Paradoxical sleep is another name for REM sleep, which is the fourth stage of sleep that occurs at the end of each sleep cycle. It acquired its name from the fact that a person in REM sleep, because of their paralyzed muscle limbs, appears to be in deep sleep. However, during REM sleep, the person’s eyes underneath their closed lids are actually moving side to side in a rapid manner. Additionally, their brain wave activity is very high, and breathing might be very rapid. REM sleep is also associated with the most vivid dreaming.