Around early Jurassic some small-sized diurnal reptiles increased the endothermic metabolism and extended their activity to dark time, to fill the void nocturnal niche. Their excellent visual capabilities, acuity, spatial resolution and chromatic discrimination were traded-off for increased sensitivity, useful for the nocturnal dim lit, but they turned defenseless against the dangerous daylight. To avoid blindness -and extinction- they rested in lightproof burrows with closed eyes during daytime. For further security, they developed a bi-stable switch separating nocturnal activity and diurnal rest. This was how the mammalian sleep was born. The development of the cortex, with improved audition and olfaction, compensated the visual impairments. The K-Pg event extinguished the dinosaurs softening the evolutionary pressure for maintaining nocturnal life. The variability in mammalian chronotypes and sleeping patterns increased greatly, but most of the newly developed variations lacked adaptive significance and only quiescence remained invariable. Therefore, quiescence must be the single vital trait of sleep.The Wilson’s Principle of Stringency: “Time-energy budgets evolve to fit to the times of greatest stringency”, explains why wildly gluttonous foraging and ceaseless reproductive activity is non-adaptive. Furtherly, the victims of predation aren’t the sleeping animals, but the immature, sick and senescent ones. Therefore, contrary to current opinion, excessive foraging and reproductive activity is non-adaptive and the claimed disadvantages of sleep are uncertain. Oppositely, quiescence, either resulting from sleep or laziness, is adaptive. We conclude that the vital function of sleep consists in enforcing quiescence in both nocturnal and diurnal mammals.