Stuart Kauffman, a theoretical biologist and author from the University of Calgary, has been hypothesizing about the possible underlying physical nature of the consciousness. Just like Roger Penrose, whom we immensely respect, Dr. Kauffman believes that quantum mechanics plays a central role, creating an unpredictable output but which is not random. So there are laws that play a part, but the result cannot be algorithmically predicted, allowing for what looks like an independent consciousness.
Article abstract from arXiv:
Since Descartes' dualism, with his res extensa and res cogitans, six fundamental problems in the philosophy and natural history of mind are these: 1. how does mind act on matter? 2. If mind does not act on matter is mind a mere epiphenomenon? 3. What might be the source of free will? 4. What might be the source of a responsible free will? 5. Why might it have been selectively advantageous to evolve consciousness? 6. What is consciousness? I approach the first five of the above six problems based on two physical postulates. First the mind-brain system is a quantum coherent, but reversibly decohering and recohering system. This allows me to answer 1) above, mind does not act causally on brain at all, rather it acausally decohers to classicity (for all practical purposes), hence has consequences for brain and body as matter. Epiphenomenalism is averted. A quantum mind, because it is acausal on Copenhagen including Born, yields a free will, but a merely random free will, not a responsible free will. Second, the most radical part of this article proposes that the quantum classical interface is not always describable by a law: specifically in a special relativity setting, no function, F, maps the present state of the system mind-brain into its future. In its place is a nonrandom yet lawless process. I seek in this non-random yet lawless process a source for a responsible free will. Finally, if the quantum-classical boundary can be non-random yet lawless, then no algorithmic simulation of the world or ourselves can calculate the real world, hence the evolutionary selective advantages for evolving consciousness to know it may be great. I make no progress on problem 6, the hard problem of qualia.