Is it possible to remain both awakened and asleep, at the sametime?

Yes it is. It's called the Maya Effect. Also known as The Old Hag effect, Moira effect or Mary effect. It is attributed to a lot of paranormal (ghost like) experiences of waking up paralyzed and having difficulty breathing and feelings of being watched, sat on and pressure on the chest or limbs. It is not an actual entity or ghost, it is the state of mind activity where one is half in the deep stage REM cycle (rapid eye movement) and half in the wakeful state. The brain actually paralyzes the body in full deep sleep (it is a mechanism of the body to prevent falls out of bed, listless movements and in a normal sleep cycle the body from roaming outside of the bed or sleep walking). The problem with the Maya Effect is that the mind ends up half asleep (subconscious) and half awake. It can cause paralysis, rapid heart rate and breathing and hallucinations (due to the subconscious state in a wakeful environment, it's where our dreams come from). In essence, yes our minds and bodies indeed can be, by science definition of the Maya Effect, in both a wakeful state and a sleeping state at the same time.

I dont think it is possible. I cant get the actual meaning of it.