The book speaks to thinking which occurs at the transition zone between deep sleep and wide awake. He speaks to a phenomenon many people have experienced, where one, in the process of waking from sleep recognizes that some problem is being solved during thought processes. As Monica Anderson once said: the secret is to keep one's eyes shut until, while waking, one fully rehearses those thoughts lest them be washed away in the flood of information arriving as one's eyes open.
Gelernter explains the phenomena in this way: during sleep, subconscious processes are in play, but logical censors are not, meaning it is possible to make connections between ideas which would otherwise not surface.
That explanation is but one of many possible, certainly serving as at the very least anecdotal evidence that there are subconscious processes in play which (possibly) entail quantum effects.