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Concept
Shadows of the Mind
Résumé
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.
Orch-OR#The Penrose–Lucas argument
In 1931, the mathematician and logician Kurt Gödel proved his incompleteness theorems, showing that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. Further to that, for any consistent formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory. The essence of Penrose's argument is that while a formal proof system cannot, because of the theorem, prove its own incompleteness, Gödel-type results are provable by human mathematicians. He takes this disparity to mean that human mathematicians are not describable as formal proof systems and are not running an algorithm, so that the computational theory of mind is false, and computational approaches to artificial general intelligence are unfounded. (The argument was first given by Penrose in The Emperor's New Mind (1989) and is developed further in Shadows of The Mind. An earlier version of the argument was given by J. R. Lucas in 1959. For this reason, the argument is sometimes called the Penrose-Lucas argument).
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