Split-brain

Definition
Split-brain is when the two hemispheres of the brain (left & right) are not connected. This is often due to surgery in which the corpus callosum is severed to avoid the spread of epileptic seizures.

(Video: YouTube)

Commentary
One might think that severing all of the connections between the two hemispheres would lead to significant impairment of functioning, yet the two halves continue to communicate-- just outside of the body (e.g., writing, talking, pointing).

There have been cases, however, in which patients behave as though they have two personalities:

Case 1...would sometimes find himself pulling his pants down with one hand and pulling them up with the other. Once, he grabbed his wife with his left hand and shook her violently, with the right hand trying to come to his wife's aid in bringing the left belligerent hand under control. Once, while I was playing horseshoes with the patient in his backyard, he happened to pick up an ax with his left hand. Because it was entirely likely that the more aggressive right hemisphere might be in control, I discretely left the scene-not wanting to be the victim for the test case of which half-brain does society punish or execute. (Gazzaniga 1970, p.107)

I wouldn't want to be the test case either.