During binocular fixation, the eyes usually point in different directions, and yet, each object is judged to lie in a single direction. It is commonly believed that a particular location in the head serves as the origin for such directional judgments. This location is known as the cyclopean eye. We argue here that observers can judge visually perceived directions from angular information alone, and do not require positional information supplied by a cyclopean eye. We show that experimental findings reported as evidence for the cyclopean concept can also be explained solely by angular information without the need for a cyclopean eye. Recent findings concerning binocular shape perception and the cyclopean illusion demonstrate that binocular perception is incompatible with vision from a single vantage point. The concept of the cyclopean eye is sometimes inappropriate and always irrelevant as far as vision is concerned.