A Mathematical Approach to the Sleep-Waking Cycle
  Three abilities - the ability to recognize sounds, the ability to visually recognize movement and the ability to keep an upright standing position - can function only with using precise measurements of the short time intervals. Other features that these abilities share are that all three are crucial for the survival and - despite this - they are turned off simultaneously during sleep. Instead, presumably, if turning each of them off periodically for a resetting is unavoidable, then doing this one at a time would be the evolutionary choice, if that were possible. This hints that all three abilities share the same time-interval measuring mechanism and this mechanism is what cannot work without a periodical resetting. Another indication that such a mechanism is shared across the whole nervous system is the ubiquity of Pavlovian conditioning. A high level theory is proposed about how such a measuring mechanism must be implemented, in the simplest way, from the point of view of the data management, and how duration can be measured by resonance. If the theory is true it could explain the purpose of the observed changes of the firing frequency of cortical neurons, why periodic sleeping is an unavoidable necessity and what might be the cause of the different stages of sleep and of yawning. The theory provides simpler and less speculative explanations of a number of the experimental results than interpretations by the existing theories (the two-stage model of memory consolidation etc.). 
Michael Rvachov
physics.gen-ph physics.bio-ph