Roger Penrose's argument that human consciousness cannot be simulated by a Turing machine — drawing on Gödel's incompleteness theorems, quantum mechanics, and the physics of spacetime.
The Gödel argument: human mathematicians can understand truths that no algorithmic system can prove — therefore human consciousness is not algorithmic. Non-computable physics: consciousness must depend on physical processes that are not computable — pointing to quantum gravity as the likely substrate. Orchestrated objective reduction (Orch-OR, developed with Hameroff): quantum processes in microtubules as the physical basis of consciousness.
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