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# Illusions in Motion: The Power of Symmetry

Our brain's preference for symmetry influences how we perceive motion

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.

Rights & Permissions

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1. 1. Ellipsoid 11:30 AM 5/1/09

I find that I can easily flip the direction of the dancer by looking at her shadow. Is this because my brain applies the "clockwiseness" of the clockwise dancer to the counterclockwise shadow, thus flipping the spin of the whole shebang?

2. 2. Cristi Stoica 06:38 AM 5/3/09

In
http://www.unitaryflow.com/2008/10/spinning-dancers-mistery.html
it is explained with animated images why the "spinning dancer" is perceived by most of us as spinning clockwise.

It is then showed why the laws of perspective indicate that she really spins counter-clockwise.

3. 3. Dolmance 01:42 PM 5/24/09

Poor Bobby Jindal.

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