Shadows of the Mind: A Search for the Missing Science of Consciousness

Shadows of the Mind: A Search for the Missing Science of Consciousness is a 1994 book by mathematical physicist Roger Penrose that serves as a followup to his 1989 book The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics. Penrose hypothesizes that:

Human consciousness is non-algorithmic, and thus is not capable of being modelled by a conventional Turing machine type of digital computer. Quantum mechanics plays an essential role in the understanding of human consciousness; specifically, he believes that microtubules within neurons support quantum superpositions. The objective collapse of the quantum wavefunction of the microtubules is critical for consciousness. The collapse in question is physical behaviour that is non-algorithmic and transcends the limits of computability. The human mind has abilities that no Turing machine could possess because of this mechanism of non-computable physics.