The notion that the brain has a resting state mode of functioning has received increasing attention in recent years. The idea derives from experimental observations that showed a relatively spatially and temporally uniform high level of neuronal activity when no explicit task was being performed. Surprisingly, the total energy consumption supporting neuronal firing in this conscious awake baseline state is orders of magnitude larger than the energy changes during stimulation. This paper presents a novel and counter-intuitive explanation of the high energy consumption of the brain at rest obtained using the recently developed intelligence and embodiment hypothesis. This hypothesis is based on evolutionary neuroscience and postulates the existence of a common information-processing principle associated with nervous systems that evolved naturally and serves as the foundation from which intelligence can emerge and to the efficiency of brain's computations. The high energy consumption of the brain at rest is shown to be related to the most probable state of an equilibrium statistical mechanics model aimed at capturing the behavior of a system constrained by power consumption and evolutionary designed to minimize metabolic demands.