How is the computational power of a human brain comparing to a turing machine?
Given that Alan Turing devised the Turing Machine model of computation by abstracting what humans actually do when they compute by hand, I think one would be very hard-pressed to prove that a Turing Machine is more powerful than a human.

[note: by 'human' I assume a person augmented by a writing implement and an unbounded supply of scratch paper (which corresponds to the tape of course).  Without that I believe a human is actually a (dynamically self-reconfigurable) finite-state machine with an extraordinarily large number of states]