1 Illusion?
1.1 The underspecification problem (UP)
Visual perception can be seen as the process by which the visual system interprets the sensory core data that come in through the retinae of the eyes (see e.g., Hatfield & Epstein 1979). The sensory core is not sufficient to specify the percept; that is, there is an explanatory gap between the information present at the retina—which is in essence two-dimensional (2D)—and the information present in the three-dimensional (3D) objects that we see. Let us call the problem that arises in having to fill this gap the “underspecification problem” (see Hecht 2000). Figure 1 illustrates the UP (underspecification problem). A given object can only project one particular image onto the projection surface (retina); however, a given projection could have been caused by an indefinite number of objects in the world. Because of this anisotropy in the mapping between the 3D object and its 2D projection, information is lost during the projective process, which cannot be regained with certainty. One could argue that the history of perception theories is more or less the history of finding solutions to reconstruct the 3D object that has caused a given projection.
Figure 1: Underspecification: The 3D origin of a given image on the retina (here approximated by the vertical projection screen) is provided by an indefinite number of objects at various orientations in space. Illustration from Gibson (1979).
In order to assess the quality of the solution offered by a given perceptual theory, we have to evaluate how it describes the gap between sensory core and percept and the mechanism by which it suggests that the gap is being bridged. The Gibsonian theory of direct perception aside—which denies the problem altogether (e.g., Gibson 1979)—we have a variety of theories to choose from. They are all constructionist in the sense that the sensory data have to be interpreted and arranged into the configuration that is most likely or most logical. The theories differ in the mechanisms they make responsible for the reconstructive process. For instance, Hermann von Helmholtz (1894) supposes inferences of unconscious nature that arrive inductively or maybe abductively at a preferred solution. Roger Shepard (1994), on the other hand supposes a recurrence to phylogenetically-acquired knowledge. He takes the regularities of the physical world or of geometry to have been internalized through the course of evolution and to be used to disambiguate competing solutions. An example of such internalized knowledge is the fact that light usually comes from above (see Figure 2). A shading gradient from light (at the top of an object) to dark (at its bottom) would thus be compatible with a convex but not with a concave object.
Figure 2: Solution of the underspecification by drawing on internalized knowledge that light comes from above. The sphere in the right panel looks convex because it is lighter at the top, whereas the same image rotated by 180° (left panel) looks concave. Have we created an illusion by juxtaposing them?
Others have proposed that the system considers statistical probabilities by defaulting to contextually appropriate, high-frequency responses (Reason 1992) or by applying the Bayes-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 exact nature of how the construction is accomplished. Note, however, that all the solutions that have been proposed abound with cognitive ingredients. The process of constructing a 3D object from the 2D retinal input is usually thought to draw on memory and on some sort of inferencing, albeit unconsciously. The next step to arriving at meaningful percepts on the basis of the 3D object—which is just as essential in perception—involves even more cognitive elements, be they unconscious or amenable to consciousness.
Here I would like to include a brief aside, which may seem obvious to the psychologist but not so obvious to the philosopher. Perceiving cannot be dissected successfully into a sensational part and a judgmental part when we are dealing with the everyday perception of meaningful objects. Perceiving is always judgmental when we see a stick or a bird, or when it comes to seeing that we can pick up the stick and that it falls down when we release it. In other words, pure sensations may be possible introspectively—sensing red, sensing heat etc.—but they are no longer possible in everyday object perception, that is a separation of sensation and judgment is not ecologically valid. Take, for instance, the falling object as given in phenomenal perception. In the sub-field of experimental psychology called “intuitive physics”, investigators have doctored physical events to contradict Newtonian physics and presented visual animations to novice or expert observers. Many of the latter do not see anything wrong with objects falling straight down when released, as opposed to following the proper parabola that they should (see section 1.3.1. on so-called cognitive illusions). This perception is reflected in motor action—people release the object in the wrong place when trying to hit a container; this perception arises in toddlers unable to reflect upon the event, and it persists after formal physics training in cases where observers have to make quick decisions. Thus, a separation into a sensation and perceptual judgment is not meaningful here. Perception of (everyday) objects and events necessarily includes a judgmental aspect, which may or may not enter consciousness.
Now, we are concerned with the question of whether the errors that arise during the perceptual process can be used to gauge where the visual system fails to capture the 3D world. We will argue that this is not the case. Research focusing on so-called optical illusions is particularly ill-suited to gain insight into how the visual system solves the UP. Illusions typically arise when errors are rather small, thus the presence or magnitude of an illusion is no predictor of the size of the UP. By and large, perceptual error is rather small when it comes to simple object properties, such as size, distance, direction of motion, etc. Errors become much larger, more interesting, and potentially dangerous when it comes to relational properties, such as seeing if an object can be lifted or if I will slip and fall when treading on a given surface. The case studies below will show that in the context of relational properties we make errors but we do not experience illusions.
1.2 The Luther illusion
Please take a close look at this painting of Martin Luther. You have certainly seen pictures of the great protestant reformer before. Does anything about this painting strike you as strange?
Figure 3: Martin Luther as painted by Lukas Cranach the Elder (1529), Hessisches Landesmuseum Darmstadt.
You may have found that he looks well nourished, as is appropriate for a monk whose enjoyment of worldly pleasures is well documented. However, I am sure you did not notice the illusion. Well, I have photoshopped the photograph and made it 15% wider than it should be. There is a discrepancy between the painting (or veridical photograph thereof) and the picture presented in Figure 3. Such discrepancies are typically considered to be the essence of illusion. For instance, Martinez-Conde & Macknik (2010, p. 4) define an illusion as “the dissociation between the physical reality and the subjective perception of an object or event”. The physical reality of the picture is distorted by 15%, but your perception was that of a correct rendition of a famous painting. Now let us add another twist to the Luther illusion (Figure 4).
Figure 4: Martin Luther right side up and upside down.
Have I taken the original photograph or have I turned around the 15% wider version? Surely, Luther looks to be slimmer in the panel on the right. If you turn the page upside down, you will see that both panels show the same picture that is 15% wider than the original. Let us assume that the inversion effect—also named fat-face-thin-illusion by Peter Thompson (Thompson & Wilson 2012)—is exactly 15 % in magnitude. Has the illusion that I introduced initially been nullified by the inversion?
The fictitious Luther illusion is meant to make the point that the mere discrepancy between physical reality and a percept should not be conceived of as illusory. It may not even be reasonable to conceive of it as an error. The stretched image may be a better representation of what we know about Luther than the "correct" picture. For instance, the picture may typically be viewed from an inappropriate vantage point that could make the stretched version more veridical even when compared to the actual Luther, were he teleported into our time. Take Figure 5. I have stretched Luther by another 50%. Now he seems a bit distorted, but not to an extent that would prevent us from recognizing him or from enjoying the picture. There is a fundamental property that needs to be added for something to be considered an illusion. I contend that this is a dual simultaneous percept that tells us that what we see is so and not so at the same time (for a detailed defence of this position see Hecht 2013). For an illusion[1] to be called thus, it has to be manifest immediately and perceptually. Calling something an illusion is only meaningful if it refers to a discrepancy that we can see. It is not meaningful if it refers to some error that we have to infer.
Figure 5: Martin Luther stretched by another 50%.
Take for instance the often-cited stick in the water that looks bent. The static image presented in Figure 6 is not an illusion. We see a bent stick; note that its shadow is bent as well, and without recourse to our experience of refraction that occurs where two media adjoin, we would not know if the stick were actually bent or if some effect of optics had created the percept. However, the moment we move the stick up and down we see the illusionm. We see the stick being bent and being straight at the same time. The illusion becomes manifest. That is, the discrepancy if not contradiction between the two percepts (here the straight and the bent stick) is available in our working memory, we become aware of it, often without being able to resolve which of the two discrepant percepts is closer to reality. In the case of the stick, the location of the bending at water level reveals that the stick is really straight; however, in most cases the illusionm remains unresolved, as for example 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 Figure 7 an illusionm, even if a researcher could show with a large dataset that the inner circle is reproduced 2% bigger than it was on the picture. However, as soon as we allow for a direct comparison and put a ruler to the center circles in Figure 8, the illusionm arises (see Wundt 1898; an interactive demonstration of the Ebbinghaus illusion can be found at http://michaelbach.de/ot/cog-Ebbinghaus/index-de.html).
Figure 7: Is the circle in the middle perceived to be bigger than it really is? Possibly an illusiond.
Figure 8: Is the circle surrounded by smaller circles perceived to be bigger than it really is, or is the center circle on the right perceived to be too small? This is the famous Titchener illusionm that was invented by Hermann Ebbinghaus and first reported by Wilhelm Wundt (1898).
Illusionsm are perceptually immediate but they appear to require some form of comparison and judgment, which supports the argument that phenomenal perception cannot be divided into a merely sensational core and a cognitive elaboration. For instance, in the case of a Necker cube or a bi-stable apparent motion quartet, the illusionm can become manifest by a mere deliberate shift of attention.
Given the severity of the UP, we should not be fascinated by the existence of error (illusionsd), but should instead be fascinated by the fact that our perceptions are pretty much on target most of the time. It is truly amazing that among the enormous range of possible interpretations of the retinal image, we usually pick the appropriate one. Illusionsm are rare special cases of ubiquitous small errors that become manifest because of some coincidence or another. Note that this assessment does not only apply to visual perception but also to other sensory modalities in which sensory information has to be interpreted and integrated. For instance, the cutaneous rabbit illusionm arises when adjacent locations on the skin of our arm are stimulated in sequence. We experience one coherent motion (a rabbit moving along our arm) rather than a sequence of unrelated taps. This "inference" can be explained by probabilistic reasoning (Goldreich 2007) and may be considered the tactile analogue of apparent motion: just as we cannot perceptually distinguish a sequence of static stimuli from real motion in the movie theater. As a matter of fact, the pauses between the intermittent frames of the movie are indispensable for motion pictures to look smooth and continuous.
Gestalt psychologists have described the constructive process by which meaningful objects emerge from the various elements in our sensory core (see e.g., Max Wertheimer 1912 for the case of apparent motion). For good reason, they have avoided the term illusion, and introduced the term emergent property for the phenomenal result of the (unconscious) process of perceptual organization. It would violate our everyday experience to call something we see an illusion just because we know a little bit about the underlying physics. Just because we know that our continuous motion percept is derived from a sequence of discrete images, this does not make the percept an illusion (neither illusionm nor llusiond).[2] By the same token, knowing that light is a wave (or a stream of photons) does not make objects in the world illusory. In fact, a discrepancy between what is really there and what we perceive is the norm, not the exception. Given my conceptual distinction, I will show how the perceptual system deals with the ubiquitous discrepancy, with the normal case of illusiond. The relatively rare cases illusionsm arise a by-product of this process. For something to deserve the name illusion, this discrepancy has to become manifest. The Ebbinghaus illusion only turns into an illusionm when we perceive a conflict, when the inner circles are seen (or inferred) to be equal in size and they look different in size at the same time. Thus, it is not the ubiquitous presence of error that makes an illusionm but the rather unusual case where this error is unmasked by a perceptual comparison process.
1.3.1 A note on so-called cognitive illusionsd
In our everyday perception, once we consider that objects are often in motion and carry meaning at the perceptual level (see Gibson’s concept of affordance, e.g., 1979) the UP is exacerbated but not changed. I argue that the nature of perceptual error is akin to cognitive error when it comes to the more complex and meaning-laden percepts of everyday perception, as opposed to line drawings that are typically referred to in the context of illusionsm. Just as with perceptual errors, cognitive errors often do not become manifest. However, if they do become manifest, they can typically be corrected with much greater ease than can perceptual illusionsm, which may well be the distinguishing feature between perceptual and cognitive error. Cognitive errors become noticeable more indirectly by recurring to a short-term memory of a dissenting fact or by reasoning—which is often faulty by itself. The literature about cognitive error is enormous. To give one classical example, we have trouble with simple syllogistic reasoning, in particular if negations are used. Wason’s famous selection task (Wason & Johnson-Laird 1972) shows how limited our abilities are (Figure 9). Imagine you have four envelopes in front of you. You are to test the statement "if there is sender information on the back side then there is a stamp on the front". Which of the 4 envelopes do you have to turn over? Do not turn over any envelope unnecessarily.
Figure 9: Which envelopes do you have to turn to test the statement “If there is sender information on the back side then there is a stamp on the front”?
Well—it is easy to see that envelope 1 has to be turned (modus ponens), but then it gets harder. Many observers think that envelope 2 needs to be turned. However, this is not the case. Only 4 has to be turned in addition to 1. A sender on its back would violate the rule (modus tollens). The majority of college students fail to solve this problem, but as soon as the context is changed, all mistakes can be eliminated. In the context of screening for drinking underage, all observers perform accurately (see Figure 10). Here again 1 and 4 need to be "turned over". Only by thinking the problem through or by noticing that the problem structure is identical to the envelope scenario and the wine drinking scenario does the error become manifest. We may or may not want to call it a cognitive illusion. This term is not widely used for such mistakes or fallacies, with the exception of Gerd Gigerenzer and his research group (see e.g., Hertwig & Ortmann 2005). However, even if we call these mistakes cognitive illusions, they are different in nature from perceptual illusionsm (which typically contain a judgmental aspect). We do not readily notice cognitive illusions. Although the distinction between perception and cognition has outlived itself (and cannot me made with clarity to begin with, see above), for practical convenience, I will continue to use the terms to emphasize cases where deliberate thought processes enter the equation. We happily live with many a fallacy without ever noticing. Millions went through their lives believing in impetus theory and seeing the sun circle around the earth, let alone holding seemingly absurd beliefs about the shape of our planet.
Figure 10: Whom do you have to query about age or beverage type to test if “Only adults have alcoholic beverages in their glass”? It is obvious that the juice drinker and the elderly person need not be queried.
Errors only turn into illusionsm when we become aware of them and at the same time cannot correct the error (easily). Just try to see the earth rotate rather than see the sun rise. It is impossible. We continue to see the sun rise above a stable horizon, never the other way around. And we continue to misjudge implication rules or widen the grasp of our fingers a tad more when reaching for an Ebbinghaus stimulus even if we know about the illusion (see Franz et al. 2000). Other errors can only be spotted when large data samples are collected and analyzed statistically. For instance, to expert golfers, the putting hole on the green looks larger than it does to novices (Witt et al. 2008; Proffitt & Linkenauger 2013). They will never become aware of this fact, although the fine-grained scaling of perception as function of skill might be functional during skill acquisition. Spectacular as they may be, such errors of which we are unaware should not be called illusionsm because almost all our perceptions and cognitions contain some degree of error. We may believe that a rolling ball comes to a stop because it has used up its impetus, or we may hold that we should aim where we want a moving ball to go rather than using the appropriate vector addition to determine where to aim. As long as our action results do not force us to reconsider, our convictions will remain unchanged. One could say that we have a model of the world, or its workings, that suffices for our purposes.
Figure 11: Technical illustration explaining the trajectory of a cannon projectile by Daniel Santbech (1561): Problematum Astronomicorum, Basel.
Why are so many researchers willing to call a small manifest discrepancy between two percepts of the same object an illusion, while gross deviations of perception or conception from physical reality are not deemed to deserve the same name? Take the straight-down belief (not illusion). Many observers take an object that is being released from a moving carrier to fall straight down rather than in a parabola (McCloskey et al. 1983). Figure 11 illustrates this belief as it was state-of-the-art physics knowledge from Aristotle through the Middle Ages. It persists today in cognition and perception. Even when impossible events of straight down trajectories are shown in animated movies, to some observers they look better than do the correct parabolas (Kaiser et al. 1992).
Note that there was a discussion at the time whether or not the transition from the upward impetus to the downward impetus was immediate or if a third circular impetus inserted itself, such that there were be two trajectory changes. The intermediary could only be thought of as linear or as a circular arc—anything else would have been too far from divine perfection. Presumably, the more principled physicists before Galileo favored the simple transition. Others, such as Aristotle himself, presumably preferred the interstition of the circular arc, as it would reconcile trajectory observation with the physics of the time. The pre-Newtonian thinking about projectile motion nicely illustrates that we see the world as in accord with our actions. To the medieval cannoneer, what he saw and understood about projectiles was sufficiently accurate, given the variance introduced by the inconsistent quality of the gunpowder and the fluctuation in the weight of cannon balls at the time.
Thus, we have argued that visual illusionsm, just as cognitive illusionsm, have to become manifest to be called such. They are a special and rare case in which the discrepancy between a percept and what an ideal observer should have seen instead is noticed. Normally this discrepancy goes unnoticed. We will now take a look at why it goes unnoticed and argue that an illusiond will only alter perception if it interferes seriously with our action requirements. As the latter vary among people, illusionsd can be private and may be very far from the truth—as, for instance, in the context of projectile motion (see Hecht & Bertamini 2000). The private aspect of perception is to be taken as unconscious in the sense of Helmholtz. For instance, we do not only think that a baseball thrown toward a catcher will accelerate after it has left the thrower’s hand (which may even be incompatible with impetus theory), but doctored visual scenes in which the ball does accelerate are judged as perfectly natural looking. This amounts to the perceptual analogue of what Herbert Simon (1990) has called satisficing in the domain of reasoning and intuitive judgment. The visual system searches until it has found a solution that is satisfactory, regardless of how far away it is from a veridical representation of the world.
To conclude this section, we believe that perception of objects, be it the stick in the water or a falling brick, is a solution to the underspecification problem. Perception is always fraught with error in the sense of a discrepancy between the percept and the underlying physics. This error only becomes manifest when a simple perceptual judgment or comparison reveals a contradiction. In all other cases the error goes unnoticed. Two such cases will now be described at length to make the point that perceptual illusiond is the rule rather than the exception.