“Consciousness seems to me to be such an important phenomenon that I cannot believe that it is something just 'accidentally' conjured up by a complicated computation.”Roger Penrose · Shadows of the Mind: A Search for the Missing Science of Consciousness · 1994 · Shadows of the Mind, cap. 1 («Consciousness and computation»)
If a human sees truths no formal procedure can prove, understanding is not computation.
Penrose starts from Gödel's incompleteness theorems. They show that for any consistent formal system, there are true statements the system cannot prove. A human mathematician, he says, 'sees' the truth of such a statement from outside the system. So understanding is not computation. From this follows his thesis about consciousness: the mind must rest on a non-computable physical process. He locates it in objective orchestrated quantum reduction, occurring in the microtubules of brain neurons, together with anaesthetist Stuart Hameroff. His favourite example is Gödel's theorem itself: the computer stays trapped inside the system, the human transcends it through understanding.
Why it matters The idea matters because it poses a hard question for artificial intelligence: if understanding is not computation, then no machine that merely runs algorithms has a mind. Even though Orch-OR is a minority view among scientists, the Gödelian challenge remains a test for any theory of minds and machines.