Michael Lockwood:
MIND, BRAIN AND THE QUANTUM (Basil Blackwell, 1989)

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Drawing from quantum mechanics and from Bertrand Russell's idea that consciousness provides a kind of "window" onto the brain, Lockwood offers a theory of consciousness as a process of perception of brain states.
By using special relativity (mental states must be in space given that they are in time), he leans towards the identity theory. Then Lockwood interprets the role of the observer in quantum mechanics as the role of consciousness in the physical world (as opposed as a simple interference with the system being observed).
Lockwood thinks that our sensations are intrinsic attributes of physical states of the brain. Consciousness scans the brain to look for sensations. It does not create them, it just seeks them.
Each observable attribute (e.g., each sensation) corresponds to an observable of the brain. The external world is a physical system in which a set of compatible observables is defined, whose state is therefore defined by a sum of eigenstates of such observables (i.e., by a sum of perspectives).
Lockwood mentions Deutsch David's "Quantum theory and the universal quantum computer" (1975), which generalizes Turing's ideas and defines a "quantum" machine in which Turing states can be linear combinations of states. The behavior of a quantum machine is a linear combination of the behavior of several Turing machines. A quantum machine can only compute recursive functions, as much as Turing's machine, but it turns out to be much faster in solving problems that exhibit some level of parallelism. In a sense a quantum computer is capable of decomposing a problem and delegating the subproblems to copies of itself in other universes.

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