There is no current adequate theory concerning the 'collapse' of the quantum mechanical wave function, but an additional theory of quantum gravity might be useful to this end. The existence of quasicrystals is evidence for some such currently unrecognized, nonalgorithmic physical process. Future theories of physics, in particular quantum gravity, can be expected to incorporate nonalgorithmic processes. These nonalgorithmic nonrandom processes will be sufficient, in some sense, to account for A5. Microtubules play a key role in neuron function.
Neurons play a key role in cognition and consciousness.
Microtubules, because they have one foot in quantum mechanics and the other in conscious thought, provide a window for nonalgorithmicity in human cognition. Quantum gravity, or something similar,via microtubules, must play a key role in consciousness and cognition. Furthermore, there are on-line papers by both Penrose and Hameroff, listed below, that will provide more details from the proponents themselves. Motivations for quantum theories of consciousness Apart from Penrose's work, there are many who have drawn connections between quantum mechanics and consciousness. There are a number of motivations that have driven people to look for such a connection.