Try the following simple experiment: Close or cover one eye. Then look up and down. You might notice that the scene appears to move down when you move your eyes up and vice versa. Yet, your sense of the world is that it is fixed and stable.
Now, take your index finger and push it gently against the eyeball of your open eye. You may notice that the whole world appears to move. Indeed, you might find this slightly nauseating.
In both situations, images moved across your retina, yet your perceptual experience was very different. This difference intrigued some of the greatest psychophysicists of the last century, such as von Holst, Mittelstaedt, and von Helmholtz. One explanation involves a concept called efference copy or corollary discharge. Prior to activating your eye muscles and thus moving your eyes, a command was given by motor areas in your brain that specified the eye movements. This command was sent not just to the eye muscles but to other regions of your brain that then compared the command to the actual consequences. If the command matched the sensory changes, that is, images moved across the retina to the extent predicted by the eye movements, then you saw the world as stable. When you pushed on your eyeball, however, no commands were sent to the eye muscles to move the eyes, so you interpreted the changing images on your retina as an indication that the whole world was moving. Thus, corollary discharge or a copy of the motor command greatly influences your interpretation of what you see.
Corollary discharge played an important role for me in learning to see in 3D. To see in stereo, you need to make vergence movements of the eyes. You turn in both eyes to see a close target and turn out both eyes to see a more distant one.

Copyright by Margaret Nelson
These vergence movements allow the object you are viewing to cast an image on corresponding parts of both retinas. Most infants develop coordinated vergence movements within the first months of life. However, I had been cross-eyed since early infancy. When I looked at an object, I fixated it with one eye and turned away the other. The eye movement commands and resulting corollary discharge that I used to look at an object were very different than those used by an individual with normal vision. As a result, I saw a much flatter view of the world.
Instruments, such as stereoscopes or amblyoscopes, have been designed to help a cross-eyed person see in stereo. However, they often don't work because they don't change the way the individual moves his or her eyes. Before I undertook optometric vision therapy, I did not interpret a view through a stereoscope as three dimensional even if the arms of the stereoscope were adjusted in a way that put the same image on both of my retinas. Looking through the stereoscope created a new visual experience for me since, being cross-eyed, my two eyes normally looked at different things. However, this situation was a bit like the "pushing eyeball" experiment that I described above. I had not commanded my eyes to move in a new way. Instead, I was passively receiving input from the stereoscope. Without eye movement commands and corollary discharge to tell me that the position of my eyes had changed, my brain did not expect to see or interpret the world any differently.
Thus, the key to learning to see in 3D was to learn how to make normal vergence movements of my eyes. This required practice with many eloquent vision therapy procedures that gave me the feedback to know where I was aiming my eyes. Corollary discharge that informed my brain of these new eye movements was necessary for me to interpret my view in a new way and to see the world in all its glorious dimensions.