THE AESTHETIC APPEAL of symmetry is obvious whether you are a child playing with a kaleidoscope or a Great Mogul emperor building the Taj Mahal as a monument to eternal love. That preference, as it turns out, greatly shapes how we see the world when items are in motion. More on that shortly.

In the natural, as opposed to man-made, world, symmetry—whether we see it in prey, predator, mate or mother—serves as an early-alert system, drawing your attention. Even an infant, who has blurry views of his or her surroundings because of not yet developed acuity, has an innate preference for symmetry. Babies stare longer at faces that have two eyes in the normal position than they do at those that have a cyclopean or a stacked-eyes configuration.

Symmetrical faces tend to be judged as more attractive than asymmetrical ones. Some researchers have postulated that this partiality may be because infestation with parasites can cause visible asymmetry in victims. As a parasite species evolves, it continuously tries to match its surface antigens to those of its host to evade immunological rejection. At the same time, there is a strong selection pressure on the host to be able to detect parasitic infestation and other abnormalities that might potentially reduce fitness and reproductive success. If parasitic infestation occurs sufficiently early in development, it can produce minor deviations from symmetry—hence the adaptive advantage of using asymmetry as a marker to avoid potential mates with poor health, weak genes or a challenged immune system.

Balance on the Whole
Early in the 20th century Gestalt psychologists started exploring the perceptual importance of symmetry. They rejected and attacked the prevailing atomistic, or reductionist, approaches to perception. The Gestaltists, beginning with Max Wertheimer, identified “laws” of perceptual organization and emphasized how the relation of all the elements in a scene, rather than the individual elements by themselves, will influence the final perception. For example, three collinear dots suggest a line, but three dots when misaligned will evoke an unmistakable perception of triangleness—even though the display lacks the shape’s hallmark of three lines and three vertices (a).

The illustration in b demonstrates one of the most basic Gestalt principles—organization of a scene into “figure” and “ground.” Even in novel, abstract images, a perceptual division exists between an object, or thing, and the background. Contours are seen to belong to the figure, which is seen to be lying in front of the shapeless ground. Here you see a black vase , but with some time and effort, you should be able to perceive an alternative percept of two white faces in profile in front of a dark ground.

Gestaltists identified many “laws” for determining what is seen as figure or ground in a display. In general, if contours are near each other, they will be perceived as belonging together, as being part of the same figure, a tendency termed the Law of Proximity. If contours are mirror-symmetric, they also will group together and define a figure, known as the Law of Symmetry.

So what happens when symmetry is pitted against proximity? Symmetry tends to dominate; that is, we usually see the shapes defined by mirror-symmetric contours as figure rather than as ground (c). Our brain is choosing symmetry to perceive objects.

Now we return to the idea of considering how symmetry can influence the processing of motion. Let us begin with apparent motion, the illusion of movement that you get when, for instance, two spatially separated spots are presented in rapid temporal succession (as in a string of Christmas bulbs that appear to jump back and forth). Even though the spots/bulbs themselves do not budge, your perception of motion between them is vivid. Because the same brain mechanisms appear to process real motion (your cat walking across the room) and apparent motion (holiday lights), apparent-motion displays provide a convenient tool for the study of motion perception.

Apparent Motion
In the 1980s one of us (Ramachandran) and our colleague Stuart M. Anstis developed an apparent-motion display called the Bistable Quartet (d). In this illusion, two dots are flashed simultaneously (frame 1 in d) on two corners of an imaginary square and then switched off and replaced by two identical dots on the remaining two corners (frame 2 in d). When frames 1 and 2 are alternated rapidly, you can see apparent motion: the dots appear to move either left-right, left-right or up-down, up-down. The perceived direction of motion is ambiguous, or bistable. You can see one or the other, but you cannot see both simultaneously. It is similar to the experience with the face-vase illusion shown in b.

If this display is rotated 45 degrees so that the dots define an imaginary diamond instead of a square, you perceive the path of motion rotated 45 degrees as well. That is, the dots appear to move back and forth along parallel diagonals. Again, there are two equally possible, mutually exclusive perceptions of motion: either along the diagonal with a positive slope or along the diagonal with a negative slope. And again, you should be able to alternate between the two.

Consider what happens when we scatter multiple Bistable Quartets randomly on a computer display screen (f). Because each one has a 50 percent probability of being seen with movement along the positive versus the negative axis, you might expect a 50–50 split. Amazingly, they all get coupled together by the brain. They end up doing exactly the same type of oscillation throughout the visual field. You can cause some brief moments of uncoupling the quartets if you expend intense mental effort, but their natural state in your perception is to remain synchronized. This experiment shows that the perception of apparent motion is not a piecemeal affair happening separately in different parts of the visual field. There is a global imposition of coherence.

Now we introduce symmetry by rearranging the field of Bistable Quartets to form a “butterfly” pattern, which is bilaterally symmetric across the vertical axis. An extraordinary thing happens: people see the quartets within each half of the display synchronized, as expected, but across the axis of symmetry, in the mirror half of the display, all the quartets are synchronized to the opposite direction of motion (g). It is as though the overall global symmetry of the form of the butterfly imposes its symmetry on the perceived motion, which necessarily means opposite directions for the two halves of the display. (We are currently exploring this phenomenon with our student Elizabeth Seckel of the University of California, San Diego.)

Ambiguous Pirouette
Thus, the need for symmetry overrides the global tendency to see identical motion throughout the visual field. All of perception depends on a hierarchy of precedence rules that determines how different “laws” interact, rules that reflect the statistical properties of the world and the organism’s need for survival.

A different experiment on the interaction between motion and symmetry, one that you can perform yourself, involves the spinning ballet dancer illusion (h; you can Google that phrase to bring up the moving display). What is on the retina is a deforming shadow—a black silhouette—but your brain makes sense of it instantly to see a young woman in full 3-D spinning on her vertical axis. If asked, you could confidently answer which direction she is spinning, clockwise or counterclockwise (as seen from above). But keep looking because, again, the direction of motion is ambiguous. With effort (or by first covering all but a small part of the moving display), you should be able to flip the direction you see her spinning.

It is fun to see a group of these figures spinning; if you have some programming skills, you can try creating it. Otherwise, you may generate a reasonable display by opening multiple new pages, each with the same image, and scattering them across your screen. Or you could employ a multilens (insect eye) fresnel lens sheet (available in novelty or science museum stores) that will optically multiply the ballerina. As with the earlier, simpler bistable motion quartets, you will perceive all the ballerinas synchronized, spinning together either rightward or leftward. (We conducted this experiment with Shai Azoulai, then a U.C.S.D. graduate student.) Again we created a symmetrical butterflylike display with multiple ballerinas, and again, most subjects instantly saw the ballerinas within one half of the axis of symmetry synchronized—but the populations on the two halves spun in opposite directions from each other. In other words, the two fields appeared to spin either toward or away from each other. The need for symmetry overrides the need for seeing synchronized motion throughout the field. (Sometimes, with mental effort, they can all be made to do the same thing, but the spontaneous preference is toward seeing opposite directions.) You can verify this result by simply putting a mirror at right angles to the computer screen next to the ballerina.

The coupling of motion and direction is based partially on the objects’ synchronicity in time (and speed). Physiologists have proposed that such perceptual groupings may arise when there is synchronization of nerve impulses that are evoked in multiple brain regions by the individual quartets or ballerinas. If so, what happens if ballerinas in different parts of the visual field spin at speeds slightly different from one another? Would they still get synchronized? What if ballerinas were of nonuniform sizes? Could you uncouple large and small ones then? Have fun!

Note: This article was originally printed with the title, "The Power of Symmertry".