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Binocular Vision and the Reversing Cube Illusion

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Author: Marc Rosner
Binocular vision is the ability to see with two eyes and determine depth.

Sometimes our senses fool us. This is the case with optical illusions: our eyes perceive things that are not there or that could not possibly exist.

Materials

• Toothpicks or wire
• Wood glue (if using toothpicks)
• Cork or other small object

Procedure

With both eyes open, it is easier to judge depth because your brain analyzes the slightly different image received by each eye. Another clue to depth is the degree to which your eye must focus on objects. Other cues to depth include light and shade, and motion. Even with one eye you can judge distance to some degree.

A synchronous satellite is an object that orbits a body at a matching rate, such as one that remains at the same point above Earth's surface.
Some people simply don't perceive the inversion described here. Everyone sees things in a slightly different way.

1. Look at the cube pictured here. Nothing could be Simpler. Which face of the cube is closest to you? At first one face appears closer—perhaps the lower—but if you stare at the cube for a moment, it will magically invert in your mind and then the opposite face will appear to be closer. Most people find the cube switches back and forth in perspective.
2. Construct a cube from 12 toothpicks and glue. First make two squares, then allow them to dry. Then stand them on end and glue on the remaining four edges. Add a toothpick as a handle protruding diagonally from one corner as shown. (Alternatively, you can make your cube from wire.)
3. Hold the handle vertically between the forefinger and thumb of one hand so that the cube is on top at normal reading distance. Close or cover up one eye. Look at the far corner of the cube. Within a matter of seconds the orientation of the cube will appear to reverse, as in the case of the perspective drawing. When the reversal occurs, pivot the handle slowly between the finger and thumb. The cube will appear to turn backward! Open the closed eye. The cube will instantly snap back to its true orientation.
4. Now hold the handle vertically with the cube on top as before. Again close one eye and fix attention on the far corner. When the illusion of reversal occurs, incline the cube away from you until the handle is horizontal. During this movement the handle will appear to bend at the point at which it is attached to the cube and the cube will swing upward until it seems to perch on one corner at the tip of the handle. When you pivot the handle, the cube will appear not only to turn in the wrong direction but also to rotate on its vertical axis as if driven by the handle through a pair of crown gears, which change the angle by 90 degrees.
5. Equip the cube with a synchronous satellite. Place a small object such as a cork on a toothpick or wire and attach the toothpick or wire to the handle of the cube so that the cork is about 2.5 cm above the equator of the cube (assuming the south pole to be the corner to which the handle is attached). When the illusion of reversal occurs and the cube is rotated, the cube and its satellite will appear to move in opposite directions.
6. Turn the model rapidly and view it from different angles to discover other unexpected effects. Sometimes curves become evident when you do this.
7. Open both eyes, and the orientation of the cube remains clear—the inversion will stop.

References

How to Really Fool Yourself: Illusions for All Your Senses by Vicki Cobb (New York: John Wiley & Sons, 1999).

Optical Illusion Magic: Visual Tricks and Amusements by Michael A. Dispezio (New York: Sterling, 1999).

lllusionWorks: www.illusionworks.com

Sandlot Science optical illusions: www.sandlotscience.com/

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