Buridan's ass was an illustration of a problem in the philosophy of free will. It referred to Jean Buridan, a French philosopher in the 14th century, and described a hypothetical experiment with a hungry donkey. If placed exactly between two mangers filled with hay, the beast would starve to death because it couldn't work out which one to go for.
The Fifth and Eighth Doctors used this concept on the Eye of Orion. They both stayed equidistant from a Raston Warrior Robot as they approached it. Unable to decide on a target as the two Doctors shared identical brain patterns, the robot deactivated. (PROSE: The Eight Doctors)