The busy beaver function
Imagine some part of the brain receives electrochemical pulses and emits pulses in such a way as to instantiate the busy beaver function—the noncomputability of the busy beaver function shows that some psychological procedures may not be computable.
The busy beaver function:
1) Given a natural number n, the busy beaver function outputs a series of marks.
2) The output is equal to the maximum number a Turing machine with only n states can write on its tape.
3) A Turing machine cannot compute what this maximum number of marks is, but a human may be able to determine this.
Selmer Bringsjord (1992),
What Robots Can And Can't Be, Boston: Kluwer Academic.
Note: The busy beaver function was first discussed by Tibor Rado (1962).