciences to be moder-ate when asked to judge it on a six-point scaleranging from very poor (1) to very good (6).Mathematics knowledge (M = 3.62, SD = 1.13)was judged better (t(179) = 11.98, p < .001)than physics knowledge (M = 2.56, SD = 1.26).The men estimated their knowledge somewhathigher than did the women, for physics (t(178)= 8.8, p < .001) and mathematics (t(178) =2.34, p < .05).

Task 1: In reality, both rods fall with thesame speed, as Galileo Galilei showed in 1590with the help of several experiments about freefall (e.g., Hermann 1981). The falling speed isindependent of their mass as long as air resist-ance is negligible. Thus, 1.5 seconds was theright answer. 40% of the test subjects answeredcorrectly. 43.3% estimated that the heavier rodwould fall faster, while 16.7% estimated that itwould fall more slowly.

Task 2: Because of the lower barycenterthe shorter rod falls faster and its fall-durationis briefer than 1.5 seconds. 46.7% of the testsubjects indicated this. 44.3% thought that thefall-duration would be the same and 10% estim-ated that the shorter rod would fall moreslowly.

Task 3: Because of the higher barycenter,the second rod falls more slowly. Therefore, itsfall-duration is longer than 1.5 seconds. Only20% of the subjects chose the right answer. 50%estimated that the rod with the higher barycen-ter would fall faster and 30% estimated that itwould fall at the same rate.

There is a direct link between the fall-dur-ation of an object and the ability to balancethis object. The longer the fall-duration, themore time there should be to move the balan-cing finger right underneath the barycenter, andhence the easier to balance (a moderate weight

assumed). We confirmed this hypothesis empir-ically in several experiments where subjects ac-tually had to balance different rods to whichweights were attached at different heights.Thus, we can predict the ability to balance dif-ferent objects by comparing their fall-duration.

Task 4: Here, the rods (same length, dif-ferent weight) had the same fall-duration—sothe ability to balance them can be assumed tobe the same, too. This was recognized by only3.3% of the test subjects, while 73% favored theheavier rod, and 23.3% the lighter one.

Task 5 (two rods, same weight, differentlength): Because of the longer fall-duration thelonger rod is easier to balance. This was as-sumed by 56.7% of the subjects. 20% estimatedboth rods to be equal and 23.3% thought theshorter one would be easier to balance.

Task 6 (additional weight): The higherthe barycenter the longer the fall-duration—andwith it the ease of balancing. Therefore, the ad-ditional object should be placed at the top ofthe rod. This was indicated by 33.3% of the testsubjects. The majority of 43.3% chose the bot-tom for placing the object, and 23.3 % chosepositions between bottom and top.

In sum, the intuitive knowledge about thefall of different objects is rather spotty. Abouthalf of the subjects knew that fall-duration isindependent of mass (Task 1) and that shorterobjects fall faster (Task 2), only 20% realizedthat the position of the barycenter is relevantand that the fall-duration increases when thebarycenter is shifted to the upper end of the rod(Task 3). This is remarkable because on a dailybasis we handle objects whose barycenter differsfrom the geometrical center, for instance a filledvs. an empty soup ladle, top-heavy tennis rack-ets, etc.

Asking directly about the act of balancingdid not reveal superior understanding. Whenasked about their ability to balance objects,people do know that longer objects are easier tobalance than shorter ones, but they do not seemto realize that the mass of the object is irrelev-ant (Tasks 4 and 5). In other words, although amajority of our subjects was able to recognizethat mass is irrelevant for fall duration, theyfailed to see the irrelevance of mass in the rela-



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tional balancing task. The involvement of theown motor action appears to have made thejudgment task more difficult. The importantrole of the position of the barycenter (i.e., massdistribution, Task 6) went equally unnoticed inthe falling and the balancing tasks. In general,knowledge about balancing properties and theunderlying physical principles can be describedas rather moderate. Do experts have a superiorunderstanding of these principles?

2.2 Extending the case study: Comparing physics experts with non-experts

As all subjects had judged their physics know-ledge to be rather limited, we chose to test agroup with formal physics training on the bal-ancing questions. We also tested a social sciencecontrol group and added two new tasks. Tasks1–3 were dropped from the study, while Tasks4–6 were included. To test for a specific heur-istic, namely that heavy objects are harder tobalance, the following two tasks were added:

Task 7: The question “Does a weight helpand if so, where would you place it?” was posedwith respect to the much lighter wooden rod (m= 40g). Thus, Task 6 was replicated with alighter rod. Finally, a more fine-graded question

was added to assess by how much expert know-ledge would be superior to normal knowledge, ifat all:

Task 8: The eighth task showed four rodsof the same material (steel, length 90cm). Onthree of them, a weight was attached at differ-ent positions (as shown in Figure 15). The sub-jects had to order them according to whichwould be easiest to balance on the tip of onefinger. Note that the height of the barycentermatters. It is equally located in the center ofrods B and D.


Participants: 84 college students, mainly ofPsychology (69 women, 15 men, age rangingfrom 19 to 66 years) and 113 college studentsof Physics, Mathematics, and Chemistry (41women, 72 men, age ranging from 18 to 27years) were tested. The students of mathemat-ics, physics, and chemistry estimated theirknowledge in mathematics (M = 2.65, SD =1.02) and physics (M = 2.68, SD = 1.07) tobe moderate. The men estimated their know-ledge of physics to be higher than did the wo-men (t(111) = -4.34, p < .001). No differencewas found for self-assessed maths skills(t(111) = -.22, p=.83).

A paper-and-pencil test was used to in-vestigate the assumptions subjects held aboutthe effect of various object properties on howeasily the respective rods could be balanced.The test booklet included eight tasks: one perpage. Each task consisted of a hypotheticalscenario illustrated by a drawing. Differentpseudo-random orders of the eight tasks wereexecuted by all students. Tasks that built uponone another were kept in their logical order.Once a given task was finished, the page had tobe turned. It was not permitted to go back to aprevious page. Depending on the task, subjectshad to make a binary choice (pick one or an-swer yes or no) or they had to grade their an-swers on a seven-point scale, according to howsure they were that one alternative would winover the other (certain win, very likely, some-what likely, equal chance, somewhat unlikely,very unlikely, certain loss).


Figure 15: In Task 8, the four rods labeled A–D shouldbe sorted according to the difficulty of balancing them.

The correct order is C–B–D–A or C–D–B–A.


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2.2.2 Results and discussion

Task 4 (equal length, different weight of therods): Only 3.6 % of all social science studentsproduced the correct solution and stated thatthe wooden and the steel rod would be equallyhard to balance. Half of them thought that thesteel rod would be easier to balance, and the re-maining subjects chose the wooden rod. Thiscorresponds well to the results obtained withthe first large student sample. The physics stu-dents, in contrast, performed better albeitnowhere near perfection. 22% of them chose thecorrect answer. 21% thought the wooden rodwould be easier to balance, and 57% thoughtthe steel rod would be easier to balance. Thus,social scientists equally chose one or the otherwhereas physicists preferred the metal rod, andat most one fifth of them knew the correct an-swer (provided they were not just guessing bet-ter than the social science students).

Task 5 (equal weight, different length):Half of the social science students (53%) cor-rectly thought that the longer rod would beeasier to balance, and less than 2% thoughtthat length did not matter. The physics stu-dents did noticeably better: 76% chose thelonger rod, and only 20% thought the shorterrod would be easier to balance. 4% thought itwould be the same with both rods.

In Task 6 (attach weight to steel rod):60.7% of the social scientists thought that aweight would make it easier. When asked toplace the weight, only 9.5% put it in the topthird (for analysis purposes the rod was dividedin three equal parts), and 44% placed it at thebottom third. Physics students fared a littlebetter. A mere 44 % thought that a weightwould improve balancing, but those who didcorrectly placed the weight at the top (40% ofall physics students).

Task 7 (attach weight to light woodenrod): Not surprisingly, performance was verysimilar to Task 6 (r= 0.76). If anything, therod’s being lighter improved performance.77.4% of the social scientists thought that aweight would make it easier. When asked toplace the weight, only 19% put it in the topthird. 45.2% put the weight in the bottom sec-

tion, and the remaining students placed it inthe middle section of the rod. Physics studentsfared a little better. 81% thought that a weightwould improve balancing. However, the correctplacement at the top was made by only 40%.Thus, in light of the results from Task 6, itseems that those who knew the correct answerwere unimpressed by the weight of the rod.However, among those experts who merelyguessed and suspected that weight would makea difference, they guessed so more often whenthe rod was lighter—increasing the salience ofthe weight.

Task 8 (order the rods): Social sciencestudents: According to the reasoning that agreater moment of inertia should facilitate bal-ancing (note that this will not hold for muchheavier rods), the correct order is C, B = D, A.Not a single subject produced this answer.16.7% chose the order A, B, D, C; another16.7% chose A, D, B, C. Only one subject con-sidered a tie, albeit with a wrong ordering (B,D, A=C).

Physics students: Notably, 6% of the sub-jects did give the correct answer of CBDA orCDBA. 94% of the subjects answered incor-rectly. Thus, the physics students were some-what more knowledgeable than the social sci-ence students.

In sum, the errors we make in perceivingthe balancing properties of simple objects arelarge. The important variable of mass distribu-tion is ignored entirely. We plainly do not seehow an object is best balanced until we try itout, even though we balance objects on a dailybasis. Most if not all observers are unable tocorrectly imagine or remember past balancingacts. Formal physics training has surprisinglylittle effect on the paper-and-pencil task for as-sessing falling and balancing of rods. Note thatthe classical mechanics knowledge that wouldhelp solve the problem should have been heldby all natural science students involved in thestudy. The fact that their answers were onlyslightly superior to novice intuitions is stunning.Why is the textbook knowledge of classicalmechanics so frail that it has not been internal-ized, such as to inform our intuitive judgmentsor at least facilitate our textbook learning?



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Throughout evolution we had to handle andwield objects by balancing them. One might ar-gue that such knowledge is not available to theventral processing stream (see Milner &Goodale 2008). However, in further tests weconfirmed that performance in our tasks did notimprove when we let subjects wield a rod beforefilling out the questionnaire. Even though ob-servers are able to feel how long a stick is whenwielding it while being blindfolded (see Turvey& Carello 1995), they are unable to exploit theavailable perceptual cues that inform themabout the balancing properties of an object.Thus, although we know shockingly little aboutbalancing, it seems to be sufficient to guide ourdaily actions. We correctly see longer sticks asbeing easier to balance, but we fail to see theimportance of mass distribution. Even wheneducated by formal physics training, our per-formance becomes only slightly more sophistic-ated. The gap between percept and realitycloses merely by a small amount. It appearsthat the visual systems of different observersadopt different private models that often in-clude rod length but not mass distribution.

2.3 The second case study: Visual cues tofriction

Let us now look at another relational propertythat may have more serious consequences forour health: friction. If we misbalance an object,we may break it, but if we misjudge the slipper-iness of the surface we walk on, we may gethurt. We need to avoid accidents on slipperyground and we have to estimate the force weneed to apply to hold an object. Importantly,we often cannot wait for haptic cues to makethis information available, but typically we haveto make the underlying judgment of slipperinesson the basis of visual cues. The mere look of awet slope may be all we have to guide our de-cision to tread forcefully or to hold on to ahand-rail and walk gingerly. The human abilityto make such visual assessments of slipperinessis not well explored. We hold that this is be-cause friction is not a simple surface propertybut rather a relational property, which can onlybe determined by relative characteristics of two

surfaces. In other words, the fact that a surfaceis rough does not imply high friction, and thefact that a surface is smooth does not implythat it is slippery. Plastic for instance, can bevery sticky on human skin but very slippery onwool or felt.

In what follows, we provide an overview offriction perception and briefly introduce venuesto visual and haptic roughness perception. Thenwe report two experiments that were conductedto assess visual and haptic judgments of frictionbetween surfaces.

2.3.1 Friction as a relational property vs. surface roughness

Some surfaces afford walking on whereas othersdo not. The information that allows the organ-ism to make potentially critical decisions aboutwhere to tread or how strong a grip should beis based on a variety of perceptual dimensions(see e.g., Michaels & Carello 1981). Even whenample opportunity is given to haptically ex-plore the surface, its felt roughness is not ne-cessarily the same as the friction between theexploring hand and the surface, let alone thefriction between the sole of the shoe and thesurface. For instance, if our hand is moist wefeel high friction when exploring a polishedmarble floor and at the same time we feel it tobe very smooth. We may even perceive it asslippery—factoring in the effect of dry vs.moist hands.

Tactile competence regarding perceptualaccess to roughness of surfaces appears to berather sophisticated (for a state-of-the-art re-view of haptic perception see Lederman &Klatzky 2009). In essence, haptic perception ofsurface roughness is better when the surface isexplored dynamically as opposed to statically.Errors are generally rather small. More inter-estingly, several studies have demonstratedthat cross-modal sensory information (e.g., vis-ion and touch) can lead to better estimates ofa texture’s roughness (e.g., Heller 1982). Otherresearch has also shown that different sensorymodalities are weighted about equally when es-timating the roughness of textures (Lederman& Abbott 1981; Lederman et al. 1986).



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Even by mere visual inspection, observersare able to see how rough a surface is (Leder-man & Klatzky 2009). Such findings may havetempted researchers to unduly reduce friction tosurface roughness. For instance, in the ergonom-ics context of accident analysis, slipperiness ofwork surfaces is typically operationalized bysurface roughness, with the implicit or explicitassumption that roughness is good enough anapproximation of friction (see e.g., Chang 1999;Chang et al. 2001; Grönqvist et al. 2001). How-ever, friction is a rather complicated propertybetween surfaces, for one because it is subjectto change with the amount of pressure one ap-plies or with the speed at which the surfacesmove relative to one another. And people ap-pear to have some difficulty judging friction(Joh et al. 2007).

Let us consider the case of a square blockof cement on a large wooden surface. The heav-ier the block, the higher the friction coefficient.And the rougher the surface of the block thehigher the friction coefficient. Thus, friction is afunction of the force applied to a given surface,of area, and of roughness. Children and adultsseem to be able to perceptually appreciate somebut not all of the above-mentioned three com-ponents of friction. This intuitive knowledge de-velops with age. Adults have some insight intothe multiplicative relation between the weight ofan object and its surface texture in cases wherethe object is pulled across a surface, whereasnine-year-old children seem to assume a simpleradditive relationship (Frick et al. 2006).

Friction is defined by the interactionbetween two surfaces, and its estimation re-quires knowledge about how different surfacescan interact. Thus, the seemingly simple visualpercept that we have of a surface as “slippery”is a rather complex physical relation that per-tains between properties of the surface and thecontact object. Physically, slipperiness is indic-ated by the friction coefficient between two sur-faces, which is usually measured by placing anobject on an adjustable ramp. As the steepnessof the ramp increases, one determines the angleat which the object starts to slip (static fric-tion) or when the object starts to move uni-formly (kinetic friction).

We can haptically judge the roughness ofsurfaces, and we are also able—to some degree—to haptically judge the friction between sur-faces. Grierson & Carnahan (2006) have shownthat individuals can haptically perceive slipperi-ness; that is estimates were significantly correl-ated with the friction coefficients between anobject’s surface and skin. In their first experi-ment, they showed that tangential motion is re-quired to judge the friction coefficient realistic-ally. In a second experiment, they examined theforce people applied to lift an object with a cer-tain weight and surface structure. The appliedforce was often higher than necessary. Next tonothing is known about our ability to judgeslipperiness based on visual information.

2.3.2 Slipperiness Experiment: Visual cues to friction of familiar surfaces

Vision has been shown to improve haptic judg-ments in endoscopic surgery. Within a simu-lated endoscopic environment, Perreault & Cao(2006) tested the effects of vision and frictionon haptic perception by measuring for how longparticipants held on to the objects with the sur-gery tool. In a second experiment, participantshad to compare the softness of pairs of simu-lated tissue. The experiments showed thatvisual and haptic feedback were equally import-ant for the task. This suggests that visual cuescan be exploited to judge slipperiness.

Presumably the main visual cue for pre-dicting slipperiness or friction is shine (gloss, re-flection, etc.) of a surface. Joh, Adolph, Camp-bell & Eppler (2006) explored which visual in-formation can serve as a warning of low frictionsurfaces. They asked their participants whichcues they use to identify slippery ground, andtested whether visual information is reliable forthe judgment of slipperiness under differentconditions (indoor and outdoor lightening).Walkers seem to rely on shine for selecting asafer, less slippery path, even though shine isnot a very reliable visual cue for indicating slip-pery ground.

With two experiments we attempted to as-sess, in more general terms, the ability to perceiveslipperiness. In our first experiment, we tried to



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find out to what extent visual and haptic inform-ation enables us to estimate friction between twosurfaces and, in particular, how far visual cues inisolation decrease the ability to judge friction. Inour second experiment, we manipulated the visualappearance of given surfaces to explore the effectsof glossiness, contrast, and undulation on per-ceived friction.

Every day we encounter different types ofsurfaces with which we are in contact. In thesesituations we do not really think about howmuch force is to be exerted in order to createsufficient friction, be it between the fingers andthe object we are grasping or between the soleof our shoes and the surface of the road wetread. Nonetheless, we rarely accidentally dropan object or slip on the road. Thus, we musthave some degree of intuitive knowledge aboutthe friction of surfaces. The experiment soughtto find out, first, if this is really the case, andthen which sensory information might guide ourestimates of friction.


33 female and 31 male subjects between 18 and52 years of age (M = 25.3; SD = 6.6) volun-teered and were paid for participating in thestudy. All had normal or corrected to normalvision, and no one reported haptic impairments.

Ten different types of surfaces (see Figure16) were glued onto separate thin quadratictiles of wood with a size of 10 x 10cm. The sur-faces were sheets of Teflon, pan liner, smoothand rough foam rubber, cloth, felt (soft andhard), and three different grades of sandpaper.

Two common reference surfaces werepicked: human skin and smooth untreatedwood. That is, the participants had to estimatethe friction of the above ten surfaces with re-spect to one or the other of the two referencesurfaces, skin or wood.

To measure the perceived friction, a rampwas used. Its slope could be adjusted to a steep-ness corresponding to the setting where the tilewas judged to start sliding down. The rampconsisted of two wooden boards connected witha hinge. It was placed in front of the participantand could be continuously adjusted (see Figure

17). A measuring stick was attached to the topof the ramp such that the experimenter couldeasily record the height of the ramp while theparticipant saw only the unmarked side of themeasuring stick. The height settings were thenconverted to slope angle, which in turn wasused to determine the friction force actingbetween ramp and probe surface.

Figure 16: The ten materials used in the first experi-ment. Top row from left to right: Teflon, pan liner,smooth and rough foam rubber, cloth. Bottom row fromleft: felt (soft and hard), three different grades of sandpa-per (320, 180, 40 in that order). All materials were moun-ted on identical square wooden tiles. The matchstick isshown to provide scale information, it was not there inthe experiment.

The slope of the ramp used to estimatethe friction of the different surfaces could bevaried from 0 to 90 degrees. We computed coef-ficients of estimated static friction for the sub-sequent analyses using the following equation:

μH = FR / FN (friction coefficient = fric-tion force / weight)

A 4 x 2 x 10 design was used, with onefour-level between-subjects factor (Condition),and two within-subject factors, Reference Sur-face (two levels: skin and wood), and SurfaceMaterial (ten levels: Teflon, pan liner, smoothand rough foam rubber, cloth, felt (soft andhard), and three different grades of sandpaper).

The factor Condition consisted of differentinstructions for exploring the surface materials(see Table 1). In the haptic-visual condition, ob-servers were asked to touch the surfaces and tovisually inspect them. In the haptic condition,the surfaces were hidden in a box at all timesand could only be explored haptically. In thevisual condition, observers were not allowed to



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touch the surfaces but could inspect them visu-ally. In the photo condition, finally, observersmerely viewed photographs of all ten surfaces.The same photographs as depicted in Figure 16were used, with the exception that the matchwas not present. The photographs were thesame size as the actual tiles (10 x 10 cm).

Subjects were allowed to look at the re-spective reference surface (skin or wood) beforemaking a set of judgments based on this refer-ence surface. They were also allowed and en-couraged to touch the reference surface regard-less of the condition in which they were tested.That is, even the group that could only visuallyinspect the test surfaces had visual and hapticexperience of the generic reference surface. Theramp itself was not to be touched in this phaseof the experiment, in order to ensure that thegroups did not differ in how they explored theramp. To envision the friction of skin, subjectswere instructed to touch the inner side of theirforearm, and to envision the friction of wood,they had a piece of wood (the same wood alsoused for the ramp) lying in front of them thatthey could touch. Half of the participants star-ted with wood as reference and then after ashort pause used skin as reference. The otherhalf started with skin and then judged wood.

Within each block, the order of the surface tileswas randomized separately for each observer.

Table 1: The four test conditions under which separategroups of subjects were asked to explore the material sur-faces.

The procedure consisted of three parts. First,subjects had to estimate the friction of the ten ma-terials, all presented successively and in randomorder. To do so, they had to adjust the slope of theramp (see Figure 17). After inspecting the refer-ence surface and the first tile, they had to set theramp’s slope to the point where they expected theparticular surface to just start slipping on theramp. The surface tiles were never physicallyplaced on the ramp. Then the remaining nine tileshad to be judged in the same manner.

In the second part, a short questionnaire wasgiven to the subjects. Finally, the procedure was


Figure 17: The ramp used to measure the estimatedfriction coefficients produced by the participants. Theramp had to be adjusted to the angle at which the re-spective tile would just about start to slide. In the case ofskin as reference surface, observers were told to imaginethe ramp to be their torso or to be covered with skin.

Figure 18: Actual and perceived coefficients of frictionbetween skin and the respective materials. The solidblack line corresponds to the actual angle of the slope atwhich the tile would indeed start to slide. The other linesrepresent subjective judgments averaged across all parti-cipants of each group respectively. Error bars indicatestandard errors of the mean.


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repeated with the other reference surface. The or-der of which reference surface was chosen first wascounterbalanced such that half the observers star-ted with wood and the other half started with skin.

2.3.4 Results

Line graphs show the actual and the averagedestimated coefficients of static friction on skin(Figure 18) and on wood (Figure 19). With theexception of Teflon on skin, friction was per-ceived, albeit underestimated. In some cases,roughness appears to have guided perception.For instance, the different grades of sand paperproduce similar friction because roughness andcontact area trade off against one another. Thecoarse paper is rougher but at the same timeprovides fewer contact points than the fine pa-per. The resultant friction is in fact comparable.However, the coarse paper was mistakenlythought to produce more friction than the finepaper.

With skin as reference surface, haptic ex-ploration improved performance but estimatesremained far from perfect. Teflon in particularwas grossly mis-estimated. The overall resultsshowed significant main effects of Material(F(5.7, 342.4)=22.85, p<.001, partial ² =.27)ηand Reference Surface (F(1.0, 60.0)=17.80,p<.001, partial ² =.23). In addition, the effectsηof Condition were more pronounced for the ref-erence surface of skin; the interactions of Mater-ial x Condition (F(17.1, 342.4)=2.92, p<.001,partial ² =.13) and between Material x Surfaceη(F(7.9, 475.2)=2.87, p=.004, partial ² =.046)ηwere significant. The interaction of Material xSurface x Condition was also significant (F(23.8,475.2)=1.69, p=.023, partial ² =.078). Conη -trasts revealed that performance was poorer inthe photo condition compared to the hapticcondition (p=.023) and the haptic-visual condi-tion (p=.007). The latter two did not differ sig-nificantly from one another or from visionalone.

The post-experimental questionnaire re-vealed that most participants attempted to useall available information and that they tried tofind out which material they were confrontedwith. After identifying the material, they estim-

ated the friction on the basis of their experi-ence. Perhaps some erroneous estimates couldbe ascribed to such cognitive influences uponfriction estimation.

In sum, static friction between a numberof different materials and the reference surfacesskin and wood were picked up, but only to alimited degree. Vision alone does transport in-formation about the relational property of fric-tion. This ability to see friction is attenuatedbut still present when photographs are used.Thus, high-resolution detail appears to be cru-cial. Surprisingly, haptic cues were not superiorto visual cues and even in combination onlytended to improve performance. Friction is gen-erally underestimated, with the exception of Te-flon and wood, which was grossly underestim-ated. Multisensory information did not helpcompared to unisensory information. It appearsthat multiple information sources improve theperception of simple properties such as rough-ness (Lederman & Abbott 1981; Lederman etal. 1986), but fail to contribute in more complexcases of assessing friction. When visual informa-tion was reduced, not surprisingly, this affectedfriction judgments negatively. The photo condi-tion produced notable judgment errors. It would


Figure 19: Actual and perceived coefficients of frictionbetween wood and the respective materials. The solidblack line corresponds to the actual angle of the slope atwhich the tile would start to slide. The other lines repres-ent subjective judgments averaged across all participantsof each group respectively. Error bars indicate standarderrors of the mean.


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be interesting to find out if this degradationcould be compensated for by providing hapticcues together with the photographs. Note, how-ever, that the photographs were able to produceestimates that correlated with actual friction.Thus, some information about roughness is pre-served in the photo and can be accessed. Therelational property of friction appears to bequalitatively different from and not reducible toroughness.

2.3.5 Friction experiment with manipulatedvisual appearance

The preceding experiment has shown that ob-servers are able to gain some information aboutfriction by visually inspecting the two involvedsurfaces together exhibiting this complex prop-erty. Given this ability, we should be able toisolate some of the relevant visual surface fea-tures upon which this ability is based. In asecond friction experiment, we limited the refer-ence surface to wood, and manipulated thevisual properties of a select number of surfaces,namely Teflon, foam rubber, and sand paper.Among the changes in visual properties werefactors that should influence perceived rough-ness and thereby potentially also friction, suchas convolving the picture with a wave pattern,or changing the contrast in the picture.

2.3.6 Method detail

55 volunteer subjects (23 men and 32 women)participated in the study. They were recruitedat the campus of the Johannes-Gutenberg Uni-versity of Mainz and at a nearby supermarket.All participants were naive with respect to thepurposes of the experiment. Their average agewas 31.8 years (SD = 12.6 and a range from age16 to 59).

We took some of the pictures of the tilesused previously. The pictures were taken on aFuji Finepix S5500 digital camera (four mega-pixels) with a resolution of 1420 x 950 pixels.One reference picture each of coarse sandpaper,structured foam rubber, and Teflon werechosen. Then these reference pictures were mod-ified using four special effects provided by

Adobe Photoshop Six. Five visual effect condi-tions (Filter) were thus created for each of thethree materials (see Figure 20 for the case ofsand paper):

Figure 20: The reference picture (n) of the sand papertile, and the four filter effects applied to the reference pic-ture: ocean effect (o), wave effect (w), reduced lightness(d), and enhanced contrast (c). Note that all pictureswere of equal size in the experiment.

1. Normal: The reference picture was the ori-ginal photo of the surface without any specialeffect.

2. Ocean: The original photo was convolvedwith the structure of an ocean surface. Aphotograph showing the ocean from abovewith its waves was put as a new layer uponthe original photograph with an opacityvalue of 25%. It added a look reminiscent ofstructured wood to the photograph. We hy-



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pothesized that the added structure wouldincrease perceived friction.

3. Wave: This filter introduced a wave patterninto the picture. This distortion effect wasused with the parameters Number of Gener-ators (5), Wavelength (Minimum 10 Max-imum 120), Amplitude (Minimum 5, Max-imum 35), Scale (horizontal 100%, vertical100%), Repeat Edge Pixels (On), and Type(Sine). This filter distorts the original struc-ture in the pattern of sine waves. We hypo-thesized that here, the added structure wouldnot change perceived friction because wavesare regular and smooth compared to theocean texture.

4. Dark: The lightness of the surface was re-duced uniformly by 50% (parameter setting:50). We hypothesized that this would reducedetail, which would decrease perceived fric-tion.

5. Contrast: The contrast was uniformly en-hanced such that the according parameterwas raised to +50. We hypothesized that theadded contrast would emphasize roughnessand thereby increase perceived friction.

The photos were printed on high-quality photopaper and shown to the volunteers in succes-sion. The “normal” reference version of one ma-terial was always shown first, and then four dif-ferent versions of the same material werepresented in changing pseudo-random orders,for each material respectively. All possible se-quences of the materials were presented to dif-ferent observers. They were asked to imaginethe surface shown on the photograph as beingthe surface of the ramp itself. The same rampas before was used (see Figure 17), but subjectswere not allowed to touch its actual woodensurface. Then they were asked to decide howsteep the ramp would have to be set for awooden tile to start sliding down on the shownsurface. The tile of wood was shown to thembeforehand and they were asked to touch it.Then they had to put the ramp at the angle atwhich they thought the wooden tile would juststart to slide. As before, we measured theheight of the ramp setting in centimetres. Withthis information, we calculated the angle with

sin( ) = height / ramp length = height / 44cmαand finally the resulting estimated friction coef-ficient for all surfaces.

2.3.7 Results

Figure 21 shows the estimated friction coeffi-cients for all three materials averaged across allfilters and across the respective reference sur-face. Friction between wood and foam rubberwas judged to be highest, friction with sandpa-per was judged intermediate, and friction withTeflon was judged to be smallest. Figure 22 de-picts the overall averages by Filter (visual ef-fect). Figure 23 shows the interaction betweenMaterial and Filter.

A repeated measurement analysis of vari-ance with Material and Filter as within-subjectfactors and gender as between-subjects factorwas conducted on the judged friction coeffi-cients; F-values were corrected by Huynh-Feldtas necessary. Material had a significant effect onestimated friction (F(2, 106)=9.54, p<.001, par-tial ² =.15). Foam rubber and paper did notηdiffer, but both were judged to produce morefriction than Teflon (p<.001 and p<.003 re-spectively).

Figure 21: Estimated friction coefficients for the threematerials independently averaged across all filters, andthe actual coefficients for the three materials on wood.Error bars indicate standard errors of the mean.

The factor Filter also had a significant in-fluence on the estimation of friction (F(4,212)=5.351, p=.001, partial ² =.092). The unη -filtered stimuli were judged to produce the



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smallest amount of friction, and all filters ap-peared to increase the subjective coefficient offriction. Figure 22 shows the estimated frictionfor all five filters averaged across all three ma-terials. The contrasts between the estimatedfriction coefficient values for “normal” and“ocean” (p<.024), “normal” and “dark”(p<.001) and “normal” and “contrast”(p<.023) were significant. Because of the some-times variable judgments, the individual con-trasts between “normal” and “wave” as well as“contrast” and “dark” failed to reach signific-ance.

Figure 22: Estimated friction coefficients for the five fil-ters averaged across the three materials. Error bars indic-ate standard errors of the mean.

We also found a significant interactionbetween the factors Material and Filter (F(8,424)=3.99, p=.002, partial ² =.070). As visibleηin Figure 23, this interaction was mainly due tothe immunity of Teflon to all filter manipula-tions and to the special effect of the increasedcontrast on foam rubber. Now let us have acloser look at the three materials and how theyfared with the different filters. Participantscould judge the friction between wood and theshown surfaces rather well, with the exceptionthat the friction of sandpaper was underestim-ated. For some reason some of the grittiness androughness of sandpaper has been lost in thephotos, whereas no such loss occurred for foamrubber and Teflon. To the experimenter, thesurface of sandpaper also did not look as roughas it did in real life.

Teflon on wood was clearly judged to bethe most slippery surface. Interestingly, the es-timated differences between the Teflon referenceand its filter-treated variants were very smallcompared to the other materials (see Figure23). Presumably, Teflon generally looks so slip-pery that a ceiling had been approached andthe filters could not significantly change the lowfriction ratings of Teflon. The surfaces that weretreated with “ocean” looked like rough wood;the manipulations “contrast” and “dark”seemed to make the structure clearer. The filter“wave” had a smaller influence on the estima-tions. Participants often said that they found itdifficult to classify the wave-treated surface.

Figure 23: Interaction between the two factors Materialand Filter. Error bars indicate standard errors of themean.

The results of this experiment clearly showthat irregular additional structure—as intro-duced into the surface by convolving the picturewith the ocean pattern—causes the perceptionthat the surface is less slippery. This was thecase for all surfaces that were not extremelyslippery to begin with. Other than hypothes-ized, reducing the lightness of the surface alsotended to produce higher ratings of friction. In-creased contrast, on the other hand, producedmixed results. Sandpaper with increased con-trast was judged to cause more friction. Con-trast had a smaller but similar effect on Teflon.However, when applied to foam rubber, in-creased contrast had no effect. Taken together,these effects demonstrate that visual aspects of



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a surface, such as its microstructure, its light-ness, and its contrast co-determine how slipperyit is judged to be with respect to a given refer-ence surface. Note, however, that the referencesurface was always wood, and simple roughnessjudgments may have guided the friction estim-ates.

To summarize the friction case study, weconducted two experiments to assess whetherobservers are able to visually perceive the com-plex relational property of friction between twosurfaces even when not allowed to touch thesurfaces. They were able to do so with limita-tions. Observers generally tended to underes-timate the degree of friction. An underestima-tion of friction as observed in these two studiescould be regarded as a conservative approach tojudging the grip force required to successfullygrasp objects. Using more force than necessaryrarely leads to disaster (consider raw eggs),whereas too little grip force causes an object toslip out of our hand and fall.

The first friction experiment comparedjudgments based upon visual inspection alone,and then after visual and haptic inspection. Vis-ion in and of itself provides valuable informa-tion; additional haptic information added sur-prisingly little. The second experiment exploredthe particular visual properties that make sur-faces look more or less slippery, but note thatthe reference surface always remained un-changed. Subjects likely differentiated betweensurfaces of different roughness insofar as rough-ness (simple property) and friction (relationalproperty) were correlated. Errors were large inparticular when the relational property to bejudged was variable. Perceiving Teflon as veryslippery (with respect to skin) when it is indeedquite the opposite is a grave perceptual error,but it is not very meaningful to call the error anillusiond. A perceptual miscategorization of therelational property of friction between surfacesmight be a more appropriate description.

3 Conclusion

I have attempted to argue that we need to re-conceive the notion of what an illusion is. In thecontext of the traditional line drawings used

over a hundred years ago to illustrate the short-comings of vision, illusionsm have begun to mis-guide our thinking about normal perception. Il-lusionsm do not indicate the error-prone natureof visual perception. On the contrary, they tendto be small compared to the many illusionsd

that go unnoticed on a regular basis. To illus-trate that this is the case, I have used two ex-amples from the domain of complex relationalproperties. This choice was based on the convic-tion that perception of everyday objects alwaysnecessarily includes judgment (be it in terms ofHelmholtzian unconscious inference, or be it interms of private models that may or may notbecome transparent to the perceiver). The no-tion that illusionsm should be of interest becausethey reveal the workings of how the visual sys-tem derives percepts from simple sensations isnot useful. It is not useful because an illusionm

only becomes manifest by a comparison processthat is at least as fraught with cognition as isthe perception of everyday relational properties.We have used the classical stick in the waterand the equally classical Ebbinghaus illusion toillustrate that illusionsm only become manifest ifa cognitive operation is performed (i.e., a per-ception-inference-cycle when moving the stick orcomparing the circle to a reference circle knownto be of identical size).

It is also impossible to investigate illusionsas merely phenomenal problems. And it is ill-conceived to limit the study of visual perceptionto seemingly simple phenomena that end up re-quiring cognition after all. Perceiving is to makeperceptual judgments, be they explicit (e.g., bysaying which of two objects is larger), or bethey altogether implicit, or merely amenable toconsciousness by an act of attention (e.g., bydetermining hand-aperture when grasping anobject). It is thus impossible to investigate illu-sions as purely perceptual errors. Instead, illu-sions always have a cognitive component in thesense that they require an act of comparison orinference. This holds for all illusionsm, even ifthey may not be amenable to consciousness. Totake illusions as a discrepancy between what wesee and what there is, is doubly mistaken. First,there is always a discrepancy (illusiond) betweena visual percept and the object in the world to



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which it refers, namely the stimulus. Andsecond, only in rare and simple cases do we no-tice this discrepancy (illusionm). The discrep-ancy is owed to the underspecification problem(UP), the qualitative information gap betweenthe two-dimensional retinal image and thericher three-dimensional percept. The UP putsthe perceptual system in a position from whichit has to draw additional information frommemory, from inference, or from internalizedstructures that have been acquired throughoutevolution. Such structures have been suggestedto include that objects are three-dimensional,that light comes from above, that gravity actsalong the main body axis when standing orwalking, or that the brightest patch in thevisual field is usually “white”. Internalizedstructures gain particular weight if the stimulusis poor. This is the case when looking at simpleline drawings and it is all the more the casewhen looking at relational properties. The qual-ity of solutions to the UP differ greatly as thefunction of the task demands, but not necessar-ily as a function of the complexity of the stimu-lus. On the one hand, the perceptual systemachieves performance that seemingly approachesperfection where precise motor action is re-quired in personal space. On the other hand, inmore remote action or vista space (for a veryuseful taxonomy of space see e.g., Grüsser 1983)some blatant errors are made. Our perceptionoften defies the most basic laws of physics.More often than not do these errors go un-noticed. To illustrate how crudely our percep-tions approximate reality even in personalspace, we have explored errors in balancing ob-jects and judging the slipperiness of surfaces.When it comes to these relational properties,our perception falls far from the truth. It ap-pears that the errors tend to be as large as theycan be without interfering with the perception–action cycle required for adequate or acceptableaction. The evolutionary fine-tuning would min-imize error until it is no longer relevant for sur-vival. In this sense, normal perception (i.e., theillusiond) is a satisficing solution. The mag-nitude of the perceptual errors many observersmake is in the league of errors associated withprobability judgments (see e.g., Kahneman et

al. 1982) and syllogistic reasoning, as opposedto the much smaller errors typically associatedwith perceptual illusionsm.

Our perception, just like our cognition,has developed to find solutions to problems thatsuffice. When reaching for an object, perceptionis accurate enough not to knock it over but tograsp it (most of the time). When judging asurface, it is accurate enough that we do notslip (most of the time). These examples arenoteworthy because they do not relegate per-ceptual error to remote vista space, where preci-sion would not matter. Toppling over an objector falling on a slippery slope concern us in per-sonal space.

In essence, the UP is solved with remark-able accuracy for simple properties of objectswithin our domain of interaction. However, assoon as the perceptual properties become morecomplex and involve the relation between two ormore objects, the perceptual system can nolonger solve the UP with any degree sophistica-tion that goes beyond the level of medievalphysics. But rather than giving up and seeingastounding illusions everywhere, the system de-grades gracefully and builds theories that sufficefor the purpose at hand. Their deviation fromreality is not experienced. These perceptual the-ories may be thought of as more or less univer-sal tools for upholding a meaningful world (inthe sense of Shepard 1994); however, it mightmake more sense to think of them as universaltools with a private touch that accommodatesindividual perception-action requirements. Ahockey player or a juggler will for instance havedeveloped private models, be they unconsciousor amenable to introspection, about friction orbalancing that are more sophisticated than thelayperson’s. Note that these models need not beexplicit, in the sense of a perceptual process, ofwhich the cognitive elements cannot be separ-ated out.

Such private adjustments and elaborationswhen solving the UP need not be made in thecase of classical geometric-optical illusionsm. Ihope the above examples and case studies haveshown that ilusionsd, such as the Luther illusion,do not require detection, and illusionsm that be-come manifest, such as the Ebbinghaus illusion,



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can be upheld because their limited magnitudemakes them irrelevant for action.

This raises the questions why illusionsm

arise at all. Illusionsm might arise as mere epi-phenomena or as meaningful warning signs forthe system to signal that a perceptual fine-tun-ing is needed. The epi-phenomenon interpreta-tion would suggest that the juxtaposition of twocontradictory percepts is a fluke and happensper-chance every once in a while. Optical illu-sionsm are merely collections of such flukes. Thewarning-sign interpretation would see in themthe purpose of fine-tuning the perceptual sys-tem. If the perceptual system subserves action,it would ideally minimize error (illusionsd), andone mechanism to do so would be the experi-ence of illusionsm. It is unclear, however, why il-lusions would have to become conscious for thisfine-tuning to work. Would the necessary re-dir-ection of attention require the experience of anillusionm? Be this as it may, the system does noteven notice error—let alone attempt such fine-tuning—when it comes to perceiving relationalproperties. Even an approximate veridical per-ception of relational properties is out of reach ofthe perceptual system. The system merely ar-rives at the first solution that satisfies our ac-tion needs. A flashy epi-phenomenon or a warn-ing system, as indicated by manifest illusionsm,is not useful here, as the discrepancy betweenpercept and reality is too large.

Now, one might ask about cases where theerror is exceedingly large and a warning may in-deed be in place. These cases are rare; but theydo, however, result in manifest illusionm, andhence are compatible with the purpose of illu-sionm that we suggest. Take for instance theperception of pain in a phantom limb. Here thesufferer does notice the illusionm. How can painbe so vividly felt in a limb that is no longerthere? The warning function of this manifest il-lusionm is obvious. For instance, learned reflexesinvolving the absent limb need to be extin-guished and reprogrammed. A more interestingcase is the infamous rubber-hand illusion(Botvinick & Cohen 1998) or the full-body illu-sion that can be created in most observers bysynchronizing their actions and perceptionswith those of an avatar seen in a VR (Virtual

Reality) presentation (see e.g., Blanke & Met-zinger 2009; Blanke 2012; Botvinick & Cohen1998; Lenggenhager et al. 2007). Only in suchextreme cases does the error manifest itself in acomplex relational case. We feel that we aresomeone or somewhere else and at the sametime feel that we are not. It seems to take suchextreme cases before we find a sizable illusiond+m

that deserves the name “illusion”. In most cases, we can adjust perceptions

once we notice that they are erroneous, be theyball trajectories or balancing properties. How-ever, this adjustment process is painfully slowand may have to draw on early stages of per-ceptual and cognitive development. It does nottake center stage, and some theoreticians wouldclaim that the adjustment process converges ona veridical understanding of the world (Gibson1979 calls this “attunement”). Others claimthat many perceptions are useful precisely be-cause they do not match or converge on theworld (e.g., the multimodal user interface the-ory of perception, Hoffman 2010). The satis-ficing nature of private perception may not re-quire a perfect solution of the UP in manycases, as long as the slips and falls remain lim-ited to a tolerable number.

Acknowledgements

Markus Homberg, Cornelius Mülenz, and ManaSaadati helped collect and analyze the balancedata; Daniel Oberfeld provided valuable inputfor the experimental designs; Elsa Krauß,Markus Landgraf, and Laura Längsfeld carriedout the friction experiments.



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http://dx.doi.org/10.1518/001872006778606886

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http://dx.doi.org/10.1146/annurev.ps.41.020190.000245

http://dx.doi.org/10.1068/I0554

http://dx.doi.org/10.3758/15.3.581


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The Illusion of the Given and Its Role in Vision ResearchA Commentary on Heiko Hecht

Axel Kohler

Illusions in vision and other modalities are captivating displays of the virtualnature of our subjective world. For this reason, illusions have been an importantsubject of scientific and artistic endeavors. In his target article, Heiko Hecht dis-cusses the utility of the illusion concept and arrives at the negative conclusionthat the traditional understanding of illusions as a discrepancy between worldand perception is misguided. In his opinion, the more interesting and revealingcases are when the discrepancy is noticed and accompanies the perceptual state,or when, in the cognitive domain, the discrepancies become exceedingly large, butgo unnoticed nonetheless. In this commentary, I argue that Hecht’s criticism of theillusion concept is interesting and deserves further study. But at the currentstage, I don’t see that the model captures the essential features of illusory states.The processes on which Hecht focuses can be considered metacognitive appraisalsof the respective sensory events, an interesting topic by itself. In the second partand as an overview, I review how research on the classical apparent-motion illu-sion has shaped our understanding of the neural underpinnings of motion percep-tion and consciousness in general.

KeywordsApparent motion | Bistability | Cognition | Illusion | Motion quartet | Multistabil-ity | Naïve realism | Perception | Phenomenal opacity | Phenomenal transpar-ency | Sensation | Vection

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1 Illusions in science and culture

A main staple of research in cognitive scienceand especially vision science has been, and stillis, the investigation of illusions. For one, it isjust an amazing fact that although we thinkthat our experience of the world is direct, welive by a subjective model of our environment.We feel that we perceive the world as it is, anaïve realism as we might call it, but we arejust not aware that the world is only presentedto us as a (re-)construction of our nervous sys-tem. In more philosophical terms, this funda-mental property of our experience has been re-

ferred to as “phenomenal transparency” (Met-zinger 2003a), the inability to recognize thatour mental states are representations. This isprobably the reason why we are baffled in caseswhen the subjective character of our perceptionbecomes evident, although this rarely occursunder natural conditions.

At least in the context of our modern cul-ture, many people will have had the experiencethat their train is leaving the station when infact they have just watched the train on the op-posite side of the platform taking off. This phe-

Kohler, A. (2015). The Illusion of the Given and Its Role in Vision Research - A Commentary on Heiko Hecht.In T. Metzinger & J. M. Windt (Eds). Open MIND: 18(C). Frankfurt am Main: MIND Group. doi: 10.15502/9783958570528 1 | 9






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nomenon is termed vection, and everybody whohas had this experience will remember the mo-ment of insight when a cue destroys the illusionof self-motion and we realize that our trainhasn’t budged. A more historical example of il-lusions under natural conditions is the waterfallillusion—, a type of motion aftereffect. Afterlooking at a waterfall or flowing water for along time, static objects, e.g., the river bank ortrees, seem to move in the direction opposite tothe previously perceived water flow, probablydue to adaptation effects in brain regions pro-cessing motion (Anstis et al. 1998). Early de-scriptions of the effect have been attributed toAristotle (384–322 BCE) and Lucretius (99–55BCE; Wade 1998). But apart from these few ex-amples, it’s rarely the case that the constructivenature of our perception is noticeable in every-day life.

Illusions have become a part of our popu-lar culture and have had a strong impact onart. A whole art movement in painting, Op Art,is based on using known and discovering newvisual illusions. It is a cultural version of visionresearch, presenting the fascinating nature of il-lusions to the public in aesthetically appealingways. Illusions also feature prominently in thework of surrealist painter Salvador Dalí andother modern artists. For such artists, the me-dium presented a way of expressing the con-structive nature of perception and signalled adeparture from realism. For painters in general,knowledge about optics and the basis of visualperception has always been important for guid-ing the construction process of paintings andthe refinement of techniques in order to achievecertain effects in the eye of the beholder. Theentwinement of science and art is scrutinized inrecent work looking at the interaction betweenfields (Zeki 1999). Two other forms of art thatwere more or less invented in close interactionwith science are photography and film-making.The very basis of TV and movie presentations isrooted in the fact that we are able to fuse arapid sequence of static images to construct anatural impression of moving objects. TV dis-plays, projectors, and computer screens workwith a certain refresh rate at which subsequentimages are presented; the rate can be as low as

24 Hz in cinematography. The basic phe-nomenon that allows us to create a natural per-ceptual flow from flickering images is referred toas apparent motion, a type of illusory motion.

Because of the fascination with illusionsand its influence on culture, illusions have beenguiding research on visual perception for a longtime—and continue to do so. But this is not theonly reason for the utilization of illusions in sci-ence. Illusions are a powerful tool for under-standing mechanisms of sensory processing inthe brain that are unexpected or counterintuit-ive. Many motion illusions where motion can beseen in static displays (often seen in the enter-tainment sections of magazines) depend on aspecific configuration of color values in directlyabutting picture elements. These configurationsof picture elements are repeated and cover theentire display, in sum creating a striking motionimpression. Psychophysical experiments showedthat the key to the illusion is the configurationof neighboring elements, whose effects cannotbe predicted by current models of visual pro-cessing. Additional neurophysiological measure-ments in the same study demonstrated that dif-ferent picture elements were processed with dif-ferent latencies in certain areas of the visualcortex, mimicking a motion signal (Conway etal. 2005). This suggested a neural explanationfor the occurrence of the illusion and led to arevision of existing models of motion selectivity.

Another driving force for the use of illu-sions in research was a resurgence of interest inunderstanding conscious perception. At the be-ginning of the 1990s, Francis Crick and ChristofKoch started to publish a sequence of concep-tual papers advocating the investigation of con-sciousness with empirical, and especially neuros-cientific methods (Crick & Koch 1990, 1995,1998). Since then the number of papers on con-sciousness has grown steadily in the domain ofcognitive neuroscience. Certain visual illusionslend themselves specifically to investigating thenature of conscious processing. Some of themost prominent paradigms display the charac-teristic of bistability or multistability: Whenpresented to observers, conscious perception al-ternates between two (bistability) or multiple(multistability) interpretations although the


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physical characteristics of the display do notchange. Rubin’s face-vase illusion and theNecker Cube are just the most prominentamong a multitude of examples for multistabil-ity (Kim & Blake 2005). The promise of usingmultistability is that it allows for disentanglingthe neural representation of the physical stimu-lus characteristics from the processes giving riseto conscious perception. The logic of the ap-proach is that changes in neural activity accom-panying switches in subjective experience dur-ing constant physical stimulation provide aguide to understanding the neural underpin-nings of consciousness.

2 Hecht’s criticism of the illusion concept

In his target article “Beyond illusions: On thelimitations of perceiving relational properties,”Heiko Hecht (this collection) begins with a dis-cussion of the traditional concept of illusion andhow it has been employed in the context of re-search on vision. In its most basic sense, an illu-sion refers to a difference between our repres-entation of a given scene and its actual physicalproperties. In an interesting take on the utilityof illusions in research, Hecht suggests that themere discrepancy between our perception andthe real world—what he calls illusiond (“d” for“discrepancy”)—is less useful than one mightthink. In simple terms, our perception is off tosome degree in many cases. But still, on theother hand it is amazing how on-target it ismost of the time: it is sufficiently accurate foran effective interaction with the world. ForHecht, the term “illusion” should be reservedfor situations when discrepancies (illusiond) aremanifest, i.e., when the error is part of the ex-perience and we become aware of it. This istermed illusionm (“m” for “manifest”) and issupposed to be the more interesting case. Themoment of insight for the train-ride illusion de-scribed above might be a good example. Inter-preting relative motion between trains as self-motion is often an adequate interpretation, butthe error is manifested in a striking fashion ex-perientially when we spot a part of the platformthat indicates unmistakably that we are still inthe same place.

In addition to the distinction between illu-siond and illusionm, Hecht is concerned with cog-nitive illusions in comparison to the well-knownperceptual illusions. His interesting observationis that when we move away from perception,the discrepancies between the real world andour judgments become even larger, sometimesto an absurd level. Humans are notoriously badat everyday physics. Hecht mentions that we seenothing wrong with fabricated scenes that glar-ingly contradict Newtonian physics, and evenour spontaneous actions reveal the same degreeof error. Nevertheless, they are hardly ever no-ticed, i.e., illusiond rarely becomes illusionm inthe cognitive domain. That this is especially thecase for relational properties Hecht demon-strates with a series of his own experiments onphysics judgments by university students. Evenparticipants that should at least have some the-oretical knowledge about the laws governing thereal world (physics students) are surprisinglybad at finding the right answers to quizzes onbalancing beams made of different materialswith different weight distributions (Experiment1) and on the slipperiness of surfaces (Experi-ment 2). In these examples, the students’ judg-ments are in stark contrast to the actual, real-world outcomes, which were also empiricallytested in addition to deriving predictions fromthe laws of physics. So even though theparadigms were chosen to be experientially ac-cessible and ecologically relevant, it seems thatour cognitive system does not care about cor-rectness or even rough approximations thatwould point it in the right direction. Even themere ordering of solutions without providingquantitative details is seldom correct.

To summarize, Hecht suggests that thesmall deviations of our perceptual representa-tions are no match for the sometimes extremediscrepancies found in the cognitive domain. Il-lusiond is the norm rather than the interestingexception in sensory processing because—atleast in vision—the full three-dimensional rep-resentation of the world has to be derived froma limited array of two-dimensional informationon the retinae. Hecht (this collection) refers tothis as the “underspecification problem.” For anefficient solution to the underspecification prob-



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lem, the system employs a range of assumptionsand constraints on the makeup of the world toguide the reconstruction process. For Hecht,perception is therefore always fraught with cog-nitive elements. This is even more so when dis-crepancy is detected; illusiond becomes illu-sionm. Then, cognitive judgments are involved,and an explicit comparison process is initiatedthat allows us to capture the discrepancy andwhich makes it experientially available.

3 The role of illusions in vision research

Hecht provides compelling evidence for the er-ror-prone nature of everyday judgments, espe-cially when it comes to relational properties.His observation of an antagonism between thesize of discrepancies and their detectability isinteresting. Moving from the perceptual to thecognitive domain, the size of discrepancies in-creases, but at the same time we are less likelyto notice those errors. But there are a fewpoints of dissent I would like to discuss in whatfollows. (1) The discussion of the cognitivenature of perception is long-standing and won’tbe solved in the near future, especially becausethe term “cognition” is notoriously imprecise.Nevertheless, I am not convinced that the cog-nitive aspect that is supposed to be part of per-ceptual as well as cognitive illusions in Hecht’sview is a necessary ingredient for a properconcept of illusion. (2) Hecht’s arguments are awelcome incentive to reflect upon the concept ofillusion and its role for research. Although hedoes not negate the role of perceptual illusionsfor vision research, he is rather critical concern-ing the utility of traditional illusion research, es-pecially with respect to the underspecificationproblem. Drawing on the vast body of researchon apparent motion, I would like to provide anexample of a positive research program that hasaccumulated valuable insights into the mechan-isms underlying visual motion processing. Thisis not necessarily in contradiction to Hecht’sstance. The focus of research on illusions has fo-cused more on the neural mechanisms of visualprocessing and specifically on the neural correl-ates of conscious perception. In this sense, theresearch lines can be seen as complementary.

Nevertheless, I would argue in conclusion thatthe term illusion is well anchored in the percep-tual domain and plays an important guidingrole for research on visual processing.

There is a long tradition in vision researchof considering the influence of cognition on per-ceptual processes. The basis for the early invest-igations on vision and, more generally, on sens-ory processing in the 19th century and early 20th

century was the distinction between sensationand perception. One of Helmholtz’s (1863)definitions captures the main line of thought:

Empfindungen nennen wir die Eindrückeauf unsere Sinne, insofern sie uns alsZustände unseres Körpers (speciell unsererNervenapparate) zum Bewusstsein kom-men; Wahrnehmungen insofern wir unsaus ihnen die Vorstellung äusserer Objectebilden.1

The definition can be seen as a continuation ofa philosophical tradition that has the intentionof separating pure states of sensory receptionfrom the more cognitive aspects concerned withthe reconstruction of the outer world. Alreadyat this time, different authors were aware of thefact that these definitions did not draw a cleardividing line between different types of sensorystates. For example, Sigmund Exner (1875)refers to Helmholtz’s definition and points toseveral examples for which the distinction be-comes muddled. His observant conclusion is thatthe philosophical concepts do not fare well inthe field of brain physiology and that contradic-tions have to be resolved in future models ofsensory processing (Exner 1875, p. 159). So des-pite its initial allure, the distinction betweensensation and perception produced more prob-lems than solutions.

An interesting recent model of the interac-tion between perception and cognition has beenproposed by Vetter & Newen (2014). They re-view the current empirical literature on cognit-ive penetration of perceptual processing and1 English:

“We call the impressions on our senses sensations, insofar as we be-come aware of them as states of our body (especially of our nervoussystem); we call them perceptions insofar as we create representa-tions of external objects.” [My translation]



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find compelling evidence that cognitive penetra-tion of perception is ubiquitous. They distin-guish four stages of processing in the sensory(visual) hierarchy: (1) basic feature detection,(2) percept estimation, (3) learned visual pat-terns, and (4) semantic world knowledge. Ac-cording to their account, almost all possible in-teractions between processing levels occur undernormal conditions and top-down connectionscan be considered forms of cognitive penetra-tion. They argue that it’s not a question ofwhether cognition influences perception, butrather of what type of interaction takes place inany given case. They advocate a move awayfrom the general conceptual question of the cog-nition-perception relationship towards an empir-ically-based consideration of the interactionsbetween different levels of the processing hier-archy.

Importantly, none of the stages character-ized by Vetter & Newen (2014) capture the cog-nitive component Hecht has in mind. The realiz-ation that there is a discrepancy between per-cept and the real world is not something in-volved in the construction of the perceptualcontent itself. It seems that this it is more alongthe lines of a metacognitive appraisal of the cur-rent situation. With reference to Metzinger’s(2003b) concept of phenomenal transparency (anaïve-realistic stance towards the perceivedworld) referred to at the beginning of the com-mentary, it is now the complementary feature ofphenomenal opacity—a situation in which therepresentational character of experience be-comes available to the subject—that might playa role here. Metzinger (2003b) refers to cases oflucid dreaming and drug-induced hallucinationsas prime examples of phenomenal opacity. Inter-estingly, it is not sufficient for him that we haveaccompanying reflexive thoughts on the natureof perceptual representations (the “philosopher’sstance”, as one could say), but we must also beattentively engaged with the perceptual contentand recognize the illusory nature of the process.Therefore, it seems to be the case that neitherthe views of Vetter & Newen nor Metzinger’sconcept of phenomenal opacity seem to capturethe cognitive component Hecht has in mind.But in my view, such models of cognitive penet-

ration are much more intimately linked with theillusion concept, because they provide an under-standing of how the very nature of the experi-ence is modulated by cognitive processes.Hecht’s model doesn’t seem to capture that as-pect, since it functions more as a cognitive com-mentary on the impenetrable perceptual pro-cess. It is unclear why this metacognitive ap-praisal should be considered a hallmark of illus-ory experiences.

When Hecht argues for abandoning theterm “illusion” in the perceptual domain, healso refers to Wertheimer’s classical work on ap-parent motion (1912) and contends that theGestalt psychologists “avoided the term illu-sion” (Hecht this collection). It is true that, forexample, Wertheimer (1912, pp. 167–168) him-self mentions in a footnote that “illusion”should not be used to refer to a discrepancy rel-ative to the physical world because his mainconcern is with mental states. (The Germanword in the original paper is “Täuschung,”which is indeed best translated as “illusion” inthis context.) Nevertheless, the passage is notvery clear on the reasons for rejecting the refer-ence to discrepancy. Again, it seems that thedistinction between sensation and perception(see above) is lingering in the background. Evenassuming a correct sensory reception (sensation)of the apparent-motion inducers, something isadded that goes beyond the raw sensory data.In a later section of the paper (Wertheimer1912, p. 228), this becomes clearer when Wer-theimer analyzes another possible meaning of“Täuschung,” i.e., failure of judgment (German:“Urteilstäuschung”). It is important for himthat apparent motion is not a result of cognitiveprocesses, of inferences of the type: “If an objectwas there just before and now is over here, itmust have moved between the points.” He isconvinced of the perceptual nature of the phe-nomenon and rejects the idea that cognitionplays an important role. Again, there is someambiguity with respect to the usage of the term“illusion” here. This being said, throughout thearticle Wertheimer uses the noun-form“Täuschung” thirty-five times and also refers toother motion illusions that were already as wellknown at the time as “Täuschung.” On my



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reading, his main intention was to prove thatapparent motion is the result of a low-level per-ceptual process and that it is indeed illusory innature.

Wertheimer’s 1912 paper, with its detailedpsychophysical investigation of the apparent-motion phenomenon is commonly considered tobe the founding event of the Gestalt movement(cf. Sekuler 1996; Steinman et al. 2000), al-though this might not be the complete picture(Wertheimer 2014). We have just passed thecentenary of Wertheimer’s seminal article, butstill there is much work to be done to provide acomplete picture of the processes involved inapparent-motion perception at behavioral, com-putational, and neurophysiological levels of de-scription. In my view, apparent motion is aparadigmatic case of an illusiond that has fertil-ized the understanding of motion processingand continues to do so. Given the roughly onehundred years of research on apparent motion,it is worthwhile to take stock (briefly) and seewhere investigations associated with thisparadigm have taken us.

Psychophysical investigations of apparentmotion are too numerous to review extensivelyhere. Early studies focused on describing thebasic features of the phenomenon. Korte’s laws(1915) are still part of textbook knowledge invision research; he described the influence ofdifferent stimulus characteristics (stimulusstrength, spatial and temporal separation etc.)on the quality of apparent-motion perception.New varieties of apparent motion were de-scribed in the following, one of the most im-portant ones being the motion quartet(Neuhaus 1930; von Schiller 1933; see video:http://www.open-mind.net/videomaterials/kohler-motion-quar-tet). This is a bistable version of apparent mo-tion, where two frames with diagonally oppos-ing dots at the corners of a virtual rectangle areflashed in alternation. The identical stimulus se-quence can be interpreted as being in vertical orhorizontal motion. During longer presentationsof the unchanging stimulus, conscious percep-tion will spontaneously switch between the pos-sible alternatives. It is therefore an importantexample of a multistable display, which allows

various interpretations with the same physicalinput. Early on, it was noticed that the integra-tion of motion inducers in the motion quartetprocessed within brain hemispheres is facilitatedrelative to integration between hemispheres(Gengerelli 1948), a fact we will come back tolater on. After a relative hiatus in the 50s and60s, apparent motion again took center stage inthe 70s. It was the basis for the work of PaulKolers (1972) on configuration effects and forthe first investigation of computational prin-ciples of motion perception by Shimon Ullman(1979). At the same time, distinctions betweendifferent types of apparent motion were intro-duced (Anstis 1980; Braddick 1974, 1980), laterculminating in the three-layered hierarchicalsystem of motion types proposed by Lu & Sper-ling (1995, 2001).

Currently, in all domains (psychophysical,computational, neurophysiological) there are on-going research endeavors cross-fertilizing eachother in the search for mechanisms underlyingillusory perception of motion. After the turn ofthe millennium, the broad availability of brain-imaging methods spurred the investigation ofthe neural mechanisms underlying apparent-mo-tion perception. By and large, the same areasthat process real motion are involved in the(Muckli et al. 2002; Sterzer et al. 2003; Sterzeret al. 2002; Sterzer & Kleinschmidt 2005), sup-porting the assumption that results from stud-ies on apparent motion can be transferred toother types of motion processing. Another inter-esting result from studies using functional mag-netic resonance imaging was that traces of thevirtual apparent-motion path, the illusory mo-tion between inducers, can already be seen inthe primary visual cortex, the earliest stage ofvisual cortical processing (Larsen et al. 2006;Muckli et al. 2005). This effect is probably me-diated through feedback connections fromhigher areas (Sterzer et al. 2006), explaining thefact that normal visual functioning is disturbedon the path of apparent motion (Yantis & Na-kama 1998) and also supporting Wertheimer’s(1912) original claim that apparent motion is aperceptual phenomenon that does not dependon cognitive inferences Animal studies are start-ing to elucidate the more fine-grained neural


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mechanisms subserving apparent-motion pro-cessing. Neurophysiological investigations in theanimal model demonstrated complex wave pat-terns of interactions between several corticalareas during the perception of apparent motion(Ahmed et al. 2008). This work also inspired aformal model of these interactions elucidatingthe computational principles underlying therepresentation of apparent motion in the brain(Deco & Roland 2010).

In my own recent research, I have specific-ally looked at interindividual differences in theperception of apparent motion and its anatom-ical basis. As mentioned above, for the bistablemotion quartet there is a difference betweenperceiving apparent motion in the vertical andhorizontal direction. Observers show a bias to-wards perceiving vertical motion when they fix-ate on the middle of the motion quartet(Chaudhuri & Glaser 1991). A possible explana-tion for this is that due to the way the visualfield is represented in the visual cortex, verticalmotion only requires integration within brainhemispheres, but horizontal motion depends onintegration between hemispheres. In fact, wecould demonstrate that the individual bias ofobservers of vertical motion could be partly pre-dicted by the quality of the neural connectionsbetween brain halves, suggesting that interhemi-spheric integration is a relevant factor (Genç etal. 2011).

The very short summary of research onapparent motion demonstrates the various in-sights this simple paradigm has inspired overthe course of the last century and beyond. It ledto a detailed description of the involved brainareas, including interindividual differences, andto processing models being developed on thecomputational and neurophysiological level. Asmentioned in the introductory section, one mainconcern in vision research associated with illu-sions is the interest in conscious perception andthe property of multistability. Both aspects arealso dominant in the apparent-motion field. Thecurrent state of research is just the startingpoint for investigations towards a deeper under-standing of the exact mechanisms. Often, theresults are still descriptive and qualitative innature and don’t allow for very specific predic-

tions with respect to the involved neural ma-chinery and dynamics. Yet the research line ispromising and has the potential to lead tobroadly applicable results. This might even bethe case for the underspecification problem, theproblem of reconstructing a full-fledged 3Dworld from a limited 2D input—one of Hecht’smain concerns. Multistability can be seen as oneparadigm case in which the nervous system hasto resolve ambiguity. For the Necker Cube, themotion quartet, and other multistable displays,the brain settles into a solution for a perceptualproblem by resolving competition among altern-atives. Therefore, research on multistabilitymight help to elucidate the core mechanismsthat give rise to the definitive subjective inter-pretations with which we represent the world.

4 Conclusion

In conclusion, Hecht’s distinction between illu-siond and illusionm and his criticism of the naïveillusion concept in vision research is interesting.When we become aware of illusions, when we sud-denly recognize the virtual character of our sub-jective world, certain metacognitive processes areinitiated that are a worthwhile subject matter forfurther investigation. In some sense they becomepart of the experience, and an important questionis whether and how the two aspects of the experi-ence interact. Nevertheless, Hecht also agrees thatperceptual representations are relatively immuneto top-down control, i.e., even in the rare cases inwhich the illusory character becomes manifest,the perceptual processes are mostly modular andimpenetrable in nature. Therefore, the question ofillusory representation can be tackled independ-ently of the question of metacognitive awareness,and continues to be an important guide for re-search on visual processing. Apart from looking atthe more conceptual question of the level atwhich the term “illusion” should be applied,which is moot to some degree, I have tried toprovide examples of relevant illusiond researchthat has made progress on the question of howthe brain processes visual information. Even forthe underspecification problem, there is opportun-ity for valuable insight, which hasn’t been ex-ploited to full potential yet in current research.



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Manifest IllusionsA Reply to Axel Kohler

Heiko Hecht

The notion of illusion as a discrepancy between physical stimulus and percept(here referred to as illusiond, as long as merely this “error” is meant) is unable tocapture the four very different cases in which illusions can arise. The observermay or may not be aware of the discrepancy, and its magnitude may be large orsmall. I argue that the special case of small error paired with awareness deservesspecial attention. Only in this case does the observer readily see the illusion,since it becomes manifest (referred to as illusionm). Illusionm is a meaningful cat-egory even in cases where illusiond cannot be determined. Illusionsm of apparentmotion and illusions of intuitive physics are solicited.

KeywordsApparent motion | Illusion | Illusionm | Intuitive physics | Manifest illusions | Rela-tional properties | Underspecification problem

Author


Commentator


Editors



1 The concept of illusion

Axel Kohler points out that illusions under-stood as discrepancy between physical stimulusand percept (illusiond) have inspired progress inthe history of experimental psychology. At firstglance, this seems to be rather obvious. How-ever, to define a discrepancy, one must have twocomparable measures of the same thing. Butthis is often not the case. Take a given lampthat looks very dim to us during the day butblindingly bright at night. How bright is thestimulus really? We are unable to determinewhich of the two cases is more illusoryd. Theperceiver does not normally notice the illusiond.Apparent motion, in contrast, which has been a

very influential paradigm, is more than mere il-lusiond. By differentiating illusions into illusiond

and illusionm, I am able to point out a strangeinconsistency between the amount of error con-tained in an illusion and the perceptual con-spicuity of this error. I argue that there are fourvarieties of discrepancy between physical stimu-lus and the related percept (illusiond). They canbe grouped by the size of the discrepancy andthe degree of awareness (see Figure 1). First,there are more or less subtle discrepancies thatare ubiquitous and go unnoticed most of thetime. In rare occasions, and usually triggered bya revealing piece of contradiction, they are no-

Hecht, H. (2015). Manifest Illusions - A Reply to Axel Kohler.In T. Metzinger & J. M. Windt (Eds). Open MIND: 18(R). Frankfurt am Main: MIND Group. doi: 10.15502/9783958570702 1 | 4






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ticed (illusionm). The second variety consists ofvery large discrepancies, such as found in manyintuitive physics examples. For instance, a watersurface may look fine even if it extends im-possibly at a large angle from the horizontal.For instance, when asked to draw the surfacelevel that water assumes in a tilted beaker, ob-servers err as if they did not know that waterremains parallel to the ground. And the moreexpert they become at avoiding spills, the largerthe error becomes. Experienced bartenders pro-duce the largest errors (see Hecht & Proffitt1995). The perception of relational propertiesdiscussed in the target article falls into this cat-egory. Here the perceptual error can be enorm-ous and still go unnoticed. Typically, we need toconsult physics books and learn about a phys-ical stimulus before we are convinced that ourperception is erroneous. When conceiving of il-lusion as mere illusiond, we fail to honor thespecial case of illusionm. Illusionsd are ubiquit-ous. As a matter of fact, the core discipline ofsensory psychology—psychophysics—can bethought of as the formal description of how aphysical stimulus differs from its percept. Itdoes so all the time. Illusionsm are a specialcase. They may warn the organism about whereadjustments to the perceptual system are neces-sary in order to avoid potentially dangerousmisjudgments. Or they may just be occasionswhere the perceptual system fails to suppressthe perceptual process that has lost out in thecompetition to resolve the underspecificationproblem.

2 Apparent motion (AM)

I thank Axel Kohler for bringing up AM (ap-parent motion) as an example of how seminalan illusion can be for research. I do concur thatit continues to be a fascinating phenomenon.However, I believe that AM did not fascinateWertheimer (1912) because it is an illusiond, butrather because it is predominantly an illusionm.Note that the timing has to be just so (i.e., aparticular combination of on-times and ISI,inter-stimuli-intervals) in order to perceive whathe called phi-motion: perfectly smooth motionpractically indistinguishable from real motion.

Most of his experiments and demonstrationshave in fact worked with suboptimal cases inwhich the perceived motion is bumpy or faint.In all these other cases of AM, the illusorynature of the percept becomes manifest. Thebistable quartet is another beautiful case of anillusionm. The mere fact that the percept canflip at will shows the illusionm to be manifest.

Figure 1: Varieties of illusions.

As an aside, the Gestalt laws can be un-derstood as an attempt to describe how the per-cept emerges from the given physical stimulus.But note that while the percept is always differ-ent from the physical stimulus, it should not bethought of as illusory just because it is the out-come of a Gestalt process. When I said thatGestalt psychologists have “avoided the term il-lusion” I was not expecting anyone to count theoccurrences of the term in Wertheimer’s 1912paper. He did use the term. I stand corrected.Note, however, that he put the term“Täuschung” in quotation marks the first timehe used it, well aware that the phenomenal ex-perience of motion is what makes the Gestalt,regardless of how it relates to the physical stim-ulus.

Another revealing aspect of AM is itspower to reveal the extent to which world-know-


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ledge is factored into our perception, uncon-sciously and the more so the less well-definedthe stimulus. Let us consider a classic AM-dis-play in which two rectangles at two locationsand at different orientations are shown in al-ternation. Whenever the ISI is short (say100ms), we see one rectangle moving on astraight path and changing its orientation con-currently. If, however, the ISI is lengthened (to,say, 500ms), then the AM-path curves (see Mc-Beath & Shepard 1989; Hecht & Proffitt 1991).The phenomenal quality of this motion is ratherephemeral. We immediately see that the motionis not distinct but fraught with uncertainty.When choosing intermediate ISI, and forcingobservers to make up their minds, some observ-ers will see the rectangle curve and others willsee it move along a straight path. And when thedisplay remains unchanged but the areabetween the rectangles is shaded, then the rect-angle appears to move along the shaded path.Thus, one can direct the motion of the rectanglealong almost arbitrary paths (e.g., Shepard &Zare 1983). Such demonstrations reveal that thevery notion of error or discrepancy betweenphysical stimulus and percept becomes shaky. Itseems rather arbitrary whether the researcherconsiders only the rectangles to be the relevantstimulus or also considers the background to bepart of the stimulus. In these AM displays, thevisual system appears to make sense of the en-tire display, not just the two moving rectangles.

3 The case for illusionm

Such resolution of the underspecification prob-lem can even annihilate an existing illusiond.Consider the sophisticated AM display we en-counter when going to the movies. And let ustake the old-fashioned kind, where the projec-tion screen is black most of the time, only inter-rupted 24 times a second by a very brief flash ofa stationary picture. Smooth motion is per-ceived. Here, the observer is typically unawareof the illusiond, but what is perceived is actuallycloser to the original scene than to the moviethat was made from it. We might even entertainthe idea that there is no illusiond, since the per-cept is very close to the original scene that was

filmed. Now, calling apparent motion illusoryd

when dealing with artificial or computer-gener-ated stimuli, but veridical when dealing with amovie, does not seem to make much sense. Thisis because, in a very deep sense, the visual sys-tem has no way of distinguishing between ac-tual motion and snapshot motion. The hard-ware we use to detect motion is built such thatit is unable to differentiate between the two.Basically, the detector for motion is designedsuch that successive excitations of the receptivefields of two motion-sensitive neurons lead tothe impression of motion. These Reichardt/Has-senstein detectors (Hassenstein & Reichardt1956) are discrete; they cannot tell the differ-ence between continuous and stroboscopic mo-tion (see e.g., Hecht 2006). Note that this holdsfor phi-motion but falls apart when ISI or dutycycle are changed.

Figure 2: Simultaneous color contrast: The orange andthe yellow squares are of the same respective color in thepanel on the left and on the right.

Let us now look at an example from thecolor domain to further challenge the notion ofillusiond. The phenomenon of color constancylets us perceive the same color even if the ambi-ent lighting changes dramatically. We see an ob-ject as blue regardless of whether the room is litby a neon light or by sunlight. It would notmake sense to call the percept of “blue” an illu-siond under neon light when the ambient light-ing is such that the object mainly reflects wavelengths of say 500 nm and to call it veridicalwhen it is lit by sunlight such that the domin-



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ant wavelength is 450 nm. In both cases, theobject appears blue. We cannot determine inprinciple which of the two cases deserves thename illusiond, if any, or if both deserve to becalled illusiond. In contrast, when the two casesare juxtaposed, an illusionm becomes manifest.In Figure 2, the center inner square surroundedby red on the left and the outer squares sur-rounded by yellow on the right are of anidentical color, as becomes manifest when oc-cluding the surrounds. Thus, illusionm becomesapparent, but illusiond cannot be defined in anymeaningful way.

4 Conclusion

In sum, the role of illusions in vision researchhas historically been very important. The begin-nings of experimental psychology have attemp-ted to measure illusionsd in terms of the discrep-ancy or error between physical stimulus andpercept. I have attempted to show that this er-ror is neither substantial enough to serve as adefinition of illusion, nor particularly fascinat-ing. Instead, illusionsd are as ubiquitous as theyare typically unnoticed or indeterminate. Incontrast, the cases that engage our imaginationusually are manifest illusionsm. The latter can bedefined even in cases where it is not meaningfulto speak of illusiond.

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Beyond Illusions - — Open MIND

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