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).
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The busy beaver function
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