Based on supportive evidence, it is proposed in this paper that rapid eye movements during paradoxical sleep actually represent nystagmus, the latter due to the occurrence of conflicting perceptions of bodily position in space. During rapid eye movements in sleep, the brain's perception of bodily position in a dream is opposed to the sensory perception of the dreamer's sleeping position. The split in perception triggers nystagmus, a physiological mechanism known to accompany motion sickness and other waking forms of spatial sense distortion. Supportive evidence from studies on motion sickness, nystagmus, and sleep is presented. A number of experiments are suggested to lend validity to the hypothesis.