Visual Illusions


A Good Eye

Pherhaps because of this reliance on dissimulation, as we saw in the discussion of cunning, the image of the eye is endemic to Detienne and Vernant’s work and it appears in in a wide range of contexts. They wrote: “In all the various domains in which mêtis operates a good eye is as important as an agile mind” (p. 303). The hunter must be vigilant, they wrote elsewhere, because “every animal with mêtis is a living eye which never closes or even blinks” (p. 29). Likewise Antilochus, when performing the deceptive maneuver with his chariot needed to keep his eye “fixed on the post” (p. 14) and “fixed on the competitor who is ahead” (p. 15).

In the context of navigation, “Odysseus steers his ship with... mêtis... his eyes fixed upon the Pleiades and Bootes” (p.236). The same is true in medicine and “the experienced eye of the doctor” (p. 2) which “must watch for the precise moment when his intervention will prove decisive” (p. 312). In terms of rhetoric, the “man of prudence, the phronimos man, is . . . the man whose success owes more to a good eye than to an unshakable knowledge” (p. 316).

The gaze by itself, it’s important to note, is not enough unless joined to the agile, experienced mind. This union is expressed in the concept of eustochia whereby the good eye is able to see similarities and differences between things; it “is an intellectual operation which lies half-way between reasoning by analogy and a skill at deciphering the signs which link what is visible to what is invisible” (p. 314).

In argumentation, this is closely related to the process known as conjecture and it has its etymological roots in celestial navigation and the plotting of the journey by the stars. The ability to reason by conjecture also plots its course by mapping like and unlike things.

Camouflage

The reason the image of the eye is so prevalent in discussions of cunning is again due to the shifting, unstable nature of mêtis itself. Not only must mêtis remain ever vigilant and ready to pounce, it also must be capable of obscuring its movement so as to approach unseen; and so mêtis also has the quality of being multicolored or shimmering. Detienne and Vernant wrote that the word mêtis is often related in the literature to another word, poikilos, which refers to “the sheen of a material or the glittering of a weapon, the dappled hide of a fawn, or the shining back of a snake mottled with darker patches” (p. 18). The dappling of the fawn, the mottling of the snake, “shields which glitter as they move” (p. 19), all describe what is essentially camouflage, a surface appearing that conceals a different truth beneath.

Camouflage hides the fawn from the hunter, conceals the approach of the snake through the grass, and disguises the number of men in the army. This disguise is effected primarily through visual means. Detienne and Vernant went on to explain “this many-coloured sheen or complex of appearances produces an effect of iridescence, shimmering, an interplay of reflections which the Greeks perceived as the ceaseless vibrations of light” (p. 18). Faced with the complex of appearances, the eye becomes fascinated, beguiled by seemingly ceaseless motion and bound in place—aporia, without escape.

For this same reason, when not multicolored, mêtis is associated with blackness and night. In the dark, the enemy can approach unseen and strike by surprise. For Detienne and Vernant, the exemplars were octopuses, that “are pure aporai and the impenetrable, pathless night that they secrete [their ink] is the most perfect image of their mêtis" (p. 38). Whether through the interplay of light or through strategic darkness, mêtis uses visual means to distract and fascinate. In effect, mêtis dissimulates, pretends to be other than it is, so it can “see without being seen” (Detienne & Vernant, 1978, p. 30).

A moiré pattern
Figure 6: The moiré pattern used in animal camouflage produces a shimmery color and a sense of movement.

For example, consider the slanted bars depicted in Figure 6. Known as a moiré pattern, the closely interspersed rectangles of alternating color create a shimmering effect. Viewers often see a spectrum of color (including pinks and violet) as well as movement. In many viewers it creates a strange combination of attraction and repulsion—an urge to look away accompanied by an inability to do so. The alternating pattern is beguiling in its effect, and it is no coincidence that such patterns are similar to the stripes of both tiger and zebra.

Gestalt Principles of Design

Patterns like the moiré, as well as other physical structures, can be used to help the eye deceive itself. Figure 7 demonstrates several related gestalt principles of design. In the figure, we can see how variations in fundamental properties related to size, shape, color, and position create the strong perception that, for example, objects are grouped and lines are continuous.

Gestalt principles are especially evident in the example titled closure, as the eye is compelled to perceive the object as a whole and to perceive a triangle overlay that is not truly present. As Rudolf Arnheim (1974) wrote in Art and Visual Perception, “the appearance of any element depends on its place and function in an overall pattern” (p. 5), so that “a whole cannot be attained by the accretion of isolated parts” (p. 5).

Six figures depicting the gestalt principles of proximity, similarity, continuity, closure, area, and symmetry
Figure 7: The common thread among these principles is the way the eye tends to percieve the whole, rather than individual parts

Instead, any figure “is grasped as an overall pattern of essential components… into which further detail can be fitted (p. 44). This gestalt method of apprehension underlies all of our powers of visual perception. But it is more complex than simply that objects are more than a sum of their parts.

To better understand this mechanism of perception we must first dispense with the naive misconception that the eye, like a camera, simply records all the material data it receives. As Arnheim writes “vision is not a mechanical recording of elements but rather the apprehension of signifi­cant structural patterns” (p.6), structural patterns which can guide or mislead, our interpretation.

Once we no longer tether visual perception to a strictly corresponding reality, we realize “the shape of an object we see does not… depend only on its retinal projection at a given moment . . . the image is deter­mined by the totality of visual experiences we have had with that object, or with that kind of object, during our lifetime” (p. 47).

If this were not so, imagine how the world would really appear to us: at all moments bobbing with each subtle twitch of our head or flick of our eyes, always obscured by the intrusion of our nose into the visual field, and always distorted as the relationships of objects we see shift in relation to our ever-changing view point. The retina itself is curved. So why don’t straight lines appear bent? As Arnheim put it: “the image is better than it should be” and went on to write “for example the eye is not corrected for spherical aberration, and yet straight lines do not look curved” (p. 69).

If the process of apprehension did not correct the data of reception, our vision would look much different than it does. Arnheim wrote “The sickening sensation pro­duced by a distorting mirror should be the normal visual reaction to most objects most of the time. This would interfere with the practical business of life since the immutable physical object would be represented by a constantly changing image” (p. 106).

Instead, we have evolved not just eyes that see, but eyes that also process the world we see according to various rules, rules that over time have proven to be beneficial. By studying Arnheim’s meticulous treatment of the various forms that demonstrate perception, we may extract, cautiously, some general rules governing the deceptive use of size, shape, and color in design, as well as a vocabulary we may usefully employ in our analysis of dark patterns.

Gradients, Shapes, and Perspective

Aside from the idea that, as part of the process of seeing, the eye interprets the world according to the simplest shape precept, other important understandings involve the use of gradients, shapes, and perspective. We are probably familiar with gradients in the form of color overlays that allow us to quickly vary the shade of color in a plot, darkening it procedurally according to certain rules, but gradients are also used in lines and angles to create depth. Any time the process involves a sequence in which later steps are varied gradually qualifies as a gradient. Because gradients create the illusion of depth, they are important, but other such spatial illusions are also created by shapes and perspective.

Two example gradients created by angled and slanted bars
Figure 8: Two kinds of gradients are depicted here—on the left the height of the bars is graded to create depth, while in the right the top and bottom angles of the bars also have a reverse gradient that creates the appearance of concavity.

Gradients work, as their name suggests, by gradually transitioning the value of visual properties, like shade, angle, or position, for instance. Typically gradients are used to ease the transition between unlike values, and this application gives us clues to how they function. Gradients, such as the ones depicted in Figure 8, above, work step-wise through minor, almost imperceptible alterations that accumulate into large differences.

Much as the dissoi logoi are able to induce a state of aporia through mechanical action like the pulley, gradients work the same on the eye to beguile it into being unable to distinguish “the similarity and dissimilarity of things” (Bizzell and Hertzberg 2001, p. 158). Through this process of progressive change, dissimilar things can be made to blend. That is, the eye can be deceived into thinking they are blended.

Three cubic shapes whose visual stability weakens
Figure 9: The varying levels of stability of cubic shapes. The figure on the left is most stable, while the figure at right is least stable, and the viewer can shift almost at will between seeing either the exterior or the interior of the figure.

Aside from mechanical advantage like a pulley, visual illusion can also be achieved through ambiguity in the structure of a figure. In the example above, the depicted cubes become less stable as one moves from left to right. The initial figure has a strong opinion on which of its faces is foremost, and it takes an effort of will for the eye to see it reversed. The central cube by contrast can just as easily be seen as exterior or interior. The final cube resists stability in any orientation and instead remains in almost constant motion as it assumes various facings.

Not only does this illustrate how ambiguous structures can beguile perspective, the left-most cube demonstrates another important aspect of how we interpret two-dimensional depictions. For, perhaps surprisingly, as Arnheim wrote

If we take photographs of a rectangular board or a wooden cube tilted in space, no two edges will look strictly parallel. All surfaces will be trapezoids converging toward depth. The same is true for the projections received by the retina. Therefore our line drawings should look quite unnatural. (p. 262)
So, if real world cubes do not in fact appears as do the cubes drawn in isometric perspective, what exactly is happening?

If, in nature, we expect all surfaces to be deformed as they recede into distance, and if we expect truly parallel lines to be convergent as they are in nature, then why does isometric perspective avoid deformation and why does it depict perfect parallelism?

Two rules of 2D depiction become pertinent: “that no aspect of visual structure will be deformed unless space perception requires it” (p.263) and that “Except for the special case of transparency, no more than one thing at a time can ever be directly visible in any one spot of the surface” (p.264). Remember, pictorial forms are not faithful reproductions of nature. As Arnheim put it, “The objects of the physical world are not squashed in the picture like a honey bee on the windshield” (p.263). Instead, something stranger is going on.

Vision and Truth

First, as we have seen, the world-as-it-is is not the way it is perceived by our eye: perceptual operations are performed on the image in the instant of its apprehension. But it is the second case that makes it all the stranger: for the world-in-the-drawing is also not the way the world would be. So there is a kind of double deceit required to produce faithful representations: first the artist’s eye is deceived in seeing the object, and second the artist’s drawing deceives the eye of its viewer.

Arnheim related the story of an artist sketching a peasant’s home while the owner watches. During the drawing, Arnheim wrote, the peasant objected, saying: “Why are you making my roof so crooked—my house is quite straight!” but when seeing the finished sketch, the peasant cried: “Painting is a strange business! Now it is my house, just the way it is”. Arnheim concluded of perspective: “it makes things look right by doing them wrong” (p. 115).

A figure depicting how a trapezoid might look when viewed at an angle.
Figure 10: This figure illustrates how a trapezoidal figure will appear, under certain circumstances, for all intents and purposes to be another shape entirely.

We may well ask what it is we are seeing in the first place. Indeed, while pictorial representation may capture a truthful percept of the original object, it is by no means necessary and often instead counterproductive. To illustrate this, Arnheim uses the example of looking through a peephole into a darkened room (as shown in Figure 10) to view a luminous trapezoid on the floor.

The viewer likely perceives the shape to be a rectangle, wrongly, not because that is the shape of the projection, but because “the frontal square is the simplest percept the projection will yield” (p. 272). Crucially, without access to additional information about distance and angular measurement, the viewer cannot determine anything further about the dimensions of the actual shape.

It is this same ambiguity that creates more complicated illusions, such as the painting the Greek sophist Philostratus described of the inside of a room covered all around with a host of soldiers in receding planes, some in full figure, some partially hidden, ranging from the legs up to just the helmet and finally just the spear points.

The illusion, Philostratus said, is “accomplished by analogy, since the problem is to deceive the eyes as they travel back along with the proper receding planes of the picture.” Arnheim went on to explain “By analogy the author apparently means the art of completing the hidden parts of an object through their simi­larity to what is visible” (p.251). As we have seen, the stepwise production of analogy is mechanical in its nature.

To what purpose? We mustn’t make the mistake of thinking things are done this way because it is the only way to do them or because it’s necessary to do them this way. An entirely different set of conventions could have just as easily arisen in place of the ones that govern pictorial representation.

Again, Arnheim pointed to Plato with a telling citation: “For if artists were to give the true proportions of their fair works, the upper part, which is farther off, would appear to be out of proportion in comparison with the lower, which is nearer; and so they give up the truth in their images and make only the proportions which appear to be beautiful, disregarding the real ones” (p. 274).

To describe something is, fundamentally, to create within the viewer an unseeing eye. In order to see-without-being-seen requires the viewer’s eye is unseeing, is blinded. Under this cover, apate, aporia, cunning makes its ploys.