Vision scientists like us seek to understand how we see, from both a psychological and a biological perspective, and our discipline has a long tradition of studying visual artists such as painters and sculptors. Scientists did not invent the vast majority of visual illusions—painters did. The visual arts often preceded the visual sciences in the discovery of fundamental vision principles, through the application of methodical—although perhaps more intuitive—research techniques.
Likewise, magicians—as the world’s premier artists of attention and awareness—have made their own discoveries. This is what drew us to their footlights, card tables, and street performances. We want magicians to help us understand cognitive illusions in the same way that artists have revealed insights about visual illusions. And in fact visual illusions are a bit like magic tricks on the page. In this chapter we’ll take a brief tour of some of our favorites.
Artists have been utilizing visual illusions since the fifteenth century, when Renaissance painters invented techniques to trick your brain into thinking that a flat canvas is three-dimensional or that a series of brushstrokes in a still life is a bowl of luscious fruit. They figured out linear perspective—the notion that parallel lines can be represented as converging so as to give the illusion of depth and distance. (Again, think of train tracks heading toward the horizon.) They realized they could manipulate atmospheric effects by making tones weaken and colors pale as they recede from view. They used the horizon or eye level as a reference point to judge the size and distance of objects in relation to the viewer. They used shading, occlusion, and vanishing points to make their paintings hyperrealistic.
In the early decades of the seventeenth century Dutch painters developed still-life easel paintings with trompe l’oeil realism. (The Attributes of the Painter by Cornelius N. Gysbrechts. Réunion des Musées Nationaux/Art Resource, N.Y.)
Trompe l’oeil is a French term that means “trick the eye.” It flourished in the seventeenth century in the Netherlands. The lifelike pictures appeared to jump from the frame.*
The “dome” of Saint Ignatius church looks like a real dome from this vantage point. (Flikr.com)
Trompe l’oeil is sometimes used on a large scale to suggest entire parts of buildings that do not actually exist. The architect of the Saint Ignatius church in Rome, Horace Grassi, had planned to build a cupola but died before finishing the church, and the money for the cupola was used for something else. Thirty years later, in 1685, the Jesuit artist Andrea Pozzo was asked to paint a fake dome on the ceiling over the altar. Pozzo was already considered a master in the art of perspective, and yet what he accomplished could hardly be believed. Even today, many visitors to Saint Ignatius’s are amazed to find out that the spectacular cupola is not real but an illusion.
Architects soon realized that they, too, could manipulate reality by warping perspective and depth cues to create illusory structures that defied perception. Need a big room in one-fourth the space? No problem. Francesco Borromini accomplished just that at the Palazzo Spada, a palace in Rome that we visited a few years ago. Borromini created the illusion of a courtyard gallery 121 feet long in a 26-foot space. There’s even a life-size sculpture at the end of the archway. Not really. The sculpture looks life-size but is actually just two feet tall.
This hallway is much shorter and the sculpture is much smaller than they appear. (Flikr.com)
Closer to home and to magic is the Grand Canal concourse at the Venetian Hotel and Casino in Las Vegas. The first time you step onto the concourse, you feel a sudden onset of twilight. That’s exactly what Susana’s mother, Laura, experienced when we first took her to Las Vegas while planning our conference. We descended from our suite after a room service lunch. Stepping out of the elevators and onto the concourse, she said, “Oh, it’s gotten so dark outside.” Susana asked her what she meant. “The sky,” Laura said. “It’s gotten dark so early.”
“But, Mamá,” Susana explained, “we’re still inside. You see the black spots in the sky? They are sprinkler heads.”
Mouth agape, Laura examined the incredible illusory sky, with its five shades of rococo blue—peacock, azure, cerulean, turquoise, and aquamarine—and wisps of mare’s tails, stratus, and cirrocumulus clouds. Laura considered it for a minute before turning to Susana and saying, “Well, why did you tell me so soon? I would have liked to enjoy it a little longer.”
Another great illusionist is the Dutch lithographer and woodcut artist Maurits Cornelis (better known as M. C.) Escher. Early in his career, Escher carved realistic scenes based on his observations and travels. Later, he turned to his imagination, rendering some of the most brilliant visual illusions in the history of art. When he was in high school, one of Steve’s favorite posters was an Escher print of the never-ending staircase (Ascending and Descending, 1960), in which a group of robed monks perpetually climb or descend an impossible staircase situated at the top of a temple. It was impossible because it circled around on itself and never ended. So how could it be drawn if it was physically impossible? Escher must have cheated somewhere in the print and failed to depict the proper structure of a real staircase. But Steve couldn’t find it, no matter how closely he looked. He realized he should examine the structure as a whole to see if there was a small systematic warp along the entire structure that allowed for the illusion.
And that’s when Steve found that he couldn’t look at the structure globally. He could only really see one area of the staircase at a time. His vision could process the details of the staircase when he centered his gaze on a specific part. But when he did that, every other area of the staircase, in his visual periphery, was left in a blur. And he realized that that was how Escher must have done it: since you can see only one local area at any given time, small, gradual errors along the entire structure could not be seen with the naked eye.
This effect challenges our hard-earned perception that the world around us follows certain inviolable rules. It also reveals that our brains construct the feeling of a global percept by sewing together multiple local percepts. As long as the local relation between surfaces and objects follows the rules of nature, our brains don’t seem to mind that the global percept is impossible.
Susana’s formal introduction to visual illusions came in 1997 when she arrived at Harvard University to study under David Hubel and Margaret Livingstone. At the time, Harvard was the mecca for the study of illusions, and in fact this is where she met Steve. Not only were Livingstone and Hubel leading the field in the study of illusions in the brain, but a number of Harvard psychologists were discovering an array of completely new phenomena.
As part of her postdoctoral training, Susana decided to choose a visual illusion and investigate its effects. Leafing through an art book, she found the perfect playground for her curiosity: op art, a field that explores many aspects of visual perception, such as the relations between geometrical shapes, variations on “impossible” figures that cannot occur in reality, and illusions involving brightness, color, and shape perception.*
Susana settled on op artist Victor Vasarely, whose Nested Squares series exhibited an odd illusion: the corners of the squares looked brighter than their straight-edged sides. But the effect wasn’t just about the lightness of the corners, because if Vasarely reversed the order of the nested squares from white-to-black (center to exterior) to black-to-white, now the corners were darker than the sides. So it seemed to be an illusion concerning contrast, and not lightness per se.
Susana searched the vision research literature and found that only a couple of people had discussed this effect previously and nobody had investigated its neural bases. And no one had looked at shapes other than squares. Squares are a special type of shape in which all of the corners are convex (all point away from the center of the square). But nobody had examined the effect for nonsquare shapes with concave corners or for shapes with corner angles other than 90 degrees. Susana realized there were many aspects of this illusion that she could study perceptually, followed by physiological research in the brain.
After several years, first as a trainee at Harvard and later as the director of her own research team, Susana learned one of the most fundamental secrets of the visual system. The previous dogma in the field had been that neurons in the first few stages of the visual system were most sensitive to the edges of object surfaces. Susana’s results showed instead that neurons of the visual system are more sensitive to the corners, curves, and discontinuities in the edges of surfaces, as opposed to the straight edges that had previously been thought to reign.
Vasarely’s Utem (1981). Nested squares of increasing or decreasing luminance produce illusory diagonals that look brighter or darker than the rest of the squares. (Courtesy of Michèle Vasarely)
Op artists were also interested in kinetic or motion illusions. In these eye tricks, stationary patterns give rise to the powerful but subjective perception of illusory motion. An example is Enigma by Isia Leviant.
Reinterpretation of Enigma (Created by and courtesy of Jorge Otero-Millan, Martinez-Conde Laboratory, Barrow Neurological Institute)
This static image of regular patterns elicits powerful illusory motion in most of us and has generated an enormous amount of interest in the visual sciences since it was created in 1981. However, the origin of the illusion—is it the brain, the eye, or a combination of both?—remains, appropriately, an enigma.
In 2006 we designed an experiment to probe this question. We asked observers to say when illusory motion sped up or slowed down as they looked at the image. At the same time, we recorded their eye movements with high precision. Before they reported “faster” motion periods, their rate of microsaccades—tiny eye movements that occur during visual fixation of an image—increased. Before “slower” or “no” motion periods, the rate of microsaccades decreased. The experiment proved that there is a direct link between the production of micro-saccades and the perception of illusory motion in Enigma. The illusion starts in the eye, not the brain.
Another of our favorite visual illusions is Mona Lisa’s smile. Her expression is often called “enigmatic” or “elusive” but, as our mentor Margaret Livingstone at Harvard University observed, the illusory nature of her smile is explained when you consider exactly how the visual system works. When you look directly at the Mona Lisa’s mouth, her smile is not apparent. But when you gaze away from her mouth, her smile appears, beckoning you. Look at her mouth, and the smile disappears again. In fact, her smile can be seen only when you look away from her mouth. This is due to the fact, mentioned earlier, that each eye has two distinct regions for seeing the world. The central area, the fovea, is where you read fine print and pick out details. The peripheral area, surrounding the fovea, is where you see gross details, motion, and shadows. When you look at a face, your eyes spend most of the time focused on the other person’s eyes. Thus, when your center of gaze is on Mona Lisa’s eyes, your less accurate peripheral vision is on her mouth. And because your peripheral vision is not interested in detail, it readily picks up shadows from Mona Lisa’s cheekbones that enhance the curvature of her smile. But when your eyes go directly to her mouth, your central vision does not integrate the shadows from her cheeks with her mouth. The smile is gone.
Mona Lisa (Leonardo da Vinci)
The Best Illusion of the Year contest, mentioned in the introduction, has been a huge success. You would think that after generations of talented, dedicated, sometimes obsessively driven visual artists and scientists tinkering and laboring at their easels, drafting tables, scratch pads, darkrooms, and PC graphics programs, this particular vein of ore would be all mined out. But it isn’t.
Consider the Leaning Tower illusion discovered by McGill University scientists Frederick Kingdom, Ali Yoonessi, and Elena Gheorghiu, which took first prize in 2007.
The two images of the Leaning Tower of Pisa are identical, but to you it seems that the tower on the right leans more. This is because your visual system treats the two images as if they were part of a single scene. Normally, two neighboring towers will rise skyward at the same right angle, with the result that their image outlines converge as they recede from view. This is one of the iron-clad laws of perspective, so invariant that your visual system automatically takes it into account. Since the outlines don’t converge in the images above, your visual system is forced to assume that the two side-by-side towers must be diverging. And this is what you “see.”
Mona Lisa up close. The three panels are simulations of how your visual system sees Mona Lisa’s smile in the far periphery (left), the near periphery (middle), and the center of gaze (right). The smile is more pronounced in the left and middle panels. (“Blurring and deblurring” by Margaret S. Livingstone, Harvard Medical School)
The Leaning Tower illusion. (F. A. A. Kingdom, A. Yoonessi, and E. Gheorghiu, McGill University)
This illusion is so basic, so simple, it is almost beyond belief that no one ever reported it before 2007. It just goes to show that there is still plenty of low-hanging fruit just waiting to be discovered in the world of illusions. Each new illusion adds depth and definition to perceptual and cognitive theory, bolstering certain hypotheses while weakening others or inspiring new ones. Some suggest new experiments. Each inches us just that much closer to understanding perception and awareness.
The illusion of sex (Richard Russell)
The only difference between these two faces is their degree of contrast. Yet one appears female and the other male. That’s because female faces tend to have more contrast between the eye and mouth (think how makeup exaggerates these features) and the rest of the face than males. Richard Russell, the Harvard University neuroscientist who created the illusion, has found that increasing the contrast of a face (more makeup!) makes it more feminine. Conversely, reducing contrast makes it look more masculine.
Next, the Rotating Snakes illusion, which was presented at the 2005 contest.
The perception of motion need not arise from actual action in the world. Rather, the perception of motion occurs when dedicated motion processing neurons in your brain are activated by specific patterns of light intensity changes in your retina.
The Rotating Snakes illusion (Akiyoshi Kitaoka)
Some stationary patterns generate the illusory perception of motion. For instance, in this illusion invented by the scientist Akiyoshi Kitaoka, the “snakes” appear to twist. But nothing is really moving other than your eyes. If you hold your gaze steady on one of the black dots in the center of each “snake,” the motion will slow down or even stop. Because holding the eyes still stops the illusory motion, eye movements must make the snakes twist. This is supported by the fact that the illusory effect is usually stronger if you move your eyes around the image.
Finally, there is the Standing Wave of Invisibility illusion, which we hope to turn into a totally new magic trick and someday in the future unveil at the Magic Castle. This is the illusion Steve discovered while working on his thesis in graduate school. He wondered what is required for an object to be visible. You might think that visibility should require only that light fall on your retina. But it can be more complicated. Illusions of invisibility show that a stimulus can be projected onto your retina and nevertheless be wholly or partly invisible.
A classic example is visual masking. In this illusion, a visual target—for instance, a black bar against a white background—is rendered invisible when two abutting black bars appear a tenth of a second after the target. What’s cool is that a target that is seen initially by the brain can be erased by a mask that enters the brain afterward.
Steve’s graduate thesis showed how the illusion works in the brain. As it turns out, the target causes two responses in your visual pathway. One, the onset response, occurs after the target turns on. A second, the after discharge, occurs after the target turns off. Other labs had ignored the after discharge because it occurs after the stimulus turns off. But Steve showed that if you inhibit the after discharge, the stimulus disappears. The same also happens if you inhibit the onset response but not the after discharge. So both the onset response to a stimulus and the after discharge contribute to the neural representation of a stimulus. He realized that if this was true, we should be able to predict a new and very powerful illusion in which a flickering target is perpetually rendered invisible by inhibiting both the onset response and the after discharge of each flicker. It worked!*
We called the new illusion the Standing Wave of Invisibility, and it unites our interest in visual illusions and magic. It is this illusion that we plan to turn into a new stage effect to wow magicians with the power of neuroscience on their own turf. To make this happen we are going to need the help of a magic studio that specializes in electrically engineered lighting effects. For now the trick is on our “to do” list.
