This what ORCH OR is all about. Penrose speaks of non-computable brain function.
Consciousness in the universe: A review of the ‘Orch OR’ theory
Stuart Hameroff a 1, Roger Penrose b 2
While more generally accepted theories assert that consciousness emerges as the complexity of the computations performed by cerebral neurons increases,[4][5] Orch OR posits that consciousness is based on non-computable quantum processing performed by qubits formed collectively on cellular microtubules, a process significantly amplified in the neurons.
The qubits are based on oscillating dipoles forming superposed resonance rings in helical pathways throughout lattices of microtubules. The oscillations are either electric, due to charge separation from London forces, or magnetic, due to electron spin—and possibly also due to nuclear spins (that can remain isolated for longer periods) that occur in gigahertz, megahertz and kilohertz frequency ranges.[2][6] Orchestration refers to the hypothetical process by which connective proteins, such as microtubule-associated proteins (MAPs), influence or orchestrate qubit state reduction by modifying the spacetime-separation of their superimposed
states.[7]
The latter is based on Penrose’s objective-collapse theory for interpreting quantum mechanics, which postulates the existence of an objective threshold governing the collapse of quantum-states, related to the difference of the spacetime curvature of these states in the universe’s fine-scale structure.[8]