In the past two decades there has been considerable focus on the effort to reach a deeper insight into the nature of consciousness via quantum mechanics. There has been very little attention paid, however, to the fact that we are endowed with two naturally recurring forms of consciousness, one experienced in the waking state, the other in the course of sleep. Waking consciousness and dreaming consciousness are intimately related but quite different in the way they are experienced. What they share in common is the continuing mystery of their connection to their neurophysiological substrate. Fred Alan Wolf is one of the few physicists who have written extensively about this mystery (Wolf, 1994).