Believe it or not, square A is the same color as square B. I examined the illusion above myself. You can too. Just copy the illusion to your computer, open it in a graphical processing program (MS Paint will work) and put the eyedropper tool over both squares. They should show the same color. This is one of the most striking optical illusions I have seen.
Just recently I have read that a woman experienced the illusion of an alien presence after her brain was stimulated by neural surgeons for epilepsy. She thought there was an unknown person in the operating room with her standing behind her motionless. Researchers say this may help shed some light on certain mental effects such as paranoia.
Then there is the phantom limb syndrome. This is the illusion that a limb still exists after it has been amputated. In the PBS show Secrets of The Mind there was a man who lost his arm, but he felt his hand on that amputated arm still existed. The neurologist Ramachandran had the man grab the cup with his phantom hand. When the neurologist moved the cup away the man reacted in pain and told Ramachandran not to do it again.
In his book The Man Who Mistook His Wife for a Hat and Other Clinical Tales, Oliver Sacks tells about a man who kept falling out of his hospital bed. Come to find out the man did not recognize one of his legs. The man thought the leg belonged to a stranger and would then roll it off his bed. Since the leg of course was his own leg and connected to his body the man too would roll out of bed. I had a similar experience with my arm when I woke up one morning. My left arm was numb because I slept on it. I touched it with my right hand and for a split second (probably because I was a little groggy still) thought my left arm was not my own. It startled me a little bit, then of course I realized that it was my own arm. I think that illusion happened because there was no feedback between my right hand and and my arm. My right hand felt the arm but since my brain could not feel the touch on the arm by my hand it did not make the connection that it was my arm--not somebody else's arm.
Ramachandran believes that and I quote "your own body is a phantom, one that your brain has temporarily constructed purely for convenience." He says there is two experiments that you can do that can prove that conjecture. One is where you can fool yourself into thinking that your nose is three feet long, and the other is an illusion where you think a rubber hand is actually your own real hand. I have not tried either of these experiments myself, but they sound really eerie especially the rubber hand experiment.
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