illusions

We see far more than meets the eyes, though not always correctly, for we experience various phenomena of illusion — departures from physical reality. Although they are errors, illusions are useful evidence of how eyes and brains normally work.

But ‘illusion’ is hard to define adequately. If illusions are departures from reality, what is reality? This is difficult to answer, for we have many descriptions of reality, in science, in art, and so on. No doubt all are incomplete and perhaps largely wrong. Certainly physics frequently changes its mind. If we take the account offered by modern physics of matter as invisible atoms in violent motion, with weird effects of quantum mechanics, this is so different from how things appear that we might be tempted to say all perception is illusion! But this is not more helpful than to say that all perceptions are dreams.

We are pushed into thinking that illusions must be departures from quite simple-minded physics, as measured with rulers, protractors, and clocks. Illusions include distortions of length, angles, and time. There are also perceptual experiences that one might call ‘ghostly fictions’ (Table 1(d) ). Some figures or objects appear impossible (Table 1(c) ). Others seem to flip from one perception to another, though there is no change of the image at the eyes (Table 1(a) ). These are weird and wonderful phenomena, which are central to art, but are hazards to the physical sciences, and can be dangerous in everyday living. They are well worth explaining.

Explaining illusions

It seems useful to try to classify phenomena of illusions, as classifications are important for all science. Chemistry and biology were transformed by the Periodic Table of the Elements, and by names for species and varieties. How shall we start for illusions? It is suggestive that illusions of seeing correspond with errors of language. Appearances of illusions fall into classes which may be named quite naturally from kinds of errors of language — ambiguities, distortions, paradoxes, and fictions.

It is intriguing that these apply both to vision and to language, for it is more than possible that language grew from pre-human classifications of objects and actions over millions of years. If the evolution of language were parasitic on these perceptual mechanisms, it might explain how language developed so rapidly for humans. It is a tricky question how much extra brain was needed for language, and how much language makes a brain more effective. This is rather like using any tool, such as an electric drill or a computer. One needs the skill to use it; but then the tool adds a lot of extra skill. Tools increase intelligence. Indeed our language, and tools of technology, are large parts of our intelligence, though we are never infallible.

Let us compare errors of language with kinds of illusions:

There seem to be four principal causes of illusions. The first is optical disturbance between objects and the eyes. The second is the physiological disturbance of signals in the ‘peripheral’ machinery of vision (in the retina and early areas of the visual cortex). The third and the fourth are extremely different — for they are cognitive. This is like mistakes of interpreting plainly visible words. This can happen by confusions of meanings (semantics), or by misapplied rules of grammar (syntactics). There are similar kinds of cognitive errors in vision and other perception, because perception is based on knowledge of the world and it works by applying general rules. Either kind of cognitive mistake can mislead, by not being appropriate to the situation. The same kinds of cognitive illusions can occur in computer vision.

Classes	Physical causes	Cognitive causes
	Optics	Physiology	Rules	Knowledge
Ambiguities	Looking	Pure yellow	Figure-ground	Hollow face
	through mist	versus	reversals
		red + green
Distortions	Mirages	Café wall	Perspective	Size-weight
		illusion	illusions	illusion
Paradoxes	Looking glass	Rotating spiral	Impossible	Magritte's
		after-effect	objects	painting of the
				mirror
Fictions	Rainbow	After-images	Ghostly shapes	Faces-in-the-fire

Here is one example of each kind:

These are examples of false perceptions of different origin. In a looking glass, one sees onself through it, yet knows one is in front of it — doubled, yet one person! Pure, monchromatic yellow light cannot be distinguished from a mixture of red and green light because they cause the same activation of the three types of colour-sensitive cones in the retina. The café wall illusion looks like a chess board, but with alternate rows displaced sideways by half a square: the horizontal rows of squares appear like long wedges, converging towards one side or the other. If you stare at a rotating spiral it appears either to shrink or expand, depending on which way it is rotating. If you then look away, whatever you are now looking at appears to do the opposite — to expand or to shrink — an example of an after-effect that is probably due to ‘fatigue’ of neurons in the visual cortex. After-images are ghost-like blobs that move with each eye movement, resulting from over-stimulation of one region of the retina. The most familiar after-images are the dark blobs that persist after looking at a light bulb or a camera flashlight. But after-images (of complementary colour and brightness) can be caused by staring intently at any pattern of high contrast. What is ‘figure’ (or object) and what is ‘ground’ (the background between objects) is the most basic perceptual decision. In ambiguous situations (such as the famous Rubin picture, with two silhouette profiles of faces, staring at each other, creating a vase shape between them) perception can flip from one interpretation to the other (from faces to vase). Perspective illusions are distortions produced by converging lines, which signal depth (even when depth is not perceived), e.g. the Ponzo illusion in Table 1. ‘Ghostly shapes’ are perceptual interpretations that go beyond the immediate information in the retinal image, as in the Kanizsa figure in Table 1. Impossible objects are representations that are not compatible with sensible ‘perceptual hypotheses’, such as the Penrose impossible triangle, or the Tri-bar in Table 1. The inside of a mask (a hollow face) appears as a normal face, with the nose sticking out, presumably because the improbable interpretation of a true hollow face is rejected. Small objects feel heavier than large objects of the same weight — because large objects are expected to be heavier. The Magritte painting shows a back view of a man looking into a mirror — but paradoxically we see the back of his head in the mirror. Faces-in-the-fire are fictional perceptual interpretations seen fleetingly in the flames of a fire.

— Richard Gregory

Bibliography

• Gombrich, E. (1960). Art and illusion. Phaidon, London.
• Gregory, R. L. (1997). Eye and brain, (5th edn). Oxford University Press.
• Robinson, J. O. (1972). The psychology of visual illusions. Hutchinson, London

See also perception; vision.

1. What are illusions?
2. Phenomenal phenomena
3. Illusions and behaviour
4. Illusions in science and art
5. Explaining illusions
6. Some principles, with examples

1. What are illusions?

Illusions are discrepancies from truths. All kinds of perceptions are subject to illusions; but generally they pass unnoticed, except when there are marked internal inconsistencies, or clear departures from what is believed to be true. As beliefs largely determine what is accepted as true, so beliefs can dismiss or affirm appearances as illusory. A ghost-hunter may accept an appearance, such as an after-image, as truly a ghost which a sceptic would reject as illusory. Believers in UFOs have seen lampshades reflected in windowpanes as flying saucers. But here we will not simply reject illusions, for many kinds will be accepted as significant phenomena of mind. Not natural phenomena of physics, but phenomenal phenomena of physiology and cognitive processes of the brain.

Although they are often called 'optical illusions' most are physiologically or psychologically caused. Optical phenomena can produce weird and wonderful visual effects — distortions of fairground mirrors, changes of size or distance with telescopes, repeated patterns with a kaleidoscope — but are these illusions? Is a rainbow an illusion? This is a phenomenon of optics, studied and explained with concepts of optics. Isn't it an illusion, only when not understood, so evoking misleading expectations? Rainbows mislead when one thinks it possible to walk under the heavenly arch, as though it were made of stone or brick, though the rainbow recedes and is always beyond touch. This is a conceptual error, perhaps best called 'delusion'. Illusions of perceptions and delusions of conceptions are linked in complex ways not fully understood.

The sun is seen as sinking to the horizon at dusk, yet we know this is due to the earth rotating under our feet. This takes us to the notion that neural signals from the eyes and other senses must be interpreted, or 'read' by the brain for meaning. There is nothing odd with the optical images in our eyes, or with the neural signals to the brain, when we see the sun setting; but they are misread. They are misread visually, even when conceptually we know what is going on. Conceptual understanding seldom destroys perceptual illusions. Perceptions and conceptions are remarkably separate in the brain, and so we continue to experience illusions though they are recognized as such, and even explained. As illusions are such robust phenomena they are easy to investigate, for they do not disappear before our eyes when we start to understand them. But 'seeing is believing' should be taken with a large pinch of salt.

All the senses can suffer illusion, but as most research has been done on vision its illusions are most fully understood, though many have controversial explanations, or even none. Here we shall make our best guess at explaining various phenomena of illusions, and attempt to classify them by kinds and causes. As we have said: some have physical optical causes (such as mirages), some are physiological (such as after-images), others are cognitive (such as the moon appearing huge when low on the horizon — see moon illusion). It seems important to put these strange phenomena into categories, because their significance, as surely for all phenomena of science, depends on explanations. Here there is something of a paradox: phenomena suggest explanations — yet explanations give meaning to phenomena. So science is ping-pong played with phenomena and explanations. As a general principle, phenomena cannot speak for themselves. Explanations are essential for giving phenomena significance, and with changes of understanding a phenomenon may appear very different. Thus, as thunder moved from theological accounts of wrath of the gods, to moving charges in physics, its meaning and implications were transformed. One might say that this to-and-fro between phenomena and explanations is the game of science, applying to illusions as to any other phenomena.

Illusions are explained by various sciences with a variety of concepts, but artists are intuitive experts, in some ways knowing more of illusions than does science. Science and art have met for centuries in technologies of painting and architecture. Now cinema and television depend on fooling eyes and brains with processes of illusion — especially the Phi phenomenon of continuous movement seen from displaced pictures switched in sequence — giving realistic smoothly moving objects from flat intermittent shadows. In painting, cinema, and television, processes of illusion are used to produce surrogate realities, and evoke wonderful fictions. Illusions of the various senses have important parts to play in music, in cooking, and of course for conjuring. They enrich life.

It is sometimes said that illusions occur only in laboratory or other artificial conditions, but this is far from true. Illusions of all the senses are frequent in normal conditions, and may be dramatic even with familiar objects in full lighting. The mast of a sailing boat looks far longer when vertical than when lying horizontal on the ground. Light regions look larger than darker areas, which can affect women's choice of dress. (Hence perhaps the popularity of the 'little black number'.) Illusions are used by gardeners and architects to improve proportions, and make properties look more spacious. Illusions occurring in everyday situations can be disastrous, as in playing golf or driving a car, or flying, and illusions can fool scientists into serious errors. Illusions deserve to be studied and understood for very practical reasons, as well as for their philosophical significance.

Although illusions are prevalent in normal conditions, admittedly the best known are seen in pictures, in children's books, and psychology texts. It is important to compare pictures — which are very special objects for vision — with normal objects we can interact with. Experiments on vision and illusion should not be limited to computer screens! Pictures would make little or no sense without years of experience of interacting with objects. Seeing what the patterns of pictures represent depends on knowledge from primary experience with touchable, tastable objects, including emotional ties with people, for appreciating portraits. Yet, curiously, the brain's perceptual knowledge is not the same as, and does not always agree with, its conceptual understanding.

2. Phenomenal phenomena

For the physical sciences illusions are nothing much more than threats to be avoided; but these out-of-this-world phenomena are important for suggesting and testing theories of how we perceive things. That there are illusions shows that at least some perceptions are not tied to the object world, as they float free of physical reality. Does the fact that some perceptions take off from object reality indicate that all perceptions are essentially separate from the physical world? This is a central question for theories of perception.

The Greeks generally thought of vision as intimately associated with objects; but with the discovery of intervening retinal images, and neural channels with long chains of synapses, some sort of indirect relation became far more plausible. Perhaps curiously, 'direct' theories are not wholly abandoned today by some philosophers and psychologists, though these accounts do seem hard to defend against what we know of physiology and cognitive processing. Illusions are embarrassing and generally ignored by 'direct pick-up' theorists. The view taken here is that perceptions are indirectly related to the object world: they are predictive, based on neural signals from the senses, and depending on knowledge derived from the past, to make sense of present signals (Gregory 1968, 1980). As accepted knowledge may be wrong, or not appropriate to the present, there is a great wealth of cognitive illusions due to signals from the senses being misread. These are cognitive rather than physiological, but are genuine phenomena, that can be studied to illuminate principles of brain and mind.

3. Illusions and behaviour

Illusions affect behaviour, yet behaviour does not always correspond to the illusion experienced. With other evidence, this has suggested there are two kinds of perception: full-blown experience of the present surroundings, essentially for planning behaviour; and an ancient far simpler system giving rapid behaviour with minimal cognitive processing, for simple actions but without consciousness. It is suggested that these have different brain pathways (dorsal and ventral), though how separate these are functionally is at present controversial (Milner and Goodale 1995). Cognitive illusions can be used to investigate this notion, and see how the pathways are functionally separate. Only the ventral system should be affected by cognitive illusions — rapid touch should not be affected by the visual illusion. Present evidence is somewhat conflicting. Only some experiments find that touch is not affected by the Titchener illusion (Fig. 5), but this may be because rapid snatch movement is difficult here. As dramatic reversal of cognitive space is given by the Hollow Face illusion (Fig. 9), we may ask: is fast touch not reversed (to agree with appearance) when the hollow mask is seen as convex? This seems to be true, as the two streams notion would predict.

Illusions of behaviour can of course be measured objectively. Illusions of subjective experience can be measured, though with more difficulty, with so-called 'psycho-physics', by comparing illusory with non-illusory perceptions. The choice of these is not always easy, because to establish an illusion we must have some reference truth; but what should be accepted as truths for comparisons? Sometimes this may seem obvious, but what for example of colours? What is an illusory colour is particularly hard to say, because we may not be able to specify any non-illusory colour for comparison.

Although such deep questions are usually avoided or ignored, there is the ever-present question of how far any perceptual experiences match physical realities. The philosopher John Locke (1632–1704) drew an interesting analogy with language (in 1690). Locke asked whether sensations (such as white or red, loud or soft) are at all like physical properties of objects and events, or rather whether they stand for very different physical characteristics, much as words stand for things that are very different from their shapes and sounds. For example, the word CAT is very different in form from the animal, yet it stands for the physically very different living pet, and calls it to mind. The physical blue of the sky is undoubtedly different from the sensation of blue, yet the experience stands for the very different physical reality, and serves us much like the word 'blue', which is totally unlike the sky or its colour, but brings it to mind.

Locke realized that neither objects nor light are coloured. Colours are created in the brain, as we now know, from various wavelengths of the electromagnetic spectrum activating 'cone' receptor cells in the retina. Locke appreciated that without eyes and suitable brains, there would be no colours in the universe.

4. Illusions in science and art

We generally see objects as very different from how science describes them — with invisible electrons and so on — so are all perceptions illusory? There is no point in saying this any more than 'everything is a dream', as such words lose meaning when there are no accepted contrasting reference 'truths'. This makes defining 'illusion' difficult, as what is accepted as illusory changes with accepted non-illusory references. These could hardly be from fundamental physics, even though we accept physics as providing the deepest truths, because its accounts are so different from how things appear that using them as reference would make all perceptions illusory.

We might say that the references we accept for non-illusions are from simple commonsense 'kitchen' physics. We check for illusion with simple measures, with kitchen-type instruments, such as rulers and scales, thermometers, and clocks. This is very different from taking fundamental physics as reference truths for perceptions. Paradoxically, we cannot use our deepest beliefs as hallmarks for true perceptions.

Illusions are important for artists who, with great skill, make use of many kinds. Should we call all pictures illusions? Pictures seldom look just the same as the scene they represent, but if they do not mislead there seems little point calling them illusory. Again, like words, they stand for reality, which is good enough for 'truth' when they are not seriously misleading.

Pictures can, however, very easily upset the visual system to produce a wealth of phenomenal phenomena: jazzing instability, systematic distortions, even impossible or paradoxical objects, as well as fictions. Representational pictures are curious objects that stand for other objects or abstractions though not by exact copying.

5. Explaining illusions

So many processes contribute to perception, it is often difficult to know which is responsible for an error or illusion, and no doubt there are more processes going on we know nothing about. Some illusions, such as the bright or dark after-images that hover around after one looks at a bright light, are clearly due to physiological adaptations of receptors in the retina.

But illusions can be caused not by systems misbehaving, but very differently, by normal functioning being inappropriate to the situation. This distinction implies that there is more to life than physiological functions; it matters what they are doing in particular circumstances. For example, the brain effectively scales up retinal images optically shrunk by object distance (as in a camera) giving 'size constancy', but this scaling may not be appropriate. Then a distortion of size or shape occurs though the physiology is working normally.

There is a danger of postulating special mechanisms, or processes, when none is needed. It is well known that the images in the eyes are optically reversed — upside down and switched left–right — yet the world looks upright, and visual right and left agree with touch. It is generally accepted that this does not need a special compensating mechanism because retinal images are not seen, as objects are seen — or they would need another eye to see them — with another picture in the brain, a regress, going on forever without getting anywhere. A compensating mechanism is not needed as they are not objects of perception but rather one stage of processing lying between objects and vision. But is this all there is to it? When the head is tilted, the world remains upright. This extends to standing on one's head, when the retinal image is reversed and yet up and down remain normal. Does head-tilt need a compensating mechanism, or does perception ignore the tilt of the head, as the brain knows it is irrelevant? Perhaps we don't really know whether there is a special mechanism here, but dizziness, and various kinds of instability, suggest there is. Nature does not always adopt neat solutions, such as simply ignoring tilts of the head, or the blind regions of the eyes. We need experiments to settle such issues and there can be surprising answers.

It was shown at the end of the 19th century, by G. M. Stratton, that after days of wearing inverting goggles the world comes to look more or less normally upright. Yet just how normal it becomes — and whether this is behavioural rather than perceptual learning — remains unclear. Another example of doubt over the need for a special mechanism is Emmert's Law — after-images appearing larger when seen as more distant — because though this seems so simple it is not fully understood.

Physiologists and psychologists often disagree when trying to explain illusions. For example, physiologists have generally explained the well-known Müller-Lyer distortion illusion (Fig. 10b) as due to neural signalling in the eyes being upset, as through 'lateral inhibition', by the angles of the 'arrowheads'. But, as already hinted, very different explanations lie in the domain of cognitive psychology. The arrowheads are perspective depth cues and may set size constancy scaling inappropriately.

These are extremely different kinds of causes. As the implications of symptoms and the phenomena of science depend on kinds of explanations — classifications are very important in medicine and science — we will now try to classify illusions by 'kinds' and 'causes'. This will lead to a tentative — this is certainly not engraved on stone — 'Peeriodic Table' of elements of perception and illusion.

A classification with causes needs some theoretical account or model of what is going on. We may start with a simple scheme like Fig. 1, 'Ins-and-outs of vision'. The central notion is that perceptions are hypotheses, rather like the predictive hypotheses of science. As in science, the process starts with signals from the (ultimately mysterious) world of physics, signalled bottom-up. The signals are interpreted, or read, with top-down knowledge. Then there are sideways general rules, such as perspective for seeing depth, and the Gestalt laws of organization or grouping output, for behaviour with feedback of errors, is essential for perceptual learning.

So, with apologies to the great Russian chemist, Dmitri Ivanovich Mendeleyev, we have the Peeriodic Table.

6. Some principles, with examples

Table 1 suggests ten main kinds of phenomena, with four main kinds of cause. The four causes have already been hinted at: optical; physiological; and two kinds of psychological or cognitive causes: misleading rules; and misleading knowledge.

The ten suggested kinds of phenomena are selected somewhat intuitively, though there are 'litmus tests' for assigning phenomena to the various categories.

The suggested kinds of perceptual phenomena are: non-sense (various kinds of blindness — from no signals from the eyes to inability to make sense of the signals); context (over space or time); grouping (generally of features organized into likely objects); instability (perceptual stability being hard to achieve); confounded ambiguity (confusing different stimuli or objects); flipping ambiguity (creating alternative perceptions for one stimulus or object); distortion (as of size or shape); unlikely (perception is greatly affected by probabilities: the more unlikely, the more the information; but if too unlikely will be rejected); paradoxical (generally from conflicting rules); fiction (going beyond the available information).

A word is needed on the two kinds of ambiguity, 'confounded' and 'flipping'. 'Ambiguity' is used in two very different senses, so the word 'ambiguity' is itself ambiguous! It may mean failing to distinguish differences ('confounded'), or, very differently, creating different perceptions from one stimulus or object ('flipping').Non-sense Total Blindness. Our lives depend on reliably not seeing — so that not seeing corresponds to nothing there. The driver moves off when not seeing another car, or person, in the way. Much of driving depends on not seeing, yet no evidence is different from evidence of nothing. As uncertainty increases with age, it is right for older drivers to be slower and more cautious, to ensure that seeing nothing corresponds with nothing to be seen.

The long-term blind do not see blackness — they see nothing. The nearest sighted people can get to this is imagining what is behind the head. One does not see black (which is a colour), one simply sees nothing. Though one may of course guess what is behind one's head, and this is important. The rare cases of adult recovery from infant blindness are theoretically interesting as well as remarkable human stories. There are many kinds of blindness, or non-sense, the most familiar being colour-blindness. There are also cognitive blindnesses.


Fig. 1. Ins-and-outs of vision: simple tentative scheme for how vision may be organized.
Inattention blindness. Conjurors (magicians) are expert at producing selective blindness by directing attention away from what is going on. A coin passes invisibly from one hand to the other by dropping it from a stationary into a moving hand, for the drop is not seen, and the coin appears magically in the moving hand. Also, conjurors direct their audience's eyes by looking away from where the action is. Attention is vital for seeing and inattention gives blindness.Agnosia. The most interesting kind of non-sense is inability to read meanings into perceptions, even failure to recognize common objects: agnosia. A famous account is Oliver Sacks's book The Man Who Mistook his Wife for a Hat (1985). Failures of perception when knowledge is not available, as in brain-damaged subjects, shows how important available knowledge is for perception.Neglect. There can be neglect of regions of space (Fig. 2). Most often the left visual field is missing, with a parietal lesion. Amazingly, the left halves of objects are missing wherever the eyes are looking.

Perhaps stranger still is:Blindsight. Blindsight is some visual ability, such as pointing to objects, though without consciousness. There may be an alternative more primitive pathway for simple perception without consciousness. This throws light on the evolution of the visual brain, and perhaps on the role of consciousness.Retinal rivalry. Red presented to one eye and green to the other gives the alternating blindness in each eye of 'rivalry'. This occurs for different shapes. So why do red–green anaglyph stereo pictures work? Common contours for the eyes prevent colour rivalry. Movement presented to one eye almost always brings sight to this eye, the other being effectively blind.Instability Jazzing. Repeated patterns of high-contrast lines produce jazzing effects, as in Op Art. Some authorities believe they stimulate movement areas of the brain directly; but it seems to be mainly due to small eye movements and 'hunting' of the lens for focus, or accommodation as it is misleadingly called. The repeated lines may stimulate on/off receptors normally signalling movement, and they may 'beat' with their immediate after-image to produce flower-like moving patterns (Fig. 3).

A major miracle of perception is achieving stability of sensory experience though we move. This applies to touch as to vision. When we handle an object it remains constant in form, though the touch signals change as we explore different parts. A room full of furniture looks stable though we move around. It is stability that needs explaining.




Table 1. Peeriodic table of the elements of the Perception and Illusion.
All movement is relative, yet normally we know from vision whether we are moving or objects are moving around us. Proprioception from the limbs helps but, remarkably, stability is achieved by vision alone when our feet are off the ground, as in a car. There are rules, originally suggested by the Gestalt psychologists, such as large distant objects tending to be accepted as stationary 'references' for seeing smaller nearer objects as moving.

There is recent evidence that decisions about what is moving can be taken early on, without complicated cognitive processing. But object knowledge comes into play — which is useful for film animators, who have to show what is supposed to be moving. Illusions of self-movement can occur thus: moving large objects can appear stationary, while smaller fixed objects seem to move — known as induced motion. This is dramatic in the fairground Haunted Swing oscillating room, where the stationary observer seems to move, even to be turning upside-down.


Fig. 2. Neglect: with cortical damage to the visual brain there can be blindness generally in the left field, but this is not simply loss of sight, and half an object may be invisible wherever the eyes are looking (from Thompson 2000).
The world normally appears stable when we move our eyes, as the movement signal at the retina is cancelled by the command signal to move the eyes. So after-images move with the eyes, as there are no retinal motion signals cancelling them. But is this all there is to it? Various illusions suggest complexities.


Fig. 3. Op Art Jazz (after Bridget Riley).



Fig. 4. Ouchi illusion: created by a Japanese designer, this is a powerful example of instability perhaps due to lack of border locking, as there are different spatial frequencies and orthogonal eyes.
Auto-kinetic effect. This is apparent motion of a small fixed light viewed in darkness. It occurs though the eyes are not moving. It is generally explained as due to the system that normally compensates eye movements — so giving stability to the world when the eyes are moved — but sending small fluctuating signals when the eyes are held still. If the eyes are held hard over to one side for a few seconds, the light usually swings round violently in the opposite direction, as the compensating system is unbalanced (Gregory 1966/97). But why does the auto-kinetic effect work only for a small light in darkness? Why doesn't a whole room look as unstable? This takes us back to the cognitive assumption of stability; a rich familiar world is assumed to be stable, so small imbalances are ignored.


Fig. 5. The Titchener illusion: the inner disks are the same size, but look different in contrast to the surrounding larger and smaller disks.
Tilted Room. A tilted room is very disturbing, as it violates basic assumptions. The assumption of horizontal for a floor is so strong, water can seem to run up hill in a tilted room.Pseudo-parallax. Curious instabilities are associated with one's own motion. Normally when we move, the world looks stable — which is remarkable as there are very complex changes of the retinal image. With lateral motion, everything rotates, counter to one's movements, around the fixation point of the eyes. This is motion parallax, which is optical but partially compensated perceptually. One sees the compensation when there are apparently different distances but not true depth — as in a perspective picture. Moving across the picture gives the extraordinary illusion of the entire scene swinging round, following one as one moves, though it is a flat picture. It appears to rotate in the opposite direction to true parallax. We may call this strange effect, of apparent but not true depth, 'pseudo-parallax'. It is most easily investigated with 3-D projected images. Another way of seeing the brain's compensation to one's own motion uses a flash after-image of a dark room: though fixed like a photograph in the eyes, features such as corners are seen to change shape as one walks around the invisible dark room, with the fixed after-image stuck in one's eyes.


Fig. 6a. The Ames Room: the odd-shaped room gives the same retinal image to the eye (placed at the right distance) as a normal rectangular room. So it must appear the same — and does — until there are objects, such as people, inside it. Then they look odd sizes while the room continues to look (falsely) like a normal rectangular room.



Fig. 6b. The Ames Room: this is what it looks like.
Portrait eyes. The eyes of a portrait following one's movements is similar to the pseudo-parallax of perspective pictures, except that the portrait effect is due to object knowledge rather than general perspective rules. The knowledge is that eyes keep looking at one as they rotate; but evidently the visual brain is not clever enough to realize that these eyes are fixed and flat. They give the same fixed image of normal eyes looking at one, so this is how they are accepted and seen.'Border locking'. Given the essential physiological fact that vision works with many parallel neural channels, and they can have different delays and other different characteristics, it is surprising that moving regions of brightness and colour remain registered. There can, however, be discrepancies, especially with large brightness differences and in dim light. For example, the instrument lights of a car can appear to move around in their dials, especially in dim light. (This was dramatic in the old Morris Minor, at least one owner stripped down the instruments looking for where they were loose!)

Registration at borders with colour printing is hard to achieve. Is there a special mechanism for visual channels? The notion of 'border locking' has been proposed, luminance normally locking colours at edges, though this can fail, as when colours have equal luminance. It has been suggested that the Café Wall distortion (Fig. 11) is due to inappropriate border locking, causing distortion in this special case (Gregory and Heard 1979).

A dramatic, recently discovered example of instability is the Ouchi illusion (Fig. 4). With small movements, the central region shifts separately from the surrounding pattern. Is this due to lack of border locking? ContextPerception works very much with contrasts. It is contrasts at edges that provide visual information. So even a simple line figure can be very effective, as in cartoons. Surrounding brightness and colours affect neighbouring regions, and so does size (Fig. 5).

Contrasts at borders are extrapolated into plain regions, which saves information transmission but can result in illusions, including perhaps Mach Bands. Colour regions with high-contrast edges appear more saturated, and there are many contrast illusions where contrast at an edge spreads to the surrounding regions, including beautiful 'neon-spreading', when colours wonderfully leak out of gaps, surely useful for painters. Confounded ambiguityThis is failure to distinguish differences. It may be due to neurological noise — limited physiological discrimination, or to lack of higher level cognitive categorizing.


Fig. 7a. The Necker Cube was discovered by a Swiss crystallographer L. A. Necker in 1832 while he was drawing crystals. When one flipped, they suddenly looked different! b. The Necker Cube with perspective is more stable.



Fig. 8a. The Danish psychologist Edgar Ruben made faces alternate with vases in fascinating ways.
A clear case of sensory confounding though there is high contrast is red light mixed with green, which looks yellow though this mixture yellow cannot be distinguished from monochromatic (single-wavelength) yellow light. This is the basis of an important test for red–green colour blindness, or 'anomaly'.

It is not surprising that different-shaped objects are confounded when they present the same or very similar stimuli to the senses. The most famous example is the Ames Room (Fig. 6).

This illusion presents the brain with a question: are the people the same size, or is the room an odd shape? Generally the room 'wins' — looking normal though it is not, and the people look different sizes even though they are the same size. Here the brain has to assess probabilities, and may guess wrongly. It may be noted that Emmert's law for after-images follows the apparent distances of the walls of the Ames Room, not the true distances. So, like any other perception, it is not directly attached to reality. Stereoscopic vision is useful as it can break through visual assumptions, which may be — and here are — wrong.Flipping ambiguityPerception can spontaneously flip between alternatives, especially with pictures or objects having equally likely alternative 'perceptual hypotheses'. There are many well-known figures that change spontaneously, flipping from one alternative to another. These phenomena reveal most clearly the dynamic nature of object perception. Related brain processes are beginning to be discovered. We may say that rival perceptual hypotheses are entertained in turn, when the brain can't make up its mind.

The most famous is the Necker Cube (Fig. 7a). A Necker Cube drawn with perspective (Fig. 7b) will stay longer in the orientation of its perspective depth.


Fig. 8b. Inkblots. Inkblots can be seen as almost anything, with slowly changing perceptual hypotheses projecting meaning. Perhaps these are truly minimal art — where the viewer does more work than the artist.
A three-dimensional wire cube is a fascinating and most revealing ambiguous object. (The wires should be black, to minimize the occlusion cue of the nearer wires hiding the further.) When it reverses in depth, it seems to stand up on a corner and rotate to follow one as one moves around it. This is because the motion parallax is misread when the apparent distances of the nearer and further faces are perceptually reversed. Also, the cube changes shape. When flipped, the apparently further face looks too large. So instead of appearing as a cube, it looks like a truncated pyramid. This is strong evidence that Constancy Scaling can work 'downwards' from the prevailing perceptual hypothesis (Gregory 1963).


Fig. 9a and b. The Hollow Face illusion: a hollow mask (the back of a 'joke' face) looks convex, until seen close up with both eyes. This is evidently knowledge driven, from our immense experience of convex faces. Rotating it is fascinating (www.richardgregory.org). Here we compare what happens to the 'top-down' knowledge-based face illusion, with depth seen 'bottom-up' from shape-from-shadows with neutral objects — lighting from above in (a) below in (b) — that could be concave or convex. They switch in depth, but the face doesn't. This separates a rule (shape-from-shading) from knowledge (that faces are convex and noses stick out).
Flipping can occur against evidence from other senses. Holding a small wire cube in the hand while seeing it depth reversed is weird. When the hand is gently rotated, the cube seems to rotate against the hand's movement. This feels (though painlessly!) as though one's wrist is broken. Recent experiments with fMRI are beginning to show where this flipping — where this perceptual decision-taking — is processed in the brain.

When there are only two accepted possibilities, flipping is between a pair of alternatives, which is dramatic, as for the Necker Cube (Fig. 7) and Rubin's Faces (Fig. 8a).

On the other hand, inkblots (Fig. 8b) may provide hundreds of slowly changing perceptions, used in psychological 'projection' tests.DistortionThese are perhaps the best-known illusions, especially systematic errors of length, or curvature, of lines. Even after a century of intensive investigation by physiologists and opticians, neurologists and psychologists, explanations for some of these effects remain controversial. Curiously, many of the well-known distortion illusions were discovered by astronomers trying to reduce errors by placing guide wires in eye-pieces for accurate measurements. It turned out that these guide wires upset the eye in dramatic, lawful ways. It was found that converging lines produce distortions such as those of (Fig. 10a) the Ponzo illusion, and (Fig. 10b) the Müller-Lyer illusion. These are large, repeatable phenomena, which are easy to measure, and are favourites for experiments. But what causes these distortions? There are optical distortions such as astigmatism. There are physiological distortions such as the Café Wall illusion (Fig. 11). And it has been suggested there are cognitive distortions, especially associated with size scaling normally giving constancy. We will look at these in some detail as some basic principles emerge.


Fig. 10a. The Ponzo illusion: the converging outer lines make one of the inner lines look longer than the other, though they are the same length. Is this a physiological distortion of signals from the eyes, or is it cognitive, the perspective convergence (like receding railway lines) setting size scaling to correct what should, in the object world, be different distances?



Fig. 10b. The Müller-Lyer illusion: a line terminated at each end with inward-pointing arrowheads (a) appears longer than a line with outward-pointing arrowheads (b).
'Physiological' distortions. A reason for believing that the Café Wall distortion is 'simply' physiological, and near the start of visual processing, is that it is strongly affected by brightness differences. It occurs only when the brightness of the narrow mortar lines lies between the brightnesses of the dark-and-light tiles. When the mortar is darker, or lighter, the wedge distortion is lost. When the 'tiles' are alternately coloured (for example red and green) with no brightness difference, there is no distortion (Gregory and Heard 1979). It may be noted that this figure has parallel lines, and lines at right angles, but no converging lines, as of perspective or any other depth cues. This makes the Café Wall illusion different from the classical 'geometrical illusions' (Fig. 11).


Fig. 11. The Café Wall illusion: found on a 19th-century café (originally a butcher's shop) in Bristol, the parallel mortar lines appear as long wedges. When originally built, the illusion would hardly have been present — for the brightness of the mortar must be between the brightnesses of the tiles. New mortar would be too bright! This seems to be a physiological error of retinal signalling. The adjustable lines on the screen above show how the illusory wedges can be measured, by matching.
The Café Wall is conceptually puzzling as it seems to contradict a principle of physics — Curie's Principle — that symmetry cannot produce asymmetry. Yet the repeated pattern of tiles is symmetrically repeated across the figure. So how can these long wedges be produced? There are two processes.

There are small-scale asymmetries in this figure for each pair of dark and light tiles. These produce local distortions, small wedges (which can be seen individually with smaller tiles). These little wedges are integrated along the figure — the second process — to give the long wedges in the figure, as also in the original wall.

What causes the small-scale 'primary' distortion? Opposite-contrast tiles seem to suck together across the neutral mortar. This effect (which we have named the 'phenomenal phenomenon') can be isolated and studied in detail. It is striking with light or dark shapes having narrow neutral edges: the rectangular or other shape expands or shrinks in lawful ways when made brighter or darker than the surround (Gregory and Heard 1983). Are these movements and distortions symptoms of 'border locking', normally serving to keep neighbouring regions together at edges, but in the Café Wall producing distortions that become dramatic when adding across the figure? This does suppose a relatively unknown process, which is dangerous; but postulating processes can give new knowledge.'Cognitive' distortions. Cognitive explanations can be complicated and speculative, so it is wise to treat them with caution. But as the human brain clearly is cognitive, with memory, intelligence, planning, and so on, no great step is involved. The question here is how much perception is cognitive. Illusion phenomena help to provide an answer. However, we have suggested that 'phenomena cannot speak for themselves'. We meet the to-and-fro ping-pong game played between phenomena and theories. Here the art of science is to be a fair umpire.

A phenomenon almost impossible to consider without cognitive concepts is the size-weight illusion. A smaller object feels heavier than a larger object of the same scale weight. This can be a kitchen experiment, with tins of different sizes filled with sugar to be the same measured weight. The smaller tin feels 20–30 per cent heavier than the larger tin of the same weight. For explanation: one anticipates a greater weight for the larger tin as larger objects are usually heavier — setting an expectation of the muscle power needed to lift them. Similarly, an empty suitcase flies up into the air (making one feel foolish!) when lifted with the expectation it will be heavy. The same kind of principle — misleading knowledge or assumptions — applies to many well-known illusions. Although they have, of course, a physiological basis. This is not relevant for the explanation when the error is due to the misapplication of the physiology, through inappropriate knowledge or false assumptions.


Fig. 12. Gestalt grouping laws.
Misleading depth cues. The well-known, often called geometrical, illusions have perspective depth features. It is suggestive that all these distortion illusions represent distance (by perspective) associated with expansion. This is the opposite of the normal shrinking of retinal images with increasing distance. Normally, this shrinking with distance is largely compensated by size scaling, giving constancy, so objects appear much the same size at different distances. This is an active scaling process that may be set wrongly. The suggestion is that perspective, or other depth cues in pictures, set the scaling inappropriately to the lines in the picture. As the picture is flat, though it represents objects in three-dimensional space, something must go wrong!

It turns out that scaling may be set either 'upwards', from depth cues, or 'downwards', from seen distance. We can use flipping ambiguity to separate 'bottom-up' from 'top-down' effects. A convenient example is a wire cube. As we have said (pages 435 — 6), when flipped in depth the further face looks too large, though there is no change of stimulus. When not flipped it looks like a cube, though the nearer face gives a larger retinal image. So here constancy scaling is following seen distance (Gregory 1963, 1970, 1997).


Fig. 13. Fraser Spiral: the circular pattern (this can be checked with a compass, or by placing a circular object over it) appears as a spiral — not because edges are shifted, but because the features are grouped to form the spiral pattern.
But scaling can also be set 'upwards', from depth cues. The simplest and the clearest example is the Ponzo illusion (Fig. 10a). The converging lines represent depth by perspective, and the cross line signalled as more distant is expanded. A similar, though less 'obvious' example, is the Müller-Lyer illusion, which is a perspective drawing of corners (Gregory 1963, 1968). What happens for these figures when they are truly three-dimensional? The distortions are destroyed when scaling is appropriate (Gregory and Harris 1975). It should be noted that scaling can be set 'upwards' by depth cues even when seen depth is countermanded by the texture of the picture's flat surface. This is evidently a simple-minded process.


Fig. 14. This famous photograph is of a dalmatian dog on a beach. But it is hard to see which features belong to the dog and which to the beach. When viewed at first upside down, the dog is essentially invisible. Once seen it is easier to see again. The knowledge it is a dog helps to group the features.
It was pointed out of the Café Wall illusion (Fig. 11) that it challenges Curie's Law, that symmetry cannot produce systematic asymmetry. This chess board-like pattern repeats across the figure and yet produces long asymmetrical wedges. It was suggested that a second process integrates little wedges (produced by local asymmetries) across the figure. Asymmetries occur in some higher level distortions, such as the Zöllner. Here there is a further possibility for what is going on. When perceptions are somewhat removed from the stimulus pattern, and from the initial signals, they may be modified downwards by scaling processes imposing large-scale distortions on symmetrical patterns. To recognize such differences depends on how the phenomena are classified, requiring experiments. In general, there are more possibilities for the 'higher' processes — such as inappropriate size scaling. So the Peeriodic Table has implications.


Fig. 15. Hogarth's engraving The Fisherman (1754). This is perhaps the earliest example of an artist deliberately playing with rules of perspective, and other cues to distance, producing wonderful paradoxes.
GroupingThe Gestalt psychologists of the first half of the 20th century stressed the importance of grouping with their Laws of Organization. Working mainly with patterns of dots, they showed that there are strong tendencies to group dots according to 'proximity', 'continuity', 'closure', and with movement, 'common fate' (Fig. 12). These principles can be used in nature and art to conceal and confuse. Camouflage is a good example. Grouping features into patterns and objects occurs at all levels of perceptual processing, from simple rules, to high level cognitive processing based on knowledge of objects. A well-known grouping illusion is the Fraser Spiral (Fig. 13).

This is easily mistaken for a distortion illusion, such as the Café Wall (Fig. 11), but it is different as edges are not shifted, but are organized into more or less appropriate patterns. The Dalmatian Dog picture (Fig. 14) is an example of object knowledge giving grouping 'downwards'.UnlikelyIt is significant that, although we tend to see what is likely, we can see things so unlikely they appear impossible, or even paradoxical. To be totally blind to unlikely objects or events would be dangerous — as they do occur, and may be hazardous, or useful. If we could see only expected things and events there could hardly be perceptual learning.ImpossibleImpossibility may be paradoxical or too unlikely. The first of these generally falls under cognitive rules, the second under knowledge. But there can be physiological paradoxes, for stimuli may conflict with other stimuli, especially when one of several parallel channels is adapted differently. The after-effect of motion from a rotating spiral appears as shrinking or expanding though without changing size, which is 'physiologically' paradoxical, movement and position being represented in parallel channels.

Pictures can present objects in paradoxical space. Perhaps the first example is Hogarth's engraving The Fisherman (1754) (Fig. 15). Striking examples are the Impossible Triangle, and the Impossible Staircase figures of Lionel and Roger Penrose (Penrose and Penrose 1958) (Fig. 16a). These are the basis of many of Maurits Escher's wonderful paradoxical pictures. It is strange that we can experience a paradox perceptually while knowing its solution conceptually, as with the Impossible Triangle model (Fig. 16b). This paradoxical perception occurs because the visual system assumes that the sides meet and touch at all three corners. At one corner they are separated in depth, though they touch optically in the eye.


Fig. 16a. Impossible Triangle Model: created as a drawing by Lionel and Roger Penrose in 1958, this is an early and the most famous Impossible figure. Here is a model, appearing impossible from critical positions — when two sides separated in depth at a corner touch at the eye, and are seen falsely as the same distance. Then a perceptual hypothesis is generated from a false premiss, and is paradoxical.



Fig. 16b. Impossible Triangle revealed: here the same object appears possible. (Hiding a corner of Figure 16a will make this, also, appear possible.)
Fiction Perceptions are far richer than the available sensory data, as perceptions are enhanced by knowledge, from previous interactions with objects. As sensory signals are almost absurdly limited, perceptions must be largely fictional — at least have fictional features — though this does not necessarily mean they are wrong. Fictions can be importantly true, though not based on current data. Such leaps beyond sensed data or measurements are common in science, often justified by verified predictions. As our sensations (or 'qualia') may be very different from physical reality, we should concede that all perception may be largely fictional.

It is useful for perception to be able to take off from stimuli — and to fill gaps — even though this can be misleading, even to creating apparent objects that are not there. The Italian artist-psychologist Gaetano Kanizsa (Kanizsa 1979) produced such superb examples of illusory contours and surfaces, he put such visual fictions on the map (Fig. 17). Though known to psychologists from the beginning of the 20th century, they had been ignored, though known in art for thousands of years, back to cave paintings. Fictional contours do not stimulate brain cells in the first stage of processing (V1). They seem to be quite low-level cognitive phenomena, obeying simple rules. They can give just about every effect of true contours, including inducing distortion illusions, and may come and go with flipping ambiguity.

These ghostly effects include 'neon-spreading' of colours, leaking through gaps in contours, which should be useful for artists. To modify a Dan Dennett remark: these mental figments extend pigments available to painters.'Filling-in' scotomas. There is a huge blind region of each retina where the optic nerve leaves for the brain, yet we do not normally see a great black cloud hovering before the eyes. Why do we not normally see this local blindness, even though it can easily be demonstrated (Fig. 18)?


Fig. 17. The Kanizsa Triangle: this is the most famous of Gaetano Kanizsa's 'fictional' figures.



Fig. 18. Filling-in (or ignoring?) a scotoma: with the left eye only, look at the dot from about 1 foot away. Move the page around a bit and the '&' will disappear, when it falls on the blind spot. As the '&' is replaced with the colour of the surrounding paper (or a pattern), is the blind region filled in or ignored?
Dennett (1991) has suggested that the blind spot may not be seen not from filling-in, but rather because the brain ignores this region, as it never gives useful information (like ignoring a boring person at a party). Yet there is evidence that the blind region is made invisible by active filling-in from copying the surrounding retinal pattern (Ramachandran and Gregory 1991). It will complete patterns, but will not add missing noses, so this is hardly cognitive. Ignoring is a neat idea, and may occur often, but nature does not always adopt the neatest solutions — and does not always please philosophers.

(Published 2004)

— Richard L. Gregory

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