You can calculate rule 110 by pen and paper, so at least the brain-pen-paper system is Turing complete. However, the brain is not a Turing machine, probably. T

You can calculate rule 110 by pen and paper, so at least the brain-pen-paper system is Turing complete. However, the brain is not a Turing machine, probably. There aren't discrete states, no transition table, no tape, etc. We probably don't store information remotely like a Turing machine does (with arbitrary symbols). There's a remote chance that the opposite is true, and there are functions humans can calculate that Turing machines can't.