Touch a pencil with all five fingertips of one hand, close your eyes, and ponder: If each fingertip forms a distinct tactile "image" of the pencil, why do you perceive a single pencil instead of five unconnected pencil fragments? The answer is that your brain has special circuits that help you build complete pictures from fragmented sensory information. In effect, these gap-filling circuits induce your brain to perceive what it expects to see, instead of what it actually sees. When these expectations accurately reflect the objective world around you, your perceptions will be on target. Sometimes, however, what your brain expects to see is far from an accurate representation of reality.
Experiment 1 Cross the index and middle fingers of your dominant hand as far as you can, forcing them apart with your other hand so that you can place your nose between the outside surfaces of the crossed fingers. Then close your eyes and vertically stroke the end of your nose between your crossed fingertips.
Congratulations—you've just become the proud owner of a second nose. Lifelong experience has taught you that simultaneous stimulation of corresponding parts of the inside of two adjacent fingers means that one object is located between them. But concurrent stimulation of the outside surfaces of the same fingers signals that your fingers are in contact with more than one object. Thus, when you cross your fingers and simultaneously touch your nose with the outside edges of your fingers, your brain interprets the resulting sensations as two noses.
Experiment 2 Continue to rub your proboscis between your crossed fingertips for another 60 seconds. The longer you do this, the stronger the sensory illusion will be because each stroke strengthens the perception that you have two noses instead of one.
Experiment 3 Cross your fingers as before, close your eyes, and rub the space between your fingers with the tip of a pencil, as shown above. Just as there were seemingly two noses in experiment 1, you will now experience two pencils. But if you open your eyes and look at your fingers, the two pencils will now feel like one because your eyes immediately see that there's a single pencil. That's because conflicts between vision and touch are almost always resolved in favor of your stronger sense—vision.
The way that expectations shape perceptions has important implications for education. The developing brain processes complex perceptions, such as how difficult an academic subject is, in much the same way it handles simpler sensory information. If a student is led to expect that mathematics is difficult, even simple numerical problems may be perceived as unsolvable. Plain as the nose on your face, what you believe determines what you achieve.