"I WISH YOU WOULDN'T KEEP appearing and vanishing so suddenly: you make one quite giddy!"

"All right," said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone.

"Well! I've often seen a cat without a grin," thought Alice; "but a grin without a cat! It's the most curious thing I ever saw in all my life."

-Lewis Carroll,
Alice's Adventures in Wonderland

The "Cheshire-cat effect" is one of two disappearing acts that have attracted my attention because of their curious visual aspects.

The other one is the "rhino-optical effect," In the former you look simultaneously at two scenes by means of a mirror held in front of one eye; if something moves in one scene, the other scene may disappear for several seconds. Sometimes the erasure is incomplete. If the partially erased scene is a face, a smile on the face might survive, leaving an eerie view reminiscent of Lewis Carroll's Cheshire cat. In the rhino-optical effect you see an object when you look away from it but it vanishes when you look directly at it.

The Cheshire-cat effect was discovered accidentally in 1978 by Sally Duensing and Bob Miller at the Exploratorium, a science and perception museum in San Francisco. They were investigating binocular fusion, the process by which your brain fuses the separate scenes viewed by your eyes. Since the eyes function with only a slight difference in perspective, you are normally not aware of the fusion. Sometimes it takes place even when the eyes are viewing different scenes. Look at your hand with your left eye and at a reflection of a hole in an otherwise featureless plane with your right eye. Because of fusion, what you perceive is your hand with a hole in it.

Duensing and Miller first employed a mirror stereoscope to separate the views. When someone looked into the device, the left eye saw a person's face (reflected twice by mirrors) and the right eye saw an illustration of a window with four panes (reflected twice by another set of mirrors). In the perceived composite view the part of the window that overlapped the face usually disappeared. Presumably the complexity of the face weakened the brain's ability to fuse the two scenes completely.

To simplify the experiment the investigators substituted a thin horizontal bar for the illustration of the window and placed behind the face a featureless white backdrop. A woman taking the test said the part of the bar seeming to overlap the face was fainter and blurrier than the rest of the bar. To determine what part of the bar was missing one of the investigators pointed toward it. When the hand entered the field of view of the observer's right eye, she exclaimed that the face had completely disappeared. Although the view of the face by the observer's left eye was still unobstructed, none of the face surfaced at the conscious level. It was as though a magician had waved a hand through a scene to make a person disappear.

The erasure of part of a view from one eye is triggered by motion in the field of view of the other eye. Duensing and Miller demonstrated the effect with a variety of moving objects, including a length of string and a spot of light. Even apparent motion serves: when one of the mirrors in front of the right eye is moved slightly, the apparent motion of the scene viewed by that eye erases the scene recorded by the other eye. The erasure can last for as long as five seconds if the eyes are kept stationary and there is no motion in the erased field of view. If the eyes move, the missing scene immediately reappears.

Duensing and Miller next replaced the bar with a featureless white background but kept the face in front of the observer's left eye. They found that erasure is sometimes incomplete. If the hand moved through only part of the right-eye view, the corresponding part of the left-eye view disappeared but the rest remained. Even when the hand swept through the right-eye view, part of the left-eye view might remain. The surviving section tended to be where the observer fixed the gaze of her left eye. If she looked directly at the smile on the face, the smile survived the erasure. Since the smile was then superposed on the background seen by the right eye, it seemed to float in space.

In one trial Miller looked into the stereoscope and Duensing sat where he could see her face with his left eye. When he swept his hand across his right-eye view of the white background, he fixed his gaze on one of her eyes. Her face disappeared except for that eye. She then pointed to the other eye. Miller saw the hand but it pointed to an empty region in his view. Presumably the hand became visible because its motion forced erasure of the corresponding part of the background seen by the right eye. Erasure can thus be turned on and off at will by an appropriate motion in one of the fields of view. Moreover, it is selective with respect to the parts of the view that are affected.

The direction in which a hand or an object moves in a field of view is usually not important, but erasure is more certain and complete if the motion is fairly slow. Erasure always requires that the eyes be held as stationary as possible. If they follow the moving object, erasure does not occur.

To test how motion can selectively erase part of a view, Duensing and Miller arranged for an observer to see two fields containing shapes [left]. When hands were waved in the upper left of the left-eye view and the upper right of the right-eye view, the top half of the fused view was immediately erased. Any of the geometric shapes could be erased by moving a hand through the corresponding field of view for the opposite eye.

In a related test an observer saw a different face with each eye. If the faces were stationary, they could be partially fused. When part of one face moved, the corresponding part of the other face disappeared. For example, if one person rolled his eyes, the other person's eyes disappeared. If both people rolled their eyes, fusion was reestablished, with the perplexing result that two irises moved in each of the two eye sockets of the composite face.

In binocular viewing one eye dominates the other in determining what perspective is brought to consciousness. Test yourself by focusing on a nearby object. Close your left eye and note the perspective your right eye has of distant objects. Repeat the procedure using only your left eye. With both eyes open, which of the monocular perspectives more closely matches the perspective of the distant objects now seen binocularly? In my case the left eye usually dominates. In the Cheshire-cat effect does a wave of a hand in the field of view of the dominated eye erase the view of the dominant eye as readily as the other way around? For me it does. A few of the people I tested report that erasure is more easily triggered by motion in one view than it is in the other.

Erasure can be modified by the illumination of the two scenes. Duensing and Miller found erasure is more complete when the background seen by one eye is bright. If the face is also well illuminated and the observer fixes his gaze on the eyes, the eyes will end up glowing when a hand is waved through the other scene.

A Cheshire-cat demonstration is now an exhibit at the Exploratorium. A person sits in a booth while someone else sits on the other side of a counter running across the booth. Both sides of the booth are covered uniformly with white Formica circles. In front of the observer is a vertical rod to which a double-sided mirror is hinged. By rotating the mirror about the rod the observer can choose which eye sees the featureless Formica reflected in the mirror. In either position one eye views the second person. To erase that person's face the observer moves a hand across the reflected Formica.

You can produce the Cheshire-cat effect by simpler means. Prop a pocket mirror vertically at the edge of a table or hold it with a steady hand. Turn it so that it reflects the scene on your right. The scene should consist of a vertical white surface bearing a simple line drawing. A large sheet of white paper with a few dark lines will serve. Put your face at the edge of the table and adjust your view so that your right eye sees the reflection of the white surface and your left eye looks across the table. Have someone sit on the other side of the table in sight of your left eye. To eliminate part or all of the person's face, pass your right hand through the reflected view of the white surface. To eliminate your view of the line drawing, pass your left hand through the view from your left eye.

In a similar arrangement I substituted a portable television set for the white surface. My right eye saw the screen and my left eye saw my wife working at the table. When the characters on the screen were stationary, I could partially fuse the two views. When a character moved, gestured or spoke, the corresponding part of the view of my wife was erased. When the scene changed as the camera switched to a new angle, my wife totally disappeared for several seconds. Try as I might, I could not overcome the phenomenon by concentration.

I was also able to demonstrate erasure without a mirror. After securing the unbound end of a writing tablet with a rubber band, I propped the tablet upright on a table with the long side horizontal and at right angles to the table edge. I positioned my head so that the tablet bisected my view. My left eye saw the tablet's colorful cover and my right eye saw the drab cardboard backing. The tablet occupied about 84 degrees in the nasal field of view of each eye. Usually my left eye dominated, but there was a perplexing fusing of the two views with frequent oscillations between them. When I moved my hand through either view, the view from the other eye was eliminated for a few seconds.

Duensing and Miller learned during their investigations that the Cheshire cat effect had been reported in 1965 under the name of movement masking by G. C. Grindley and Valerie Townsend of the University of Cambridge. Their experimental arrangement was similar to the setups I have described. An observer sat with his chin on a rest that kept his head stationary. The left eye saw a white cardboard screen and the right eye saw an identical screen reflected from a mirror. A black wood arm was pivoted in such a way that it could rotate across the field of view of the right eye at a controlled rate.

A small x and a square were marked on the cardboard seen by the left eye. The observer fixed his gaze on the x. When the wood arm was rotated, it appeared to cross over the square because of the observer's fusion of the two scenes. The motion often resulted in the brief disappearance of the square. Usually the square disappeared just as the arm seemed to pass over it, as though it were rubbed out by the arm. In other trials the square disappeared just before or after the arm seemed to pass over it. Most of the 50 subjects experienced all three effects during the tests. They found the erasure by the arm eerie. One of them reported, "You see that there is a connection but cannot feel at all sure about the exact sequence."

The square sometimes disappeared only in part, growing faint on one side or another. The duration of its disappearance was hard to predict. Sometimes it came back suddenly and at other times it came back slowly. Grindley and Townsend suggested that the sudden reappearance might be due to a saccadic eye movement, an involuntary jerk of the eye. Presumably the apparent motion of the left-eye scene resulting from the saccadic movement caught the attention of the brain, restoring perception of the square. When the observers were told to follow the rotation of the arm, the square never disappeared.

In another set of trials two squares were placed at the same height on the cardboard seen by the left eye. The wood arm was shortened so that it appeared to pass over only the square on the right. Most often only that square disappeared, but occasionally both of them vanished. Grindley and Townsend also experimented with complex displays in one or both views. When the arm passed over an object seen by the right eye, an object in the corresponding position in the view from the left eye disappeared. Sometimes when the arm seemed to touch the edge of a drawing or something that could be interpreted as being solid, the entire object immediately disappeared.

Erasure depended on the rotational speed of the arm. It was most frequent when the arm moved at 20 degrees per second. It was half as frequent when the speed was decreased to five degrees per second or increased to 90 degrees. The duration of erasure did not seem to be influenced by the rotational speed.

Grindley and Townsend also found that the proximity of the square and the point on which the left eye was fixated strongly affected the ability of the wood arm's motion to erase the square. They mounted the square on the right-hand side of the cardboard seen by the left eye and had the observer fix his view at a point to the left of the square. First he viewed a point far from the square. After a number of trials he moved his fixation point closer to the square for more trials. As the fixation point approached the square, the frequency with which the square disappeared fell off.

How does the human visual system achieve the Cheshire-cat effect? I am not certain of the answer but can offer a speculation. Normally the system attempts to fuse the views from the eyes to produce a single, sensible view. The point of concentration is wherever the eyes are focused, because that point produces an image on the fovea of each eye. The fovea produces the most acute vision. The other parts of the scene appear as less distinct images on the rest of the retina. Perhaps as an aid to survival the visual system is "wired" to be alert to motion in the peripheral part of the view.

Look straight ahead at a stationary scene. Wave your right hand on the far-right side of the scene in such a way that your left eye cannot see the motion. If your eyes were seeing separate scenes as in the demonstrations of the Cheshire-cat effect, the motion would erase the far-right section of what you see with the left eye. Since your eyes are seeing approximately the same scene from slightly different perspectives, there is no apparent erasure. I believe that in fact there is an erasure but that there is no evidence for it after fusion brings the scene to consciousness. Either the erasure is too far from the line of sight to gain attention or all the detail lost by the left eye is filled in by the right eye.

I tested my hunch by placing two brightly colored, separated objects on the opposite side of the room. Then I positioned two nearby obstacles so that only my left eye saw the colored objects. When I fixed my gaze on a point between the colored objects, I saw both of them because my left eye was dominant. When I waved my hand at the far right of my right-eye view (my left eye could not see the motion), the rightmost object disappeared. The object at the left was still visible. It is evident that I can erase part of a scene in normal viewing.

Why, during a Cheshire-cat effect, does motion through the full view of one eye sometimes leave part of the view of the other eye unerased? What survives is the part that produces an image on the fovea of the eye in which erasure seems to take place. Erasure is due to a warning system monitoring what is seen with the rest of the retina. For the same reason erasure is absent if your eye follows the moving object. Since the object then always produces an image on the fovea of that eye, the warning system leading to an erasure of the view from the other eye is not triggered.

The rhino-optical effect was named by Alistair P. Mapp and Hiroshi Ono of the University of York in England The name stems from the fact that the eyes of a rhinoceros are separated by a large protrusion of the skull. The effect is easily demonstrated. If you wear glasses, remove them. Close your left eye and fix the view from your right eye on an object directly in front of you. Slowly bring a finger of your left hand forward from your left ear, being careful not to move your right eye. When the finger first moves into view, hold it steady in that position Without turning your head, rotate your right eye toward the finger in order to see it. If the protrusion of the bridge of your nose is large enough, the finger disappears behind it. If you turn your eye forward again, the finger reappears.

A similar disappearance of an object viewed directly was described in 1844 by the British investigator David Brewster, who is remembered for his work in optics and vision. To repeat , his demonstration cut a rectangular . opening in a sheet of cardboard. Hold the sheet several centimeters in front of your right eye and close your left eye. Have someone place two narrow objects several centimeters away from the other side of the sheet. While you fix your gaze on the left side of the opening, have object A positioned so that it is barely occluded by that side of the opening. Have object B positioned so that its right side is barely visible along the right side of the opening. When the objects are in place, you can see B but not A. Without moving your head shift your gaze to the right side of the opening. A appears and B disappears. If you again turn your gaze to the left side of the opening, A disappears and B reappears.

Brewster termed this effect ocular parallax. In the rhino-optical demonstration the bridge of your nose functions as the left side of the opening and your finger serves as object A. The finger is visible only when you look away from it. Both demonstrations depend on the fact that the region in which the light rays are refracted by the eye (in the cornea and the lens) is separated from the center point about which the i eye rotates. Assume that all the refraction in the eye can be represented by a lens at the front of a spherical eye. When the eye looks directly at A, none of the light rays from it reach the lens and so A is not seen. The rays that travel toward the eye are blocked by the obstacle (either the bridge of the nose or the left side of the rectangular opening). The rest of the rays travel in the wrong direction.

When you rotate the eye rightward about its center point so that it looks directly ahead, the action moves the lens into some of the rays from A that skirt the edge of the obstacle. The lens refracts those rays onto the retina so that A is seen. The image is blurry but recognizable.

Mapp and Ono found that the rhinooptical effect does not work for everyone. If the bridge of the nose is flat, as it was in the case of the East Asians they tested, the observer sees the finger better when the eye rotates to view it directly. You can obtain a similar result if you look directly ahead with your right eye only (your left eye is closed) while moving a finger of your right hand forward from your right ear to the point where the finger first becomes visible. When you then rotate your eye toward the finger, more of the finger becomes visible.

Bibliography

THE CHESHIRE CAT EFFECT. Sally Duensing and Bob Miller in Perception, Vol. 8, No. 3, pages 269-273; 1979.

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