It is hard to see how one could begin to develop a quantum-theoretical description of brain action when one might well have to regard the brain as "observing itself" all the time!
Roger PenroseWe have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.
Roger PenroseI imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.
Roger Penrose