Far Out Corners - Your experience of the world influences what you see.

Far Out Corners

 

Your experience of the world influences what you see. 

 

When they first glance at this exhibit, many people say, "What's the big deal? It's just a bunch of boxes." But there are no boxes at all. A closer look reveals that the Far Out Corners exhibit is a cluster of corners lit from below. When you walk past the exhibit with one eye closed, the cubes will seem to turn mysteriously so that they follow your movement. 

 

• A large cardboard box measuring about 19 x 15 inches (48 x 38 cm).
• Flat black spray paint.
• Thick, white, nonflexible posterboard measuring at least 15 x 15 inches (38 x 38 cm).
• X-Acto™ knife or matte knife.
• Masking tape or transparent tape.
• A bright free-standing lamp.
• Adult help.

(1 hour or less) You can cut the inside corners from square-cornered containers, such as clean milk cartons or tissue boxes, or you can make your own corners from posterboard. To make your own, use an X-Acto™ knife or matte knife to cut the posterboard into nine squares, each of which measures 5 x 5 inches (13 x 13 cm).
Now use three of the squares to construct a partial cube or corner in the following fashion: Tape two squares together at one edge; open each of the two squares into a right angle; tape the third square on top of the first two squares. Make three partial cubes, or corners.



Spray-paint the inside of the large cardboard box black. When the box is dry, arrange the corners so that two are side by side on the bottom of the box, as shown. Make sure the hollow open sides of each corner are facing out toward you and down. Tape them so they are tilted up at a small angle. Place the third corner as far forward as possible on top of the original two, also tilted upward. Tape all three corners in place. Now position the light so that it shines directly into the box.

(15 minutes or more)Stand back ten feet and close one eye. With a little mental effort, you can see the corners that you have constructed as three-dimensional cubes rather than hollow corners.

Walk back and forth parallel to the box. Notice that the cube on top seems to be following you as you move.

The first step to successfully seeing the top partial cube turn with you lies in your ability to perceive it as a complete six-sided figure. This perception has a lot to do with being raised in a society that recognizes cubes as a common shape. Your brain is used to seeing cubes, so it fills in the rest of the cube shape, even though this partial cube only has three sides.

As you move past the exhibit, your view of the corners changes in a way that would not make any sense if the corners were stationary cubes. Your eye-brain system is used to seeing things that are near you move faster than things that are farther away. When you are riding in a car, for example, nearby objects seem to whiz by, whereas distant objects seem to follow you at a slower pace. Since you perceive this inside corner to be the outside of a solid cube, your brain "sees" the corner farthest from you as being the closest. To maintain this misconception, your brain perceives a rapid rotation of the cube as your angle to the corner changes.


The diagram above shows how this illusion works. In the real situation, as your eye moves to the right, it sees more of side A. In order to see more of side A of the imagined corner, the perceived cube must be seen to rotate as you move.
 

 

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Falling Feather - Prove to yourself that Galileo was right!

Falling Feather

 

Prove to yourself that Galileo was right! 

 

In a famous demonstration, Galileo supposedly dropped a heavy weight and a light weight from the top of the Leaning Tower of Pisa to show that both weights fall at the same acceleration. Actually, this rule is true only if there is no air resistance. This demonstration lets you repeat Galileo's experiment in a vacuum. 

 

• A clear, plastic, rigid-walled tube with at least a 1 inch (2.5 cm) inner diameter and at least 3 feet (90 cm) long. Available at your local plastic store. (Longer tubes show the effect more clearly.)
• A solid rubber stopper and a one-hole rubber stopper to fit in the ends of the plastic tube.
• A section of copper tubing about 4 inches (10 cm) long that fits tightly in the hole in the rubber stopper (glass tubing can be used if care is taken).
• A thick-walled flexible plastic or rubber vacuum tubing about 6 feet (180 cm) long.
• A coin and a feather (or a small piece of paper).
• A vacuum pump (use a regular lab vacuum pump if available; if not, use a small hand pump such as Mityvac®).
• 2 hose clamps.
• Adult help.

(30 minutes or less)

Insert the solid stopper firmly into one end of the plastic tube. Put the coin and feather in the tube. Push the copper tube through the one-hole stopper, and firmly insert the stopper in the other end of the plastic tube. Push the vacuum tubing over the copper tube and secure it with a hose clamp, if needed. Attach the other end of the vacuum tubing to the pump; again, use a hose clamp if needed.

(15 minutes or more)

Invert the tube and let the objects fall. Notice that the feather falls much more slowly than the coin. Now pump the air out of the tube and invert it again (the pump can remain attached while you invert the tube). Notice that the feather falls much more rapidly than before - in fact, it falls almost as fast as the coin. Let the air back into the tube and repeat the experiment. (Try to avoid rubbing the wall of the tube; otherwise, static electricity may make the feather stick to it.)

Galileo predicted that heavy objects and light ones would fall at the same rate. The reason for this is simple. Suppose the coin has 50 times as much mass as the feather. This means that the earth pulls 50 times as hard on the coin as it does on the feather. You might think this would cause the coin to fall faster. But because of the coin's greater mass, it's also much harder to accelerate the coin than the feather - 50 times harder, in fact! The two effects exactly cancel out, and the two objects therefore fall with the same acceleration.

This rule holds true only if gravity is the only force acting on the two objects. If the objects fall in air, then air resistance must also be taken into account. Larger objects experience more air resistance. Also, the faster an object is falling, the more air resistance it feels. When the retarding force of the air just balances the downward pull of gravity, the object will no longer gain speed; it will have reached what is called its terminal velocity. Since the feather is so much lighter than the coin, the air resistance on it very quickly builds up to equal the pull of gravity. After that, the feather gains no more speed, but just drifts slowly downward. The heavier coin, meanwhile, must fall much longer before it gathers enough speed so that air resistance will balance the gravitational force on it. The coin quickly pulls away from the feather.

The terminal velocity of a falling human being with arms and legs outstretched is about 120 miles per hour (192 km per hour) - slower than a lead balloon, but a good deal faster than a feather!

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Fading Dot - Now you see it; now you don't. An object without a sharp edge can fade from your view

Fading Dot

 

Now you see it; now you don't. An object without a sharp edge can fade from your view. 

 

A fuzzy, colored dot that has no distinct edges seems to disappear. As you stare at the dot, its color appears to blend with the colors surrounding it. 

 

• Pink paper (1 sheet).
• Blue paper dot (about 1 inch [2.5 cm] in diameter).
• Waxed paper.

(5 minutes or less)

Use the blue paper to make a 1 inch (2.5 cm) dot, and place the dot in the center of the pink paper. Cover the paper with a sheet of waxed paper. Look through the waxed paper at the colored papers below. Lift the waxed paper from the pink paper until you see very faint blue color in a field of pale pink.

(15 minutes or more)

Stare at a point next to the fuzzy dot for a while without moving your eyes or your head. The blue will gradually fade into the field of pink. As soon as you move your head or eyes, notice that the dot reappears. Experiment with other color combinations.

Even though you are not aware of it, your eyes are always making tiny jittering movements. Each time your eyes move, they receive new information and send it to your brain. You need this constant new information to see images.

Your eyes also jitter when you look at this dot, but the color changes at the edge of the dot (as seen fuzzily through the waxed paper) are so gradual that your eyes can't tell the difference between one point on the dot and a point right next to it. Your eyes receive no new information, and the image seems to fade away. If the dot had a distinct border, your eyes would immediately detect the change when they jittered, and you would continue to see the dot.

You may have noticed that, although the dot fades, just about everything else in your field of vision remains clear. That's because everything else you see has distinct edges.

For more information, we suggest you read the sections on lateral inhibition and chromatic lateral inhibition in Seeing the Light, by David Falk, Dieter Brill, and David Stork (Harper & Row, 1986).

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