So, what accounts for those "aha" moments? Is it all mumbo-jumbo or is there a method to the madness? How does the subconscious mind reveal answers that have been plaguing the mind?
Four states can be identified (1) Preparation, when mind deliberates the problem (2)Incubation, when the conscious mind is preoccupied with other things, and the subconscious mind active (3) Illumination, when in period of relaxation one can access the creative flow of intelligence and (4) Verification, post illumination.
Roger Penrose, one of the world's greatest mathematical physicist, restates Plato's argument that mathematical concepts, structures and forms exist in their ideal state in a non-material realm that can be experienced by any human intellect. Paul Davies states that "Perhaps the greatest scientific discovery of all time is that nature is written in mathematical code...once we have cracked the code for some particular system, we can read nature like a book". For example, an un-tutored mathematical prodigy, Srinivasa Ramanujan could almost pluck out ready-made results at will. So breaking the nature code gives access to most discoveries.
When scientists tried to find the smallest building blocks of nature, it went down from molecule to atom to sub atom to electrons and quarks to a realization that sub-atomic realities are nothing but non-material waves moving through non-material fields. What binds all existence is the intelligence or consciousness, as non-material waves obey laws of nature that can be exactly modeled by mathematical formulas cognized in the human mind. And that mind and nature are so closely intertwined that at the sub-atomic level, observing a system can change the system, and that the universe is seeming less like a great machine and more like a great thought
The parallelity and the unity between the intelligence displayed by the human mind and the intelligence of nature and the access of the human intelligence to this source of creative intelligence source of nature could be the source of these subjective knowledge examples.
Source : Freedom from Disease - Hari Sharma, New Age Books